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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 either 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Circuit That Exhibits Parity Measurement
In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical 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 (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 nature. ... [...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 : 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 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 note that in quantum mechanics, A^\ast typically means the complex conjugate only, and not the conjugate transpose. Alternative characterizations Hermit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Theory
Quantum information is the information of the quantum state, 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 Observable, observables cannot be precisely mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Markov Model
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it X — with unobservable ("''hidden''") states. As part of the definition, HMM requires that there be an observable process Y whose outcomes are "influenced" by the outcomes of X in a known way. Since X cannot be observed directly, the goal is to learn about X by observing Y. 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 handwriting recognition, handwriting, gesture recognition, part-of-speech tagging, musical score following, partial discharges and bioinformatics. Definition Let X_n and Y_n be discrete-time stochastic processes and n\geq 1. The pair (X_n,Y_n) is a ''hidden Markov model'' if * X_n is a Markov process whose behavior is not directly observable ("hidden"); * \operatorname\bigl(Y_n \i ... [...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. They 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. 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 matrices relative to some basis. Usually we use the ''computational basis'', which unless we compare it with something, just means that for a ''d''-level quantum system (such as a qubit, a quantum register ... [...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, where he ... [...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. Reversible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitary Operator
In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken as operating ''on'' a Hilbert space, but the same notion serves to define the concept of isomorphism ''between'' Hilbert spaces. A unitary element is a generalization of a unitary operator. In a unital algebra, an element of the algebra is called a unitary element if , where is the identity element. Definition Definition 1. A ''unitary operator'' is a bounded linear operator on a Hilbert space that satisfies , where is the adjoint of , and is the identity operator. The weaker condition defines an ''isometry''. The other condition, , defines a ''coisometry''. Thus a unitary operator is a bounded linear operator which is both an isometry and a coisometry, or, equivalently, a surjective isometry. An equivalent definition is the following: Definition 2. A ''unitary operator'' is a bounded linear operator on a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fidelity Of Quantum States
In quantum mechanics, notably in quantum information theory, fidelity is a measure of the "closeness" of two quantum states. It expresses the probability that one state will pass a test to identify as the other. The fidelity is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space. Given two density operators \rho and \sigma, the fidelity is generally defined as the quantity F(\rho, \sigma) = \left(\operatorname \sqrt\right)^2. In the special case where \rho and \sigma represent pure quantum states, namely, \rho=, \psi_\rho\rangle\!\langle\psi_\rho, and \sigma=, \psi_\sigma\rangle\!\langle\psi_\sigma, , the definition reduces to the squared overlap between the states: F(\rho, \sigma)=, \langle\psi_\rho, \psi_\sigma\rangle, ^2. While not obvious from the general definition, the fidelity is symmetric: F(\rho,\sigma)=F(\sigma,\rho). Motivation Given two random variables X,Y with values (1, ..., n) ( categorical random variab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Science
Quantum information science is an interdisciplinary field that seeks to understand the analysis, processing, and transmission of information using quantum mechanics principles. It combines the study of Information science with quantum effects in physics. It includes theoretical issues in computational models and more experimental topics in quantum physics, including what can and cannot be done with quantum information. The term quantum information theory is also used, but it fails to encompass experimental research, and can be confused with a subfield of quantum information science that addresses the processing of quantum information. Scientific and engineering studies To understand quantum teleportation, quantum entanglement and the manufacturing of quantum computer hardware requires a thorough understanding of quantum physics and engineering. Since 2010s, there has been remarkable progress in manufacturing quantum computers, with companies like Google and IBM investing heavily ... [...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 ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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