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Quantum Register
In quantum computing, a quantum register is a system comprising multiple qubits. It is the quantum analogue of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register. Definition It is usually assumed that the register consists of qubits. It is also generally assumed that registers are not density matrices, but that they are pure, although the definition of "register" can be extended to density matrices. An n size quantum register is a quantum system comprising n pure qubits. The Hilbert space, \mathcal, in which the data is stored in a quantum register is given by \mathcal = \mathcal\otimes\mathcal\otimes\ldots\otimes\mathcal where \otimes is the tensor product. The number of dimensions of the Hilbert spaces depends on what kind of quantum systems the register is composed of. Qubits are 2-dimensional complex spaces (\mathbb^2), while qutrits are 3-dimensional complex spaces (\mathbb^3), etc. For a regist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computing
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of wave-particle duality, both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations Exponential growth, exponentially faster than any modern "classical" computer. Theoretically a large-scale quantum computer could post-quantum cryptography, break some widely used encryption schemes and aid physicists in performing quantum simulator, physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications. The basic unit of information in quantum computing, the qubit (or "quantum bit"), serves the same function as the bit in classical computing. However, unlike a classical bit, which can be in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Amplitude
In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square of the modulus of this quantity at a point in space represents a probability density at that point. Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link that was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding, and the probability thus calculated is sometimes called the "Born probability". These probabilistic concepts, namel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Circuit
In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly other actions. The minimum set of actions that a circuit needs to be able to perform on the qubits to enable quantum computation is known as DiVincenzo's criteria. Circuits are written such that the horizontal axis is time, starting at the left hand side and ending at the right. Horizontal lines are qubits, doubled lines represent classical bits. The items that are connected by these lines are operations performed on the qubits, such as measurements or gates. These lines define the sequence of events, and are usually not physical cables. The graphical depiction of quantum circuit elements is described using a variant of the Penrose graphical notation. Richard Feynman used an early version of the quantum circuit notation in 1986. Rever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Proposed Quantum Registers
A practical quantum computer must use a physical system as a programmable quantum register. Researchers are exploring several technologies as candidates for reliable qubit implementations. * Superconducting quantum computing (qubit implemented by the state of nonlinear resonant superconducting circuits containing Josephson junctions) * Trapped ion quantum computer (qubit implemented by the internal state of trapped ions) * Neutral atom quantum computer (qubit implemented by internal states of neutral atoms trapped in an optical lattice or an array of dipole traps, i.e. optical tweezers) * Quantum dot computer, Spin (physics), spin-based (e.g. the Loss-DiVincenzo quantum computer) (qubit given by the spin states of trapped electrons) * Quantum dot computer, spatial-based (qubit given by electron position in double quantum dot) * Quantum computing using engineered quantum wells, which could in principle enable the construction of a quantum computer that operates at room temperature * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Superposition
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system. An example is a qubit used in quantum information processing. A qubit state is most generally a superposition of the basis states , 0 \rangle and , 1 \rangle: : , \Psi \rangle = c_0, 0\rangle + c_1, 1\rangle, where , \Psi \rangle is the quantum state of the qubit, and , 0 \rangle, , 1 \rangle denote particular solutions to the Schrödinger equation in Dirac notation weighted by the two probability amplitudes c_0 and c_1 that both are complex numbers. Here , 0 \rangle corresponds to the classical 0 bit, and , 1 \r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flip-flop (electronics)
In electronics, flip-flops and latches are electronic circuit, circuits that have two stable states that can store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will output its state (often along with its logical complement too). It is the basic storage element in sequential logic. Flip-flops and latches are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems. Flip-flops and latches are used as data storage elements to store a single ''bit'' (binary digit) of data; one of its two states represents a "one" and the other represents a "zero". Such data storage can be used for storage of ''state (computer science), state'', and such a circuit is described as sequential logic in electronics. When used in a finite-state machine, the output and next state depend not only on its current input, but also on its current stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Vector
In mathematics, a unit vector in a normed vector space is a Vector (mathematics and physics), vector (often a vector (geometry), spatial vector) of Norm (mathematics), length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat"). The term ''normalized vector'' is sometimes used as a synonym for ''unit vector''. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., :\mathbf = \frac=(\frac, \frac, ... , \frac) where ‖u‖ is the Norm (mathematics), norm (or length) of u and \, \mathbf\, = (u_1, u_2, ..., u_n). The proof is the following: \, \mathbf\, =\sqrt=\sqrt=\sqrt=1 A unit vector is often used to represent direction (geometry), directions, such as normal directions. Unit vectors are often chosen to form the basis (linear algebra), basis of a vector space, and every vector in the space may be written as a linear combination form of unit vectors. Orthogonal coordinates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Sphere
In mathematics, a unit sphere is a sphere of unit radius: the locus (mathematics), set of points at Euclidean distance 1 from some center (geometry), center point in three-dimensional space. More generally, the ''unit -sphere'' is an n-sphere, -sphere of unit radius in -dimensional Euclidean space; the unit circle is a special case, the unit -sphere in the Euclidean plane, plane. An (Open set, open) unit ball is the region inside of a unit sphere, the set of points of distance less than 1 from the center. A sphere or ball with unit radius and center at the origin (mathematics), origin of the space is called ''the'' unit sphere or ''the'' unit ball. Any arbitrary sphere can be transformed to the unit sphere by a combination of translation (geometry), translation and scaling (geometry), scaling, so the study of spheres in general can often be reduced to the study of the unit sphere. The unit sphere is often used as a model for spherical geometry because it has constant sectional cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Space
In computer science, a state space is a discrete space representing the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space. The angular position of an undamped pendulum is a continuous (and therefore infinite) state space. Definition State spaces are useful in computer science as a simple model of machines. Formally, a state space can be defined as a tuple [''N'', ''A'', ''S'', ''G''] where: * ''N'' is a Set (mathematics), set of states * ''A'' is a set of arcs connecting the states * ''S'' is a nonempty subset of ''N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Axioms
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. There are several other (equivalent) approaches to formalising probability. Bayesians will often motivate the Kolmogorov axioms by invoking Cox's theorem or the Dutch book arguments instead. Kolmogorov axioms The assumptions as to setting up the axioms can be summarised as follows: Let (\Omega, F, P) be a measure space such that P(E) is the probability of some event E, and P(\Omega) = 1. Then (\Omega, F, P) is a probability space, with sample space \Omega, event space F and probability measure P. First axiom The probability of an event is a non-negative real number: :P(E)\in\mathbb, P(E)\geq 0 \qquad \forall E \in F where F is the event space. It follows (when combined with the second axiom) that P(E) is alwa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Born Rule
The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that position. It was formulated and published by German physicist Max Born in July 1926. Details The Born rule states that an observable, measured in a system with normalized wave function , \psi\rang (see Bra–ket notation), corresponds to a self-adjoint operator A whose spectrum is discrete if: * the measured result will be one of the eigenvalues \lambda of A, and * the probability of measuring a given eigenvalue \lambda_i will equal \lang\psi, P_i, \psi\rang, where P_i is the projection onto the eigenspace of A corresponding to \lambda_i. : (In the case where the eigenspace of A corresponding to \lambda_i is one-dimensional and spanned by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
