What is a qubit?

In quantum computing, a charge qubit is a qubit whose basis states are charge states (e.g. states which represent the presence or absence of excess Cooper pairs in the island). In superconducting quantum computing, a charge qubit is formed by a tiny superconducting island (also known as a Cooper-pair box) coupled by a Josephson junction to a superconducting reservoir (see figure). The state of the qubit is determined by the number of Cooper pairs which have tunneled across the junction. In contrast with the charge state of an atomic or molecular ion, the charge states of such an "island" involve a macroscopic number of conduction electrons of the island. The quantum superposition of charge states can be achieved by tuning the gate voltage U that controls the chemical potential of the island. The charge qubit is typically read-out by electrostatically coupling the island to an extremely sensitive electrometer such as the radio-frequency single-electron transistor.

Charge qubit

Typical T coherence times for a charge qubit are on the order of 1–2 μs. Recent work has shown T times approaching 100 μs using a type of charge qubit known as a transmon inside a three-dimensional superconducting cavity. Understanding the limits of T is an active area of research in the field of superconducting quantum computing.

To-date, the realizations of qubits that have had the most success are ion traps and NMR, with Shor's algorithm even being implemented using NMR. However, it is hard to see these two methods being scaled to the hundreds, thousands, or millions of qubits necessary to create a quantum computer. Solid-state representations of qubits are much more easily scalable, but they themselves have their own problem: decoherence. Superconductors, however, have the advantage of being more easily scaled, and they are more coherent than normal solid-state systems.

Superconducting charge qubits have been progressing quickly. They were first suggested in 1997 by Shnirman, and by 2001 coherent oscillations were observed.

In quantum computing, a qubit () or quantum bit (sometimes qbit) is the basic unit of quantum information—the quantum version of the classical binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include: the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states/levels simultaneously, a property which is fundamental to quantum mechanics and quantum computing.

Qubit

The coining of the term "qubit" is attributed to Benjamin Schumacher. In the acknowledgments of his 1995 paper, Schumacher states that the term "qubit" was created in jest during a conversation with William Wootters. The paper describes a way of compressing states emitted by a quantum source of information so that they require fewer physical resources to store. This procedure is now known as Schumacher compression.

A binary digit, characterized as 0 and 1, is used to represent information in classical computers. A binary digit can represent up to one bit of Shannon information, where a bit is the basic unit of information.
However, in this article, the word bit is synonymous with binary digit.

In classical computer technologies, a "processed" bit is implemented by one of two levels of low DC voltage, and whilst switching from one of these two levels to the other, a so-called forbidden zone must be passed as fast as possible, as electrical voltage cannot change from one level to another "instantaneously".

There are two possible outcomes for the measurement of a qubit—usually taken to have the value "0" and "1", like a bit or binary digit. However, whereas the state of a bit can only be either 0 or 1, the general state of a qubit according to quantum mechanics can be a coherent superposition of both. Moreover, whereas a measurement of a classical bit would not disturb its state, a measurement of a qubit would destroy its coherence and irrevocably disturb the superposition state. It is possible to fully encode one bit in one qubit. However, a qubit can hold more information, e.g. up to two bits using superdense coding.

For a system of "n" components, a complete description of its state in classical physics requires only "n" bits, whereas in quantum physics it requires 2−1 complex numbers.

In quantum mechanics, the general quantum state of a qubit can be represented by a linear superposition of its two orthonormal basis states (or basis vectors). These vectors are usually denoted as
formula_1
and
formula_2. They are written in the conventional Dirac—or "bra–ket"—notation; the formula_3 and formula_4 are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, \

In a paper entitled: "Solid-state quantum memory using the P nuclear spin", published in the October 23, 2008 issue of the journal "Nature", a team of scientists from the U.K. and U.S. reported the first relatively long (1.75 seconds) and coherent transfer of a superposition state in an electron spin "processing" qubit to a nuclear spin "memory" qubit. This event can be considered the first relatively consistent quantum data storage, a vital step towards the development of quantum computing. Recently, a modification of similar systems (using charged rather than neutral donors) has dramatically extended this time, to 3 hours at very low temperatures and 39 minutes at room temperature. Room temperature preparation of a qubit based on electron spins instead of nuclear spin was also demonstrated by a team of scientists from Switzerland and Australia.

In quantum computing, a qubit is a unit of information analogous to a bit (binary digit) in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ways more powerful than classical bits for some tasks. Qubits are used in quantum circuits and quantum algorithms composed of quantum logic gates to solve computational problems, where they are used for input/output and intermediate computations.

Physical and logical qubits

A physical qubit is a physical device that behaves as a two-state quantum system, used as a component of a computer system. A logical qubit is a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit subject to unitary transformations, has a long enough coherence time to be usable by quantum logic gates (c.f. propagation delay for classical logic gates).

, most technologies used to implement qubits face issues of stability, decoherence, fault tolerance and scalability. Because of this, many physical qubits are needed for the purposes of error-correction to produce an entity which behaves logically as a single qubit would in a quantum circuit or algorithm; this is the subject of quantum error correction. Thus, contemporary logical qubits typically consist of many physical qubits to provide stability, error-correction and fault tolerance needed to perform useful computations.

1-bit and 2-bit quantum gate operations have been shown to be universal. A quantum algorithm can be instantiated as a quantum circuit.

A logical qubit specifies how a single qubit should behave in a quantum algorithm, subject to quantum logic operations which can be built out of quantum logic gates. However, issues in current technologies preclude single two-state quantum systems, which can be used as physical qubits, from reliably encoding and retaining this information for long enough to be useful. Therefore, current attempts to produce scalable quantum computers require quantum error correction, and multiple (currently many) physical qubits must be used to create

The quantum threshold theorem

The approach of topological qubits, which takes advantage of topological effects in quantum mechanics, has been proposed as needed many fewer or even a single physical qubit per logical qubit. Topological qubits rely on a class of particles called anyons which have spin that is neither half-integral (fermions) nor integral (bosons), and therefore obey neither the Fermi–Dirac statistics nor the Bose–Einstein statistics of particle behavior. Anyons exhibit braid symmetry in their world lines, which has desirable properties for the stability of qubits. Notably, anyons must exist in systems constrained to two spatial dimensions or fewer, according to the spin–statistics theorem, which states that in 3 or more spatial dimensions, only fermions and bosons are possible.

A qubit (or quantum bit) is a unit of information that can be in a superposition of two states, denoted as formula_1 and formula_2. The general superposition can be written as formula_3where formula_4 and formula_5. If one measures the state of the qubit in the orthonormal basis composed of formula_1 and formula_2, one gets the result formula_1 with probability formula_9 and the result formula_2 with probability formula_11.

Algorithmic cooling

Algorithmic cooling is an algorithmic method for transferring heat (or entropy) from some qubits to others or outside the system and into the environment, which results in a cooling effect. This method uses regular quantum operations on ensembles of qubits, and it can be shown that it can succeed beyond Shannon's bound on data compression. The phenomenon is a result of the connection between thermodynamics and information theory.

The cooling itself is done in an algorithmic manner using ordinary quantum operations. The input is a set of qubits, and the output is a subset of qubits cooled to a desired threshold determined by the user. This cooling effect may have usages in initializing cold (highly pure) qubits for quantum computation and in increasing polarization of certain spins in nuclear magnetic resonance. Therefore, it can be used in the initializing process taking place before a regular quantum computation.

Quantum computers need qubits (quantum bits) on which they operate. Generally, in order to make the computation more reliable, the qubits must be as pure as possible, minimizing possible fluctuations. Since the purity of a qubit is related to von Neumann entropy and to temperature, making the qubits as pure as possible is equivalent to making them as cold as possible (or having as little entropy as possible). One method of cooling qubits is extracting entropy from them, thus purifying them. This can be done in two general ways: reversibly (namely, using unitary operations) or irreversibly (for example, using a heat bath). Algorithmic cooling is the name of a family of algorithms that are given a set of qubits and purify (cool) a subset of them to a desirable level.

This can also be viewed in a probabilistic manner. Since qubits are two-level systems, they can be regarded as coins, unfair ones in general. Purifying a qubit means (in this context) making the coin as unfair as possible: increasing the difference between the probabilities for tossing different results as much as possible. Moreover, the entropy previously mentioned can be viewed using the prism of information theory, which assigns entropy to any random variable. The purification can therefore be considered as using probabilistic operations (such as classical logical gates and conditional probability) for minimizing the entropy of the coins, making them more unfair.

The case in which the algorithmic method is reversible, such that the total entropy of the system is not changed, was first named "molecular scale heat engine", and is also named "reversible algorithmic cooling". This process cools some qubits while heating the others. It is limited by a variant of Shannon's bound on data compression and it can asymptotically reach quite close to the bound.

A more general method, "irreversible algorithmic cooling", makes use of irreversible transfer of heat outside of the system and into the environment (and therefore may bypass the Shannon bound). Such an environment can be a heat bath, and the family of algorithms which use it is named "heat-bath algorithmic cooling". In this algorithmic process entropy is transferred reversibly to specific qubits (named reset spins) that are coupled with the environment much more strongly than others. After a sequence of reversible steps that let the entropy of these reset qubits increase they become hotter than the environment. Then the strong coupling results in a heat transfer (irreversibly) from these reset spins to the environment. The entire process may be repeated and may be applied recursively to reach low temperatures for some qubits.

Algorithmic cooling can be discussed using classical and quantum thermodynamics points of view.

The classical interpretation of "cooling" is transferring heat from one object to the other. However, the same process can be viewed as entropy transfer. For example, if two gas containers that are both in thermal equilibrium with two different temperatures are put in contact, entropy will be transferred from the "hotter" object (with higher entropy) to the "colder" one. This approach can be used when discussing the cooling of an object whose temperature is not always intuitively defined, e.g. a single particle. Therefore, the process of cooling spins can be thought of as a process of transferring entropy between spins, or outside of the system.

The concept of heat reservoir is discussed extensively in classical thermodynamics (for instance in carnot cycle). For the purposes of algorithmic cooling, it is sufficient to consider heat reservoirs, or "heat baths", as large objects whose temperature remains unchanged even when in contact with other ("normal" sized) objects. Intuitively, this can be pictured as a bath filled with room-temperature water that practically retains its temperature even when a small piece of hot metal is put in it.

Using the entropy form of thinking from the previous subsection, an object which is considered hot (whose entropy is large) can transfer heat (and entropy) to a colder heat bath, thus lowering its own entropy. This process results in cooling.

Unlike entropy transfer between two "regular" objects which preserves the entropy of the system, entropy transfer to a heat bath is normally regarded as non-preserving. This is because the bath is normally not considered as a part of the relevant system, due to its size. Therefore, when transferring entropy to a heat bath, one can essentially lower the entropy of their system, or equivalently, cool it. Continuing this approach, the goal of algorithmic cooling is to reduce as much as possible the entropy of the system of qubits, thus cooling it.

Algorithmic cooling applies to quantum systems. Therefore, it is important to be familiar with both the core principles and the relevant notations.

The above description is known as a quantum pure state. A general mixed quantum state can be prepared as a probability distribution over pure states, and is represented by a density matrix of the general form formula_12, where each formula_13 is a pure state (see ket-bra notations) and each formula_14 is the probability of formula_15 in the distribution. The quantum states that play a major role in algorithmic cooling are mixed states in the diagonal form formula_16 for formula_17. Essentially, this means that the state is the pure formula_1 state with probability formula_19 and is pure formula_2 with probability formula_21. In the ket-bra notations, the density matrix is formula_22. For formula_23 the state is called pure, and for formula_24 the state is called completely mixed (represented by the normalized identity matrix). The completely mixed state represents a uniform probability distribution over the states formula_1 and formula_2.

The state formula_27 above is called formula_28-polarized, or formula_28-biased, since it deviates by formula_28 in the diagonal entries from the completely mixed state.
Another approach for the definition of bias or polarization is using Bloch sphere (or generally Bloch ball). Restricted to a diagonal density matrix, a state can be on the straight line connecting the antipodal points representing the states formula_1 and formula_2 ("north and south poles" of the sphere). In this approach, the formula_28 parameter (formula_34) is exactly the distance (up to a sign) of the state from the center of the ball, which represents the completely mixed state. For formula_35 the state is exactly on the poles and for formula_24 the state is exactly in the center. A bias can be negative (for example formula_37), and in this case the state is in the middle between the center and the south pole.

In the Pauli matrices representation form, an formula_28-biased quantum state is formula_39.

Since quantum systems are involved, the entropy used here is von Neumann entropy. For a single qubit represented by the (diagonal) density matrix above, its entropy is formula_40 (where the logarithm is to base formula_41). This expression coincides with the entropy of an unfair coin with "bias" formula_28, meaning probability formula_19 for tossing heads. A coin with bias formula_35 is deterministic with zero entropy, and a coin with bias formula_24 is fair with maximal entropy (formula_46.

The relation between the coins approach and von Neumann entropy is an example of the relation between entropy in thermodynamics and in information theory.

An intuition for this family of algorithms can come from various fields and mindsets, which are not necessarily quantum. This is due to the fact that these algorithms do not explicitly use quantum phenomena in their operations or analysis, and mainly rely on information theory. Therefore, the problem can be inspected from a classical (physical, computational, etc.) point of view.

The physical intuition for this family of algorithms comes from classical thermodynamics.

The basic scenario is an array of qubits with equal initial biases. This means that the array contains small thermodynamic systems, each with the same entropy. The goal is to transfer entropy from some qubits to others, eventually resulting in a sub-array of "cold" qubits and another sub-array of "hot" qubits (the sub-arrays being distinguished by their qubits' entropies, as in the background section). The entropy transfers are restricted to be reversible, which means that the total entropy is conserved. Therefore, reversible algorithmic cooling can be seen as an act of redistributing the entropy of all the qubits to obtain a set of colder ones while the others are hotter.

To see the analogy from classical thermodynamics, two qubits can be considered as a gas container with two compartments, separated by a movable and heat-insulating partition. If external work is applied in order to move the partition in a reversible manner, the gas in one compartment is compressed, resulting in higher temperature (and entropy), while the gas in the other is expanding, similarly resulting in lower temperature (and entropy). Since it is reversible, the opposite action can be done, returning the container and the gases to the initial state. The entropy transfer here is analogous to the entropy transfer in algorithmic cooling, in the sense that by applying external work entropy can be transferred reversibly between qubits.

The basic scenario remains the same, however an additional object is present - a heat bath. This means that entropy can be transferred from the qubits to an external reservoir and some operations can be irreversible, which can be used for cooling some qubits without heating the others. In particular, hot qubits (hotter than the bath) that were on the receiving side of reversible entropy transfer can be cooled by letting them interact with the heat bath. The classical analogy for this situation is the Carnot refrigerator, specifically the stage in which the engine is in contact with the cold reservoir and heat (and entropy) flows from the engine to the reservoir.

The intuition for this family of algorithms can come from an extension of Von-Neumann's solution for the problem of obtaining fair results from a biased coin. In this approach to algorithmic cooling, the bias of the qubits is merely a probability bias, or the "unfairness" of a coin.

Two typical applications that require a large number of pure qubits are quantum error correction (QEC) and ensemble computing. In realizations of quantum computing (implementing and applying the algorithms on actual qubits), algorithmic cooling was involved in realizations in optical lattices. In addition, algorithmic cooling can be applied to "in vivo" magnetic resonance spectroscopy.

Quantum error correction is a quantum algorithm for protection from errors. The algorithm operates on the relevant qubits (which operate within the computation) and needs a supply of new pure qubits for each round. This requirement can be weakened to purity above a certain thershold instead of requiring fully pure qubits. For this, algorithmic cooling can be used to produce qubits with the desired purity for quantum error correction.

Ensemble computing is a computational model that uses a macroscopic number of identical computers. Each computer contains a certain number of qubits, and the computational operations are performed simultaneously on all the computers. The output of the computation can be obtained by measuring the state of the entire ensemble, which would be the average output of each computer in it. Since the number of computers is macroscopic, the output signal is easier to detect and measure than the output signal of each single computer.

This model is widely used in NMR quantum computing: each computer is represented by a single (identical) molecule, and the qubits of each computer are the nuclear spins of its atoms. The obtained (averaged) output is a detectable magnetic signal.

Nuclear magnetic resonance spectroscopy (sometimes called MRS - magnetic resonance spectroscopy) is a non-invasive technique related to MRI (magnetic resonance imaging) for analyzing metabolic changes "in vivo" (from Latin: "within the living organism"), which can potentially be used for diagnosing brain tumors, Parkinson's disease, depression, etc. It uses some magnetic properties of the relevant metabolites to measure their concentrations in the body, which are correlated with certain diseases. For example, the difference between the concentrations of the metabolites glutamate and glutamine can be linked to some stages of neurodegenerative diseases, such as Alzheimer's disease.

Some uses of MRS focus on the carbon atoms of the metabolites (see carbon-13 nuclear magnetic resonance). One major reason for this is the presence of carbon in a large portion of all tested metabolites. Another reason is the ability to mark certain metabolites by the C isotope, which is more easy to measure than the usually used hydrogen atoms mainly because of its magnetic properties (such as its gyromagnetic ratio).

In MRS, the nuclear spins of the atoms of the metabolites are required to be with a certain degree of polarization, so the spectroscopy can succeed. Algorithmic cooling can be applied "in vivo", increasing the resolution and precision of the MRS. Realizations (not in vivo) of algorithmic cooling on metabolites with C isotope have been shown to increase the polarization of C in amino acids and other metabolites.

MRS can be used to obtain biochemical information about certain body tissues in a non-invasive manner. This means that the operation must be carried out at room temperature. Some methods of increasing polarization of spins (such as hyperpolarization, and in particular dynamic nuclear polarization) are not able to operate under this condition since they require a cold environment (a typical value is 1K, about -272 degrees Celsius). On the other hand, algorithmic cooling can be operated in room temperature and be used in MRS "in vivo," while methods that required lower temperature can be used in biopsy, outside of the living body.

The algorithm operates on an array of equally (and independently) biased qubits. After the algorithm transfers heat (and entropy) from some qubits to the others, the resulting qubits are rearranged in increasing order of bias. Then this array is divided into two sub-arrays: "cold" qubits (with bias exceeding a certain threshold chosen by the user) and "hot" qubits (with bias lower than that threshold). Only the "cold" qubits are used for further quantum computation. The basic procedure is called "Basic Compression Subroutine" or "3 Bit Compression".

The reversible case can be demonstrated on 3 qubits, using the probabilistic approach. Each qubit is represented by a "coin" (two-level system) whose sides are labeled 0 and 1, and with a certain bias: each coin is independently with bias formula_28, meaning probability formula_19 for tossing 0. The coins are formula_49 and the goal is to use coins formula_50 to cool coin (qubit) formula_51. The procedure:
After this procedure, the average (expected value) of the bias of coin formula_51 is, to leading order, formula_57.

Coins formula_50 are used for C-NOT operation, also known as XOR (exclusive or). The operation is applied in the following manner: formula_59, which means that formula_60 is computed and replaces the old value of formula_54, and formula_55 remain unchanged. More specifically, the following operation is applied:
Now, the result of coin formula_67 is checked (without looking at formula_68). Classically, this means that the result of coin formula_63 must be "forgotten" (cannot be used anymore). This is somewhat problematic classically, because the result of coin formula_63 is no longer probabilistic; however, the equivalent quantum operators (which are the ones that are actually used in realizations and implementations of the algorithm) are capable of doing so.

After the C-NOT operation is over, the bias of coin formula_71 is computed using conditional probability:

Coins formula_82 are used for C-SWAP operation. The operation is applied in the following manner: formula_83, which means that formula_68 are swapped if formula_72.

After the C-SWAP operation is over:
The average bias of coin formula_89 can be calculated by looking at those two cases, using the final bias in each case and the probability of each case:
Using the approximation formula_101, the new average bias of coin formula_89 is formula_57. Therefore, these two steps increase the polarization of coin formula_51 on average.

The algorithm can be written using quantum operations on qubits, as opposed to the classical treatment. In particular, the C-NOT and C-SWAP steps can be replaced by a single unitary quantum operator that operates on the 3 qubits. Although this operation changes qubits formula_50 in a different manner than the two classical steps, it yields the same final bias for qubit formula_51. The operator formula_107 can be uniquely defined by its action on the computational basis of the Hilbert space of 3 qubits:
In matrix form, this operator is the identity matrix of size 8, except that the 4th and 5th rows are swapped. The result of this operation can be obtained by writing the product state of the 3 qubits, formula_116, and applying formula_107 on it. Afterwards, the bias of qubit formula_51 can be calculated by projecting its state on the state formula_1 (without projecting qubits formula_50) and taking the trace of the result (see density matrix measurement):

formula_121, where formula_122 is the projection on the state formula_1.

Again, using the approximation formula_101, the new average bias of coin formula_51 is formula_57.

The irreversible case is an extension of the reversible case: it uses the reversible algorithm as a subroutine. The irreversible algorithm contains another procedure called "Refresh" and extends the reversible one by using a heat bath. This allows for cooling certain qubits (called "reset qubits") without affecting the others, which results in an overall cooling of all the qubits as a system. The cooled reset qubits are used for cooling the rest (called "computational qubits") by applying a compression on them which is similar to the basic compression subroutine from the reversible case. The "insulation" of the computational qubits from the heat bath is a theoretical idealization that does not always hold when implementing the algorithm. However, with a proper choice of the physical implementation of each type of qubit, this assumption fairly holds.

There are many different versions of this algorithm, with different uses of the reset qubits and different achievable biases. The common idea behind them can be demonstrated using three qubits: two computational qubits formula_127 and one reset qubit formula_63.

Each of the three qubits is initially in a completely mixed state with bias formula_129 (see the background section). The following steps are then applied:
Each round of the algorithm consists of three iterations, and each iteration consists of these two steps (refresh, and then compression). The compression step in each iteration is slightly different, but its goal is to sort the qubits in descending order of bias, so that the reset qubit would have the smallest bias (namely, the highest temperature) of all qubits. This serves two goals:
When writing the density matrices after each iteration, the compression step in the 1st round can be effectively treated as follows:
The description of the compression step in the following rounds depends on the state of the system before the round has begun and may be more complicated than the above description. In this illustrative description of the algorithm, the boosted bias of qubit formula_51 (obtained after the end of the first round) is formula_137, where formula_138 is the bias of the qubits within the heat bath. This result is obtained after the last compression step; just before this step, the qubits were each formula_138-biased, which is exactly the state of the qubits before the reversible algorithm is applied.

The contact that is established between the reset qubit and the heat bath can be modeled in a several possible ways:
In both ways, the result is a reset qubit whose bias is identical to the bias of the qubits in the bath. In addition, the resulted reset qubit is uncorrelated with the other ones, independently of the correlations between them before the refresh step was held. Therefore, the refresh step can be viewed as discarding the information about the current reset qubit and gaining information about a fresh new one from the bath.

The goal of this step is to reversibly redistribute the entropy of all qubits, such that the biases of the qubits are in descending (or non-ascending) order. The operation is done reversibly in order to prevent the entropy of the entire system from increasing (as it cannot decrease in a closed system, see entropy). In terms of temperature, this step rearranges the qubits in ascending order of temperature, so that the reset qubits are the hottest. In the example of the three qubits formula_49, this means that after the compression is done, the bias of qubit formula_51 is the highest and the bias of formula_63 is the lowest. In addition, the compression is used for the cooling of the computational qubits.

The state of the system will be denoted by formula_150 if the qubits formula_151 are uncorrelated with each other (namely, if the system is in a product state) and their corresponding biases are formula_152.

The compression can be described as a sort operation on the diagonal entries of the density matrix which describes the system. For instance, if the state of the system after a certain reset step is formula_153, then the compression operates on the state as follows:

This notation denotes a diagonal matrix whose diagonal entries are listed within the parentheses. The density matrices formula_155 represent the state of the system (including possible correlations between the qubits) before and after the compression step, respectively. In the above notations, the state after compression is formula_156.

This sort operation is used for the rearrangement of the qubits in descending order of bias. As in the example, for some cases the sort operation can be described by a simpler operation, such as swap. However, the general form of the compression operation is a sort operation on the diagonal entries of the density matrix.

For an intuitive demonstration of the compression step, the flow of the algorithm in the 1st round is presented below:

After the 1st round is over, the bias of the reset qubit (formula_167) is smaller than the bias of the heat bath (formula_168). This means that in the next refresh step (in the 2nd round of the algorithm), the reset qubit will be replaced by a fresh qubit with bias formula_168: this cools the entire system, similarly to the previous refresh steps. Afterwards, the algorithm continues in a similar way.

The number of rounds is not bounded: since the biases of the reset qubits asymptotically reach the bias of the bath after each round, the bias of the target computational qubit asymptotically reaches its limit as the algorithm proceeds. The target qubit is the computational qubit that the algorithm aims to cool the most. The "cooling limit" (the maximum bias the target qubit can reach) depends on the bias of the bath and the number of qubits of each kind in the system. If the number of the computational qubits (excluding the target one) is formula_170 and the number of reset qubits is formula_171, then the cooling limit is formula_172. In the case where formula_173, the maximal polarization that can be obtained is proportional to formula_174. Otherwise, the maximal bias reaches arbitrarily close to formula_175. The number of rounds required in order to reach a certain bias depends on the desired bias, the bias of the bath and the number of qubits, and moreover varies between different versions of the algorithm.

There are other theoretical results which give bounds on the number of iterations required to reach a certain bias. For example, if the bias of the bath is formula_176, then the number of iterations required to cool a certain qubit to bias formula_177 is at least formula_178.

In a quantum computer, the fundamental unit of information (called a quantum bit or qubit), is not binary but rather more quaternary in nature. This qubit property arises as a direct consequence of its adherence to the laws of quantum mechanics, which differ radically from the laws of classical physics. A qubit can exist not only in a state corresponding to the logical state 0 or 1 as in a classical bit, but also in states corresponding to a blend or quantum superposition of these classical states. In other words, a qubit can exist as a zero, a one, or simultaneously as both 0 and 1, with a numerical coefficient representing the probability for each state. A quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state.

Lateral computing

Lateral computing is a lateral thinking approach to solving computing problems.
Lateral thinking has been made popular by Edward de Bono. This thinking technique is applied to generate creative ideas and solve problems. Similarly, by applying lateral-computing techniques to a problem, it can become much easier to arrive at a computationally inexpensive, easy to implement, efficient, innovative or unconventional solution.

The traditional or conventional approach to solving computing problems is to either build mathematical models or have an IF- THEN -ELSE structure. For example, a brute-force search is used in many chess engines, but this approach is computationally expensive and sometimes may arrive at poor solutions. It is for problems like this that lateral computing can be useful to form a better solution.

A simple problem of truck backup can be used for illustrating lateral-computing. This is one of the difficult tasks for traditional computing techniques, and has been efficiently solved by the use of fuzzy logic (which is a lateral computing technique). Lateral-computing sometimes arrives at a novel solution for particular computing problem by using the model of how living beings, such as how humans, ants, and honeybees, solve a problem; how pure crystals are formed by annealing, or evolution of living beings or quantum mechanics etc.

Chess position analysis can be used to illustrate the logical thinking. The following board position describes a chess problem which has to be solved with two moves.
The white has several options to make a move and checkmate the black. The move Rd5 × Rd7 or Rf7 × Rd7 will immediately provide material advantage to white. There are similar moves which capture pieces and provide immediate material advantages to the white. But a knight move Nc6 which does not provide any material advantage, provides a solution for checkmate for black in two moves.
This is an example which illustrates the use of logical thinking. The logical thinking in chess progresses by evaluating the immediate material gain in each move. This will result in a solution which will require more number of moves or failure to checkmate. However, the not so obvious move of knight results in a very powerful checkmate. Even though this move does not look logical, it is the solution to two-move checkmate problem. A computer programmed to play chess might miss out some good opportunities if it does a material-based search to find moves.

The attempts to use logic programming such as prolog to represent knowledge and build artificial intelligent systems has not provided the anticipated thrust to solving interesting problems. The lack of generalization and learning capability of these systems and exponential growth of the IF-THEN ELSE rules has made this approach unpopular. An example to illustrate the failure of the rule-based system is the following flawed proof:

This would imply that 4 = 5, which a wrong result. While taking the square roots, the step of considering the signs has been missed. This has resulted in an absurd outcome. A rule-based system, even if it missed a simple rule in its database may yield such an unacceptable output.

Another interesting mathematical proof gone wrong is as follows:

If a = 1, then we get an absurd result of 1 = 2

Lateral thinking is technique for creative thinking for solving problems. The brain as center of thinking has a self-organizing information system. It tends to create patterns and traditional thinking process uses them to solve problems. The lateral thinking technique proposes to escape from this patterning to arrive at better solutions through new ideas. Provocative use of information processing is the basic underlying principle of lateral thinking,

The provocative operator (PO) is something which characterizes lateral thinking. Its function is to generate new ideas by provocation and providing escape route from old ideas. It creates a provisional arrangement of information.

Water logic is contrast to traditional or rock logic. Water logic has boundaries which depends on circumstances and conditions while rock logic has hard boundaries. Water logic, in someways, resembles fuzzy logic.

Lateral computing does a provocative use of information processing similar to lateral-thinking. This is explained with the use of evolutionary computing which is a very useful lateral-computing technique. The evolution proceeds by change and selection. While random mutation provides change, the selection is through survival of the fittest. The random mutation works as a provocative information processing and provides a new avenue for generating better solutions for the computing problem.

Lateral computing takes the analogies from real-world examples such as:Differentiating factors of "lateral computing":It is very hard to draw a clear boundary between conventional and lateral computing. Over a period of time, some unconventional computing techniques become integral part of mainstream computing. So there will always be an overlap between conventional and lateral computing. It will be tough task classifying a computing technique as a conventional or lateral computing technique as shown in the figure. The boundaries are fuzzy and one may approach with fuzzy sets.

Lateral computing is a fuzzy set of all computing techniques which use unconventional computing approach. Hence Lateral computing includes those techniques which use semi-conventional or hybrid computing. The degree of membership for lateral computing techniques is greater than 0 in the fuzzy set of unconventional computing techniques.

The following brings out some important differentiators for lateral computing.
Parallel computing focuses on improving the performance of the computers/algorithms through the use of several computing elements (such as processing elements). The computing speed is improved by using several computing elements. Parallel computing is an extension of conventional sequential computing. However, in lateral computing, the problem is solved using unconventional information processing whether using a sequential or parallel computing.

There are several computing techniques which fit the Lateral computing paradigm. Here is a brief description of some of the Lateral Computing techniques:

Swarm intelligence (SI) is the property of a system whereby the collective behaviors of (unsophisticated) agents, interacting locally with their environment, cause coherent functional global patterns to emerge. SI provides a basis with which it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model.

One interesting swarm intelligent technique is the Ant Colony algorithm:

Agents are encapsulated computer systems that are situated in some environment and are capable of flexible, autonomous action in that environment in order to meet their design objectives. Agents are considered to be autonomous (independent, not-controllable), reactive (responding to events), pro-active (initiating actions of their own volition), and social (communicative). Agents vary in their abilities: they can be static or mobile, or may or may not be intelligent. Each agent may have its own task and/or role. Agents, and multi-agent systems, are used as a metaphor to model complex distributed processes. Such agents invariably need to interact with one another in order to manage their inter-dependencies. These interactions involve agents cooperating, negotiating and coordinating with one another.

Agent-based systems are computer programs that try to simulate various complex phenomena via virtual "agents" that represent the components of a business system. The behaviors of these agents are programmed with rules that realistically depict how business is conducted. As widely varied individual agents interact in the model, the simulation shows how their collective behaviors govern the performance of the entire system - for instance, the emergence of a successful product or an optimal schedule. These simulations are powerful strategic tools for "what-if" scenario analysis: as managers change agent characteristics or "rules," the impact of the change can be easily seen in the model output

By analogy, a computational grid is a hardware and software infrastructure that provides dependable, consistent, pervasive, and inexpensive access to high-end computational capabilities. The applications of grid computing are in:

The autonomic nervous system governs our heart rate and body temperature, thus freeing our conscious brain from the burden of dealing with these and many other low-level, yet vital, functions. The essence of autonomic computing is self-management, the intent of which is to free system administrators from the details of system operation and maintenance.

Four aspects of autonomic computing are:

This is a grand challenge promoted by IBM.

Optical computing is to use photons rather than conventional electrons for computing. There are quite a few instances of optical computers and successful use of them. The conventional logic gates use semiconductors, which use electrons for transporting the signals. In case of optical computers, the photons in a light beam are used to do computation.

There are numerous advantages of using optical devices for computing such as immunity to electromagnetic interference, large bandwidth, etc.

DNA computing uses strands of DNA to encode the instance of the problem and to manipulate them using techniques commonly available in any molecular biology laboratory in order to simulate operations that select the solution of the problem if it exists.

Since the DNA molecule is also a code, but is instead made up of a sequence of four bases that pair up in a predictable manner, many scientists have thought about the possibility of creating a molecular computer. These computers rely on the much faster reactions of DNA nucleotides binding with their complements, a brute force method that holds enormous potential for creating a new generation of computers that would be 100 billion times faster than today's fastest PC. DNA computing has been heralded as the "first example of true nanotechnology", and even the "start of a new era", which forges an unprecedented link between computer science and life science.

Example applications of DNA computing are in solution for the Hamiltonian path problem which is a known NP complete one. The number of required lab operations using DNA grows linearly with the number of vertices of the graph. Molecular algorithms have been reported that solves the cryptographic problem in a polynomial number of steps. As known, factoring large numbers is a relevant problem in many cryptographic applications.

Field-programmable gate arrays (FPGA) are making it possible to build truly reconfigurable computers. The computer architecture is transformed by on the fly reconfiguration of the FPGA circuitry. The optimal matching between architecture and algorithm improves the performance of the reconfigurable computer. The key feature is hardware performance and software flexibility.

For several applications such as fingerprint matching, DNA sequence comparison, etc., reconfigurable computers have been shown to perform several orders of magnitude better than conventional computers.

The Simulated annealing algorithm is designed by looking at how the pure crystals form from a heated gaseous state while the system is cooled slowly. The computing problem is redesigned as a simulated annealing exercise and the solutions are arrived at. The working principle of simulated annealing is borrowed from metallurgy: a piece of metal is heated (the atoms are given thermal agitation), and then the metal is left to cool slowly. The slow and regular cooling of the metal allows the atoms to slide progressively their most stable ("minimal energy") positions. (Rapid cooling would have "frozen" them in whatever position they happened to be at that time.) The resulting structure of the metal is stronger and more stable. By simulating the process of annealing inside a computer program, it is possible to find answers to difficult and very complex problems. Instead of minimizing the energy of a block of metal or maximizing its strength, the program minimizes or maximizes some objective relevant to the problem at hand.

One of the main components of "Lateral-computing" is soft computing which approaches problems with human information processing model. The Soft Computing technique comprises Fuzzy logic, neuro-computing, evolutionary-computing, machine learning and probabilistic-chaotic computing.

Instead of solving a problem by creating a non-linear equation model of it, the biological neural network analogy is used for solving the problem. The neural network is trained like a human brain to solve a given problem. This approach has become highly successful in solving some of the pattern recognition problems.

The genetic algorithm (GA) resembles the natural evolution to provide a universal optimization. Genetic algorithms start with a population of chromosomes which represent the various solutions. The solutions are evaluated using a fitness function and a selection process determines which solutions are to be used for competition process. These algorithms are highly successful in solving search and optimization problems. The new solutions are created using evolutionary principles such as mutation and crossover.

Fuzzy logic is based on the fuzzy sets concepts proposed by Lotfi Zadeh. The degree of membership concept is central to fuzzy sets. The fuzzy sets differ from crisp sets since they allow an element to belong to a set to a degree (degree of membership). This approach finds good applications for control problems. The Fuzzy logic has found enormous applications and has already found a big market presence in consumer electronics such as washing machines, microwaves, mobile phones, Televisions, Camcoders etc.

Probabilistic computing engines, e.g. use of probabilistic graphical model such as Bayesian network. Such computational techniques are referred to as randomization, yielding probabilistic algorithms. When interpreted as a physical phenomenon through classical statistical thermodynamics, such techniques lead to energy savings that are proportional to the probability p with which each primitive computational step is guaranteed to be correct (or equivalently to the probability of error, (1–p). Chaotic Computing is based on the chaos theory.

Fractal Computing are objects displaying self-similarity at different scales. Fractals generation involves small iterative algorithms. The fractals have dimensions greater than their topological dimensions. The length of the fractal is infinite and size of it cannot be measured. It is described by an iterative algorithm unlike a Euclidean shape which is given by a simple formula. There are several types of fractals and Mandelbrot sets are very popular.

Fractals have found applications in image processing, image compression music generation, computer games etc. Mandelbrot set is a fractal named after its creator. Unlike the other fractals, even though the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. I.e., the Mandelbrot set is infinitely complex. But the process of generating it is based on an extremely simple equation. The Mandelbrot set "M" is a collection of complex numbers. The numbers "Z" which belong to "M" are computed by iteratively testing the Mandelbrot equation. "C" is a constant. If the equation converges for chosen "Z", then "Z" belongs to "M".
Mandelbrot equation:

A Randomized algorithm makes arbitrary choices during its execution. This allows a savings in execution time at the beginning of a program. The disadvantage of this method is the possibility that an incorrect solution will occur. A well-designed randomized algorithm will have a very high probability of returning a correct answer. The two categories of randomized algorithms are:

Consider an algorithm to find the "k" element of an array. A deterministic approach would be to choose a pivot element near the median of the list and partition the list around that element. The randomized approach to this problem would be to choose a pivot at random, thus saving time at the beginning of the process. Like approximation algorithms, they can be used to more quickly solve tough NP-complete problems. An advantage over the approximation algorithms, however, is that a randomized algorithm will eventually yield an exact answer if executed enough times

Human beings/animals learn new skills, languages/concepts. Similarly, machine learning algorithms provide capability to generalize from training data. There are two classes of Machine Learning (ML):One of the well known machine learning technique is Back Propagation Algorithm. This mimics how humans learn from examples. The training patterns are repeatedly presented to the network. The error is back propagated and the network weights are adjusted using gradient descent. The network converges through several hundreds of iterative computations.

This is another class of highly successful machine learning techniques successfully applied to tasks such as text classification, speaker recognition, image recognition etc.

There are several successful applications of lateral-computing techniques. Here is a small set of applications that illustrates lateral computing:Above is a review of lateral-computing techniques. Lateral-computing is based on the lateral-thinking approach and applies unconventional techniques to solve computing problems. While, most of the problems are solved in conventional techniques, there are problems which require lateral-computing. Lateral-computing provides advantage of computational efficiency, low cost of implementation, better solutions when compared to conventional computing for several problems. The lateral-computing successfully tackles a class of problems by exploiting tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness and low solution cost. Lateral-computing techniques which use the human like information processing models have been classified as "Soft Computing" in literature.

Lateral-computing is valuable while solving numerous computing problems whose mathematical models are unavailable. They provide a way of developing innovative solutions resulting in smart systems with Very High Machine IQ (VHMIQ). This article has traced the transition from lateral-thinking to lateral-computing. Then several lateral-computing techniques have been described followed by their applications. Lateral-computing is for building new generation artificial intelligence based on unconventional processing.

'QUBIT' is the annual technical fest of the Department of Computer Science. It is a prestigious technological event in the state with papers presented from all over the country. It has risen beyond its technical reach and incorporated cultural aspects with the introduction of Lan-Gaming, Treasure Hunts, Fun Stalls etc. giving it an all round reach. It is organised during the month of March right from the year of its inception without fail. It is a technical symposium for young minds and meeting ground for tech-enthusiasts from around the country.

Mahatma Gandhi Institute of Technology

Mahatma Gandhi Institute of Technology (or MGIT) is a technological institution located in Gandipet, Hyderabad, Telangana, India.
It was started in 1997 by the Chaitanya Bharathi Educational Society (CBES), Hyderabad, registered under the Societies Registration Act. The annual intake is 900 students in undergraduate level and 108 students in postgraduate level. The institute is affiliated to Jawaharlal Nehru Technological University, Hyderabad (JNTUH) and offers the four-year Bachelor of Technology, in eight disciplines and two-year Master of Technology, in six disciplines prescribed by JNTU. The college is accredited by the National Board of Accreditation and is ISO 9001:2000 certified.
The institute offers a four-year bachelor's degree Bachelor of Technology, in eight disciplines:

The institute offers a two-year master's degree Master of Technology, in four departments:

Every semester has a minimum of eight courses, which includes a minimum of two laboratory courses. Students are required to attain a total of 216 of the possible 224 credits and attend the institute for duration of not less than four years and not more than eight years to be considered for the award of the degree. The institute follows JNTU’s attendance regulation, which requires students to put in a minimum class attendance of 65% to progress to the next semester. External (university) exams are held every semester in the campus and consolidated results in all these exams count towards the final aggregate grading.

The minimum criterion for admission is 60% marks in the Intermediate/10+2 Examination. Students are admitted primarily based on their ranks in the Engineering Agricultural and Medical Common Entrance Test EAMCET, held by the JNTUH every year.It also takes lateral entry admissions based on TS ECET ranks.

The institute has nine departments:

Nirvana is organized by MGIT in March every year. It started in 2004. Musicians and DJs are invited to perform at the show.

MAGISTECH is an event organized by ISTE Students’ Chapter-MGIT which is held annually on 15 and 16 September. The event provides a platform for the engineering students to interact and share their ideas with the other students across the country. The themes of paper presentation competition cover the entire spectrum of engineering and technology. Other major events include the Robotics competition and Tantra (a design competition in which a problem statement is given). This event is conducted as part of the celebrations of Engineers’ Day, the birth day of "Bharath Ratna Sir Mokshgundam Visvesvaraya".

'MICROCOSM' is the annual technical fest of Department of Electronics and Communication Engineering.

'POTENZIA' is the annual technical fest of Department of Electrical and Electronics Engineering.

'TECHNOVATION' is the annual technical fest of Department of Mechanical Engineering (Mechatronics).

'YUKTI' is the annual technical fest of Department of Information Technology.

'METALLON' is the annual technical fest of Department of Metallurgy and Materials Technology.

'CINFRA' is the annual technical fest of Department of Civil Engineering.


When was Demopolis founded?

The Demopolis Historic Business District, currently officially known as Demopolis Historic District, is a historic district in the city of Demopolis, Alabama, United States. Demopolis had its beginnings in 1817 with the Vine and Olive Colony. The historic district is a ten block area, roughly bounded by Capitol Street, Franklin Street, Desnouettes Street, and Cedar Avenue.

Demopolis Historic Business District

The district boundaries were increased, and name was changed to the actual one on October 2014.

Demopolis was founded after the fall of Napoleon's Empire and named by a group of French expatriates, a mix of exiled Bonapartists and other French migrants who had settled in the United States after the overthrow of the colonial government in Saint-Domingue following the failed Saint-Domingue expedition. The name, meaning in Greek "the People's City" or "City of the People", was chosen to honor the democratic ideals behind the endeavor. First settled in 1817, it is one of the oldest continuous settlements in Alabama. It was incorporated on December 11, 1821.."

Demopolis, Alabama

Demopolis is the largest city in Marengo County, Alabama, United States. The population was 7,483 at the time of the 2010 United States Census.

The city lies at the confluence of the Black Warrior and Tombigbee rivers. It is situated atop a cliff composed of the Demopolis Chalk Formation, known locally as White Bluff, on the east bank of the Tombigbee River. It is at the center of Alabama's Canebrake region and is also within the Black Belt.

Organizing themselves first in Philadelphia, French expatriates petitioned the U.S. Congress to sell them property for land to colonize. Congress granted approval by an act on March 3, 1817 that allowed them to buy four townships in the Alabama Territory at $2 per acre, with the provision that they cultivate grape vines and olive trees. Following advice obtained from experienced Western pioneers, they determined that Alabama would provide a good climate for cultivating these crops. By July 14, 1817, a small party of pioneers had settled at White Bluff on the Tombigbee River, at the present site of Demopolis, founding the Vine and Olive Colony.

Most prominent and wealthiest among the immigrants was Count Lefebvre Desnouettes, who had been a cavalry officer with the rank of Lieutenant-General, under Napoleon. Considered Napoleon's best friend, he had ridden in Napoleon's carriage during his failed invasion of Russia. Other prominent figures among them included Lieutenant-General Baron Henri-Dominique Lallemand, Count Bertrand Clausel, Joseph Lakanal, Simon Chaudron, Pasqual Luciani, Colonel Jean-Jerome Cluis, Jean-Marie Chapron, Colonel Nicholas Raoul, and Frederic Ravesies. Most of these expatriates had little interest in pioneer life and sold their shares in the colony, remaining in Philadelphia. By 1818, the colony consisted of only 69 settlers.

Due to a variety of adversities, their pioneering efforts were not the great success for which they had hoped. Following a survey in August 1818, they were to find that their new homes did not fall under the territories encompassed by the congressional approval, and the Vine and Olive Colony was soon forced to move. They learned that their actual land grants began less than a mile to the east of their newly cleared land. After abandoning the settlement of Demopolis, they soon established two other towns, Aigleville and Arcola.

Upon learning of the survey and that the French grants lay elsewhere, American settlers began to quickly purchase the property of the former French settlement with the intent of turning it into a major river port. A land company was formed in 1819 with the express purpose of purchasing the land and laying off of a town, the White Bluff Association (later renamed the Company of the Town of Demopolis). George Strother Gaines was named as the company spokesman and he bought the town site atop White Bluff as soon as it offered for sale. Commissioners for the company were George Strother Gaines, James Childress, Walter Crenshaw, Count Charles Lefebvre Desnouettes, and Dr. Joseph B. Earle.

The commissioners were responsible for overseeing the survey of the site, lot sales, and the early operations of the town. The commissioners laid off the site into streets, blocks, and lots, with a block of roughly two acres divided into eight lots. The Demopolis Town Square, encompassing one city block, was established in 1819. The first lots were sold beginning on April 22, 1819. When Count Desnouettes died in 1822, Allen Glover was appointed to replace him. As other commissioners retired they were succeeded by David E. Moore, William H. Lyon, Thomas McGee, and George N. Stewart.

The streets were laid off utilizing a grid plan, using Philadelphia as a model. The original streets running north-south were named for trees, such as Ash, Cedar, Cherry, and Chestnut. Exceptions were made for Commissioners, Strawberry, and Market (now Main) streets. Several short north-south streets were also named for commissioners, such as Desnouettes, Earle, Glover, Griffin, and McGee. The east-west streets were named for national and local heroes, as well as commissioners, such as Childress, Fulton, Gaines, Lyon, Monroe, Washington, Franklin, Jefferson, and Jackson. Most streets were designed to be wide. A strip of land that was remain public property, for the use of all, was the land adjoining the Tombigbee River from where Riverside Cemetery is today, to the southwest of the city proper, all the way to the Upper Landing in the north, with Arch Street following the route along the top of the cliff. Only the portion of Arch Street adjacent to the cemetery remains intact.
Some flaws and limitations of the original town plan had become apparent by the late 1820s and 1830s. The typical town lots, at wide and deep were not conducive to the building of the stately homes desired by the more prosperous citizens of the town, although some grand mansions did begin to appear by the late 1820s. One of the first was the brick -story Federal-style Allen Glover house at the foot of Capitol street. It was one of the, if not the, first neoclassical structure to appear in Marengo County. It was soon followed by Bluff Hall, built in 1832 by Allen Glover for his daughter, Sarah Serena, and son-in-law, Francis Strother Lyon.

One major flaw in the town plan was that there was no clearly defined business district, resulting in commercial and residential buildings mixed together all over town. This eventually resulted in numerous blighted areas. Some stores did open around the town square, however, and warehouses started to appear adjacent to the town's three major river landings, Upper Landing, above the modern Demopolis Yacht Basin and Marina, Webb's Landing at the western terminus of Washington Street, and Lower Landing to the west of Riverside Cemetery and the Whitfield Canal.
By the 1830s Demopolis had developed into a regional commercial river hub, attracting American and European-born craftsmen and merchants including the Beysiegle, Breitling, Breton, Dupertuis, Foster, Hummell, Kirker, Knapp, Marx, Michael, Mulligan, Oberling, Rhodes, Rudisill, Rosenbaum, Schmidt, Shahan, Stallings, and Zaiser families. Numerous plantation owners also established town houses in the community or on its outskirts, including the Allen, Ashe, Curtis, DuBose, Foscue, Glover, Griffin, Lane, Lyon, McAllister, Prout, Reese, Strudwick, Tayloe, Whitfield, and Vaughan families. However, unlike many other towns in the Canebrake and Black Belt, Demopolis was never overwhelmed by a homogeneous planter class that came to dominate so many of the others. During these years and those to come, the rivers brought in a large itinerant population with a desire for raucous entertainment. This created a profitable and brisk trade for those operating taverns, and did much to earn early Demopolis a reputation for decadence.

During the 1840s many of the streets laid out by the town fathers had yet to be opened to traffic. The town council focused much of its attention on clearing the intended streets of obstacles and opening them to traffic, other street improvements, and the building of wooden sidewalks along major thoroughfares. The council also approved measures for protecting trees in the common areas and streets. Several town ordinances were enacted in 1842 to further restrain the enslaved African American population. These included the prohibition of selling or purchasing any article or commodity from or to a slave without written permission from their master or overseer, no slave was allowed to purchase alcohol without written consent, if any slave were convicted of assault upon "any white man, negro, or mulatto" the owner would be fined $50, any slave caught running "any horse, gelding, or mule" through town would be subject to fifteen lashes unless the owner pays a fine of $1, any slave caught driving any wagon or cart or driving a horse or mule on or across the sidewalks of the town would be subject to 10 lashes, unless the owner pays a fine of 50 cents.
With its eclectic mix of citizenry, Demopolis was slow to erect houses of worship. In fact, a group of Methodist ministers convened nearby in 1843 pronounced Demopolis as "wholly irreligious." Mainline Protestant churches were slow to take root, in fact no churches at all were built in Demopolis until 1840. Prior to that time various denominational groups met in a log assembly house on the town square until it was torn down in 1844. A Baptist group had been established in the 1820s, but ended due to a lack of support. The Episcopalians established a congregation in 1834, but did not build their Trinity Episcopal Church until 1850. A Presbyterian congregation was established in 1839 and completed their first church, a brick structure now known as Rooster Hall, on the town square in 1843. The Methodist congregation was established in 1840 and the first building was completed in 1843. Present in Demopolis from the beginning, the Catholic congregation in town was listed as a mission of Saint John the Baptist in Tuscaloosa in 1851. It was switched to Selma in 1880. They met in a small frame church and private homes until the current Saint Leo the Great was built in 1905. The Jewish congregation, B'nai Jeshurun, was established in 1858, although the community had been present since the 1840s. B'nai Jeshurun was the fourth Jewish congregation established in Alabama. They initially met in homes and businesses until eventually building a Moorish Revival-style temple in 1893.
By the 1850s several palatial steamboats were visiting the town as a regular stop on the Mobile to Columbus, Mississippi route along the Tombigbee. These included the "Forest Monarch", "Alice Vivian", and the ill-fated "Eliza Battle". Several others were dedicated to almost exclusively to Demopolis and the cotton trade, including the "Allen Glover", "Canebrake", "Cherokee", "Demopolis", "Frank Lyon", "Marengo", and the "Mollie Glover". Major hotels during this same period included the Planter's Hotel, later known as Madison House Hotel, and the River Hotel.

The year 1853 saw a yellow fever epidemic strike the city, with some interments in an ill-defined two acre cemetery to the north of town in the river bend. The Jewish Cemetery was established in 1878 to the east of town on Jefferson Street. The Glover Mausoleum was completed on the banks of the Tombigbee in 1845, with the burial of many family members in and around it. This led to the establishment of the main burial ground for the city, Riverside Cemetery, officially opened with the sale of additional plots to the public in 1882. A circular Gothic Revival-style amphitheater, complete with a crenelated roof-line, was completed in 1859 north of town in Webb's Bend at the fairgrounds. The fairgrounds and its buildings covered approximately and hosted a variety of events until the outbreak of the Civil War.

By 1860, the population within the town limits had grown to approximately 1,200 people. The wealthiest citizens were, in order from the highest real and property values, Gaius Whitfield, Goodman G. Griffin, Nathan B. Whitfield, Augustus Foscue, Francis S. Lyon, Gottlieb Breitling, George F. Glover, Simeon Wheeler, Daniel F. Prout, George G. Lyon, Henry W. Reese, Benjamin N. Glover, Cecile Fournier Poole, Evelina H. Henley, David Compton, Jr., Alexander M. McDowell, Augustus Zaiser, Alexander Fournier, Timothy G. Cornish, and Luther G. Houston. The town began to attract new entertainments, such as musical and dramatic performances, concert artists, lecturers, circuses, and carnivals, but the reality of war soon ended all of that.

Marengo County, with its large number of slaveholders, was decidedly in favor of the secession from the Union and the formation of the Confederate States of America. These feelings ran high in the county's largest town also. Prominent secessionists included Nathan B. Whitfield, Francis S. Lyon, Goodman G. Griffin, Kimbrough C. DuBose, George B. Lyon, Dr. James D. Browder, and George E. Markham. However, many other powerful men in town had opposed secession, including Benjamin Glover Shields, William H. Lyon, Jr., William B. Jones, Pearson J. Glover, Gaius Whitfield, Alfred Hatch, Joel C. DuBose, Robert V. Montague, and Henry Augustine Tayloe. In the end, however, most men on both sides of the argument joined in the Confederate cause once secession was inevitable.
With the start of the Civil War, several Confederate companies drew heavily from the population of the Demopolis area and Marengo County. These included the 4th, 11th, 21st, 23rd, and 43rd Alabama Infantry Regiments in addition to the 8th Alabama Cavalry, Company E of the Jeff Davis Legion, and Selden's Battery. During the course of the war, more of these men would be lost to exhaustion, disease, and malnutrition than to battle. The city itself, on two navigable rivers and a railroad, became home to a number of Confederate installations and offices. These included commissary and quartermaster offices and warehouses, engineers' offices and workshops, a large ordnance depot, two large hospitals, offices of the medical purveyor of the Department of Alabama, Mississippi, and East Louisiana, and a huge military encampment at the fairgrounds in Webb's Bend. These brought in thousands of soldiers into town at a time, one that had just over a thousand of its own inhabitants prior to the war, putting an enormous strain on food and accommodations in the town. Many hundreds of the soldiers who died in the hospitals during the war were buried in a Confederate cemetery on the south end of Webb's Bend, but the site is under water today, following the damming of the river below Demopolis in the 20th century.

After the loss of its primary east-west railroad during the war, the Confederate government completed the Alabama and Mississippi Rivers Railroad from Selma through Demopolis and on to Meridian, Mississippi in 1862. The project had been in the works since the 1850s, but several miles between Demopolis and Uniontown had not been finished when war erupted. As the war raged in all directions around Demopolis in 1864, the city was subjected to a huge influx of war refugees. Nathan B. Whitfield noted in his journal that those from Mobile had taken every available vacant house and the others were crowded with natives along with their descendants and relatives.
March 1865 saw Demopolis preparing to defend the town against Union threats, with the fortification of key positions. Three circular batteries, surrounded by earthworks, were constructed and other fortifications built across the southern reaches of town. With the impending fall of Selma in early April, during Wilson's Raid, all of the railroad's rolling stock was sent full of supplies westward through Demopolis and on to Meridian. A flotilla of eighteen Confederate gunboats and packet ships were relocated to the Tombigbee River at Demopolis around this same time. These included the CSS "Nashville", CSS "Morgan", CSS "Baltic", the "Southern Republic", "Black Diamond", "Admiral", "Clipper", "Farrand", "Marengo" and "St. Nicholas".

With the surrender of the last of the Confederates, Demopolis was left a much different city from what it had been prior to the war. At the end of May 1865, the townspeople learned that an occupying force of Federal soldiers, the 5th Minnesota Infantry, were en route to occupy the town. Once there, they occupied the former fairgrounds. Despite the usual unpleasantness associated with the occupation of many defeated Southern towns, two of the Minnesota commanders, Colonel William B. Gere and General Lucius Frederick Hubbard apparently came to be well-liked by the townspeople. Despite some bright spots in relations, the Episcopal Church in the South was slow to give up on the notion of the Confederacy, resulting in the military governor of Alabama closing all Episcopal churches in the state, effective on September 20, 1865. Trinity Episcopal Church in Demopolis was put under Federal guard, and during this time the church mysteriously burned down. Blame was placed on the soldiers for intentionally burning it, but this has never been born out by the facts. Aside from all of this, the more pressing matter was the devastated economy of the community and surrounding countryside, a problem that would continue through the Reconstruction era.
During Reconstruction, the new authorities in charge of the government decided to move the county seat of Marengo from its central location in Linden to Demopolis by an act approved on December 4, 1868. The county appointed Richard Jones, Jr., Lewis B. McCarty, and Dr. Bryan W. Whitfield to build or buy a new courthouse in Demopolis. They negotiated the purchase of the Presbyterian church on the town square, now known as Rooster Hall, for the sum of $3000. It was conveyed to the county on April 8, 1869. The county built a fireproof brick building next door to the former church in 1869–70 to house the probate and circuit clerk offices. This building serves as Demopolis City Hall today. The move of the county seat was highly controversial, and the Alabama Legislature set April 18, 1870 as the date for a county-wide referendum to decide if Dayton, Demopolis, or Linden would become the county seat. Due to the closeness of the vote and voting irregularities, a run-off between Linden and Demopolis was set for May 14, 1870. Irregularities appeared again and votes from Dayton, mostly in favor of Linden, were rejected by the board of supervisors. Linden continued an attempt to persuade the state legislature to move the county seat back to their town, with success in February 1871. The former courthouse buildings reverted from county ownership to Demopolis and remain city property today.

The struggle to rebuild the economy of Demopolis and the surrounding region continued into the 20th century. The growing, trading, and milling of cotton continued to be a major basis of the economy up until the World War I-era. The boll weevil infestations of the 1920s and the Great Depression of the 1930s finally ended the one-crop farming system.

Demopolis had electric lights, water works and a sewerage system, chert-covered streets, paved sidewalks, and a fire department by the second decade of the 20th century. It was increasingly serving as a major banking and retail hub in the region during this time. Major financial institutions included the Commercial National Bank, City Bank and Trust Company, and Robertson Banking Company. One of the first large department stores of note in the area, Mayer Brothers, built its three-story brick building adjacent across from the public square in 1897 and operated for most of the 20th century. That building is now utilized by Robertson Banking Company. The Rosenbush Furniture Company was established in 1895 and operated until 2002. The J. H. Spight Grocery was established in 1901 as one of the earliest and most successful grocery stores for more than 50 years, prior to the era of corporate chain stores. Although the community had many newspapers throughout its first 100 years, the only one to survive into the 21st century, The Demopolis Times, was established in 1904.
A number of theaters sprang up in the city, beginning in the late 19th century. Rooster Hall, following its incarnations as a church, courthouse, and then a city property, was leased for use as the Demopolis Opera House from 1876 to 1902. It hosted live dramatic performances, civic lectures, and minstrel shows. The Braswell Opera House, with its ornate interior and private box galleries, opened on October 23, 1902 with a performance of Louisiana playwright Epsy William's "Unorna". It continued as an entertainment venue into the 1920s and was eventually demolished in 1972–73. The first theater built for the presentation of motion pictures, the Elks Theater, opened on October 1, 1915. It was renamed the Si-Non in 1916. The building was restored during the 1990s.

Following the demise of cotton production, beef cattle farming and, more recently, catfish aquaculture became new major agricultural pursuits. Industrial activities became the major sources of employment by mid-century, with the cement, lumber, and paper industries playing a prominent role in the city's economy into the 21st century.

Demopolis is located at 32°30'34" North, 87°50'14" West (32.509465, −87.837265). According to the U.S. Census Bureau, the city has a total area of, of which is land and (2.00%) is water.

Major roads include two U.S. highways: U.S. Route 80 runs east–west through the city and U.S. Route 43 runs north–south. Alabama state highways include State Route 8, State Route 13, and nearby State Route 69 and State Route 28. A proposed Interstate 85 extension from Interstate 59/20 near the Mississippi state line to Interstate 65 near Montgomery is planned to pass near the city. A bus system is operated by West Alabama Transportation.

Demopolis is served by several railway companies, including Norfolk Southern Railway, BNSF Railway, and the Alabama and Gulf Coast Railway.

The Alabama State Port Authority has inland docks at the Port of Demopolis with direct access to inland and intracoastal waterways serving the Great Lakes, the Ohio and Tennessee rivers and the Gulf of Mexico via the Tennessee-Tombigbee Waterway.

The Demopolis Municipal Airport is located northwest of the city, adjacent to Airport Industrial Park and the Tennessee-Tombigbee Waterway. It has a 5,000-foot runway and a ten-unit hangar.

Intercity bus service is provided by Greyhound Lines.

During the 2000 United States Census, there were 7,540 people, 3,014 households, and 2,070 families residing in the city. The population density was 616.4 people per square mile (238.0/km). There were 3,311 housing units at an average density of 270.7 per square mile (104.5/km). The racial makeup of the city was 50.90% Black or African American, 47.75% White, 0.09% Native American, 0.20% Asian, none Pacific Islander, 0.48% from other races, and 0.58% from two or more races. 0.98% of the population were Hispanic or Latino of any race.

There were 3,014 households out of which 34.9% had children under the age of 18 living with them, 43.1% were married couples living together, 22.5% had a female householder with no husband present, and 31.3% were non-families. 28.9% of all households were made up of individuals and 12.3% had someone living alone who was 65 years of age or older. The average household size was 2.48 and the average family size was 3.05.

In the city, the population was spread out with 29.1% under the age of 18, 8.4% from 18 to 24, 26.6% from 25 to 44, 21.6% from 45 to 64, and 14.3% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 81.5 males. For every 100 females age 18 and over, there were 75.0 males.

The median income for a household in the city was $26,481, and the median income for a family was $35,752. Males had a median income of $37,206 versus $20,265 for females. The per capita income for the city was $16,687. About 26.0% of families and 30.6% of the population were below the poverty line, including 38.3% of those under age 18 and 21.1% of those age 65 or over.

During the 2010 United States Census, there were 7,483 people, 3,049 households, and 1,998 families residing in the city. The population density was 613.4 people per square mile (236.1/km). There were 3,417 housing units at an average density of 280.1 per square mile (107.8/km). The racial makeup of the city was 50.1% Black or African American, 47.3% White, 0.1% Native American, 0.5% Asian, none Pacific Islander, 1.1% from other races, and 0.8% from two or more races. 2.4% of the population were Hispanic or Latino of any race.

There were 3,049 households out of which 31.2% had children under the age of 18 living with them, 38.6% were married couples living together, 23.3% had a female householder with no husband present, and 34.5% were non-families. 31.2% of all households were made up of individuals and 12.0% had someone living alone who was 65 years of age or older. The average household size was 2.42 and the average family size was 3.04.

In the city, the population was spread out with 27.0% under the age of 18, 8.8% from 18 to 24, 24.1% from 25 to 44, 25.3% from 45 to 64, and 14.8% who were 65 years of age or older. The median age was 37.1 years. For every 100 females, there were 80.7 males. For every 100 females age 18 and over, there were 78.2 males.

The median income for a household in the city was $35,583, and the median income for a family was $49,973. Males had a median income of $50,734 versus $31,520 for females. The per capita income for the city was $21,116. About 19.1% of families and 26.8% of the population were below the poverty line, including 25.4% of those under age 18 and 27.5% of those age 65 or over.

Demopolis is governed by a mayor–council system. The mayor is elected at large to a four-year term and functions as the executive officer, appointing department heads and advisory board members and signing off on all motions, resolutions and ordinances passed by the council.

The city council consists of five members who are elected from single member districts. The council controls all legislative and policy-making for the city through the use of ordinance, resolution or motion. The council also adopts the annual budget and confirms appointments made by the mayor.

The city runs its own citywide public school system, the Demopolis City School District. Private schools in the city include one integrated Christian school, West Alabama Christian School. The city is also home to the Demopolis Higher Education Center. The facility, which opened in 2004, is a 15,000 square feet structure, including a library and open area student atrium, a science lab, conference room, six multimedia classrooms, and two computer labs; Community Rooms provide one of the largest and most modern meeting spaces in Marengo County. The University of West Alabama is the managing partner of the center.

Gaineswood is an antebellum historic house museum on the National Register of Historic Places and is a listed National Historic Landmark. It was built between 1843–61 in an asymmetrical Greek Revival style. It features domed ceilings, ornate plasterwork, columned rooms, and most of its original furnishings. Gaineswood is owned and operated by the Alabama Historical Commission.

Bluff Hall is an antebellum historic house museum on the National Register of Historic Places. It was built in 1832 in the Federal style and modified in the 1840s to reflect the Greek Revival style. It is owned and operated by the Marengo County Historical Society.

Laird Cottage is a restored 1870 residence with a mix of the Greek Revival and Italianate styles. It currently serves as the headquarters of the Marengo County Historical Society and also houses history exhibits and the works of Geneva Mercer, a Marengo County native who gained fame as an artist and sculptor. She served as an intern to Giuseppe Moretti, the sculptor who created Birmingham's monumental "Vulcan". Following her internship, she lived and worked with Moretti and his wife until his death.

Other historic sites in Demopolis include White Bluff, the Demopolis Historic Business District, Demopolis Town Square, Lyon Hall, Ashe Cottage, the Curtis House, the Glover Mausoleum, and the Foscue-Whitfield House.

The Marx and Newhouse families of Demopolis were reputedly the inspiration for "The Little Foxes", a Broadway play. The melodrama was written by Lillian Hellman, whose maternal ancestors were all natives of Demopolis. It was first performed in 1939, with Alabama-born actress Tallulah Bankhead giving a legendary performance in the lead role of Regina. This hit production ran a year on Broadway. The 1941 film version was directed by William Wyler and starred Bette Davis, Herbert Marshall and Teresa Wright. It was nominated for an Academy Award for Best Picture in 1941. In 1949 the play was adapted into an opera by Marc Blitzstein, under the title "Regina".

Lillian Hellman's 1946 play, "Another Part of the Forest", was also loosely based on her Demopolis ancestors.

The 1949 film, "The Fighting Kentuckian", is set in Demopolis and tells a story about an interaction with the original French settlers. The basic plots features two Kentuckians returning from service with Andrew Jackson's forces in the War of 1812. Their unit passes through the port of Mobile, Alabama, where John Breen, played by John Wayne, meets the pretty Fleurette De Marchand, played by Vera Ralston, from Demopolis. He makes sure the unit passes through Demopolis on its way back home and he stays there as the unit leaves. He discovers that De Marchand is about to marry a wealthy riverman and a love triangle ensues, with Breen eventually winning out.

The climate in this area is characterized by hot, humid summers and generally mild to cool winters. According to the Köppen Climate Classification system, Demopolis has a humid subtropical climate, abbreviated "Cfa" on climate maps.

Demopolis, Alabama

Demopolis is the largest city in Marengo County, Alabama, United States. The population was 7,483 at the time of the 2010 United States Census.

The city lies at the confluence of the Black Warrior and Tombigbee rivers. It is situated atop a cliff composed of the Demopolis Chalk Formation, known locally as White Bluff, on the east bank of the Tombigbee River. It is at the center of Alabama's Canebrake region and is also within the Black Belt.

Demopolis is located at 32°30'34" North, 87°50'14" West (32.509465, −87.837265). According to the U.S. Census Bureau, the city has a total area of, of which is land and (2.00%) is water.

Demopolis is served by several railway companies, including Norfolk Southern Railway, BNSF Railway, and the Alabama and Gulf Coast Railway.

The Alabama State Port Authority has inland docks at the Port of Demopolis with direct access to inland and intracoastal waterways serving the Great Lakes, the Ohio and Tennessee rivers and the Gulf of Mexico via the Tennessee-Tombigbee Waterway.

The Demopolis Municipal Airport is located northwest of the city, adjacent to Airport Industrial Park and the Tennessee-Tombigbee Waterway. It has a 5,000-foot runway and a ten-unit hangar.

Intercity bus service is provided by Greyhound Lines.

In the city, the population was spread out with 29.1% under the age of 18, 8.4% from 18 to 24, 26.6% from 25 to 44, 21.6% from 45 to 64, and 14.3% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 81.5 males. For every 100 females age 18 and over, there were 75.0 males.

Demopolis is governed by a mayor–council system. The mayor is elected at large to a four-year term and functions as the executive officer, appointing department heads and advisory board members and signing off on all motions, resolutions and ordinances passed by the council.

The city council consists of five members who are elected from single member districts. The council controls all legislative and policy-making for the city through the use of ordinance, resolution or motion. The council also adopts the annual budget and confirms appointments made by the mayor.

Bluff Hall is an antebellum historic house museum on the National Register of Historic Places. It was built in 1832 in the Federal style and modified in the 1840s to reflect the Greek Revival style. It is owned and operated by the Marengo County Historical Society.

Other historic sites in Demopolis include White Bluff, the Demopolis Historic Business District, Demopolis Town Square, Lyon Hall, Ashe Cottage, the Curtis House, the Glover Mausoleum, and the Foscue-Whitfield House.

Lillian Hellman's 1946 play, "Another Part of the Forest", was also loosely based on her Demopolis ancestors.

The climate in this area is characterized by hot, humid summers and generally mild to cool winters. According to the Köppen Climate Classification system, Demopolis has a humid subtropical climate, abbreviated "Cfa" on climate maps.

Demopolis Town Square, currently officially known as Confederate Park, is a historic park in the city of Demopolis, Alabama, United States. It is one of the oldest public squares in the state. Demopolis had its beginnings in 1817 with the Vine and Olive Colony, and the park was established in 1819. The park covers one city block, bounded by Main, Capitol, Walnut, and Washington Streets.

Demopolis Town Square

The park was renamed "Confederate Park" in 1923, at request of United Daughters of the Confederacy.

The park contains several historic structures, including a Victorian-era gazebo near the corner of Walnut Avenue and Washington Street, the Demopolis City Hall, built in 1869–70 as a courthouse annex, and the old Presbyterian Church, built in 1843 and now known as Rooster Hall. The former church served as the Marengo County Courthouse from 1868 until 1871, when the county seat was temporarily moved from Linden. The park's center features a large cast iron fountain that was installed in 1895. The park is often used for the city's festivals, most notably for many of the Christmas on the River events. The park was added to the National Register of Historic Places on 29 November 1975.