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Parity Measurement
Parity measurement (also referred to as Operator measurement) is a procedure in quantum information science used for error detection in quantum qubits. A parity measurement checks the equality of two qubits to return a true or false answer, which can be used to determine whether a correction needs to occur.Steane, Andrew M. (2006). A tutorial on quantum error correction. ''Quantum Computers, Algorithms and Chaos'', 1-32. https://www2.physics.ox.ac.uk/sites/default/files/ErrorCorrectionSteane06.pdf Additional measurements can be made for a system greater than two qubits. Because parity measurement does not measure the state of singular bits but rather gets information about the whole state, it is considered an example of a joint measurement. Joint measurements do not have the consequence of destroying the original state of a qubit as normal quantum measurements do. Mathematically speaking, parity measurements are used to project a state into an eigenstate of an operator and to acquire ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Circuit That Exhibits Parity Measurement
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fidelity Of Quantum States
In quantum mechanics, notably in quantum information theory, fidelity quantifies the "closeness" between two density matrices. It expresses the probability that one state will pass a test to identify as the other. It is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space. Definition The fidelity between two quantum states ''\rho'' and ''\sigma'', expressed as density matrices, is commonly defined as:R. Jozsa, ''Fidelity for Mixed Quantum States'', J. Mod. Opt. 41, 2315--2323 (1994). DOI: http://doi.org/10.1080/09500349414552171 :F(\rho, \sigma) = \left(\operatorname \sqrt\right)^2. The square roots in this expression are well-defined because both \rho and \sqrt\rho\sigma\sqrt\rho are positive semidefinite matrices, and the square root of a positive semidefinite matrix is defined via the spectral theorem. The Euclidean inner product from the classical definition is replaced by the Hilbert–Schmidt inner product. As ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Theory
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields. Its study is also relevant to disciplines such as cognitive science, psychology and neuroscience. Its main focus is in extracting information from matter at the microscopic scale. Observation in science is one of the most important ways of acquiring information and measurement is required in order to quantify the observation, making this crucial to the scientific method. In quantum mechanics, due to the uncertainty principle, non-commuting observables cannot be precisely measured simultaneously, as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Markov Model
A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or ''hidden'') Markov process (referred to as X). An HMM requires that there be an observable process Y whose outcomes depend on the outcomes of X in a known way. Since X cannot be observed directly, the goal is to learn about state of X by observing Y. By definition of being a Markov model, an HMM has an additional requirement that the outcome of Y at time t = t_0 must be "influenced" exclusively by the outcome of X at t = t_0 and that the outcomes of X and Y at t < t_0 must be conditionally independent of at given at time . Estimation of the parameters in an HMM can be performed using maximum likelihood estimation. For linear chain HMMs, the Baum–Welch algorithm can be used to estimate parameters. Hidden Markov models are known for their applications to thermodynamics, statistical mechanics, physics, chem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Gate
In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. Quantum logic gates are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are reversible computing, reversible. It is possible to perform classical computing using only reversible gates. For example, the reversible Toffoli gate can implement all Boolean functions, often at the cost of having to use ancilla bits. The Toffoli gate has a direct quantum equivalent, showing that quantum circuits can perform all operations performed by classical circuits. Quantum gates are unitary operators, and are described as unitary matrix, unitary matrices relative to some orthonormal Basis (linear algebra), basis. Usually the ''computational basis'' is used, which unless comparing it with somethin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hadamard
Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations. Biography The son of a teacher, Amédée Hadamard, of Jewish descent, and Claire Marie Jeanne Picard, Hadamard was born in Versailles, France and attended the Lycée Charlemagne and Lycée Louis-le-Grand, where his father taught. In 1884 Hadamard entered the École Normale Supérieure, having placed first in the entrance examinations both there and at the École Polytechnique. His teachers included Tannery, Hermite, Darboux, Appell, Goursat, and Picard. He obtained his doctorate in 1892 and in the same year was awarded the for his essay on the Riemann zeta function. In 1892 Hadamard married Louise-Anna Trénel, also of Jewish descent, with whom he had three sons and two daughters. The following year he took up a lectureship in the University of Bordeaux, ... [...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] |
Hermitian Matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and : A \text \quad \iff \quad a_ = \overline or in matrix form: A \text \quad \iff \quad A = \overline . Hermitian matrices can be understood as the complex extension of real symmetric matrices. If the conjugate transpose of a matrix A is denoted by A^\mathsf, then the Hermitian property can be written concisely as A \text \quad \iff \quad A = A^\mathsf Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are A^\mathsf = A^\dagger = A^\ast, although in quantum mechanics, A^\ast typically means the complex conjugate onl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generator Matrix
In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix. Terminology If G is a matrix, it generates the codewords of a linear code ''C'' by : w=sG where w is a codeword of the linear code ''C'', and s is any input vector. Both w and s are assumed to be row vectors. A generator matrix for a linear , k, dq-code has format k \times n, where ''n'' is the length of a codeword, ''k'' is the number of information bits (the dimension of ''C'' as a vector subspace), ''d'' is the minimum distance of the code, and ''q'' is size of the finite field, that is, the number of symbols in the alphabet (thus, ''q'' = 2 indicates a binary code, etc.). The number of redundant bits is denoted by r = n - k. The ''standard'' form for a generator matrix is, : G = \begin I_k , P \end, where I_k is the k \times k identity m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Science
Quantum information science is a field that combines the principles of quantum mechanics with information theory to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it does not include experimental research and can be confused with a subfield of quantum information science that deals with the processing of quantum information. Scientific and engineering studies Quantum teleportation, Quantum entanglement, entanglement and the manufacturing of quantum computers depend on a comprehensive understanding of quantum physics and engineering. Google and IBM have invested significantly in quantum computer hardware research, leading to significant progress in manufacturing quantum computers since the 2010s. Currently, it is possible to create a quantum computer with over 100 qub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity-check Matrix
In coding theory, a parity-check matrix of a linear block code ''C'' is a matrix which describes the linear relations that the components of a codeword must satisfy. It can be used to decide whether a particular vector is a codeword and is also used in decoding algorithms. Definition Formally, a parity check matrix ''H'' of a linear code ''C'' is a generator matrix of the dual code, ''C''⊥. This means that a codeword c is in ''C ''if and only if the matrix-vector product (some authors would write this in an equivalent form, c''H''⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. That is, they show how linear combinations of certain digits (components) of each codeword equal zero. For example, the parity check matrix :H = \left \begin 0&0&1&1\\ 1&1&0&0 \end \right, compactly represents the parity check equations, :\begin c_3 + c_4 &= 0 \\ c_1 + c_2 &= 0 \end, that must be satisfied for the vector (c_1, c_2, c_3, c_4) to be a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
