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Swap Test
The swap test is a procedure in quantum computation that is used to check how much two quantum states differ, appearing first in the work of Barenco et al. and later rediscovered by Harry Buhrman, Richard Cleve, John Watrous, and Ronald de Wolf. It appears commonly in quantum machine learning, and is a circuit used for proofs-of-concept in implementations of quantum computers. Formally, the swap test takes two input states , \phi\rangle and , \psi\rangle and outputs a Bernoulli random variable that is 1 with probability \textstyle\frac - \frac ^2 (where the expressions here use bra–ket notation). This allows one to, for example, estimate the squared inner product between the two states, ^2, to \varepsilon additive error by taking the average over O(\textstyle\frac) runs of the swap test. This requires O(\textstyle\frac) copies of the input states. The squared inner product roughly measures "overlap" between the two states, and can be used in linear-algebraic applications, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Watrous (computer Scientist)
John Harrison Watrous is the Technical Director of IBM Quantum Education at IBM and was a professor of computer science at the David R. Cheriton School of Computer Science at the University of Waterloo, a member of the Institute for Quantum Computing, an affiliate member of the Perimeter Institute for Theoretical Physics and a Fellow of the Canadian Institute for Advanced Research.John Watrous at the Canadian Institute for Advanced Research website. He was a faculty member in the Department of Computer Science at the from 2002 to 2006 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Logic 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. 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 orthonormal basis. Usually the ''computational basis'' is used, which unless comparing it with something, just means that for a ''d''-level quantum system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fredkin Gate
The Fredkin gate (also controlled-SWAP gate and conservative logic gate) is a computational circuit suitable for reversible computing, invented by Edward Fredkin. It is ''universal'', which means that any logical or arithmetic operation can be constructed entirely of Fredkin gates. The Fredkin gate is a circuit or device with three inputs and three outputs that transmits the first bit unchanged and swaps the last two bits if, and only if, the first bit is 1. Background The Fredkin gate, conceptualized by Edward Fredkin and Tommaso Toffoli at the MIT Laboratory for Computer Science, was a pivotal advancement in the field of reversible computing and conservative logic. Developed within the framework of conservative logic, the gate is designed to align computing processes with fundamental physical principles such as the reversibility of dynamical laws and the conservation of energy. The technical rationale behind the Fredkin gate is rooted in addressing the inefficiencies of tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hadamard Gate
The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric, involutive, linear operation on real numbers (or complex, or hypercomplex numbers, although the Hadamard matrices themselves are purely real). The Hadamard transform can be regarded as being built out of size-2 discrete Fourier transforms (DFTs), and is in fact equivalent to a multidimensional DFT of size . It decomposes an arbitrary input vector into a superposition of Walsh functions. The transform is named for the French mathematician Jacques Hadamard (), the German-American mathematician Hans Rademacher, and the American mathematician Joseph L. Walsh. Definition The Hadamard transform ''H''''m'' is a 2''m'' × 2''m'' matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2''m'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bra–ket Notation
Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically designed to ease the types of calculations that frequently come up in quantum mechanics. Its use in quantum mechanics is quite widespread. Bra–ket notation was created by Paul Dirac in his 1939 publication ''A New Notation for Quantum Mechanics''. The notation was introduced as an easier way to write quantum mechanical expressions. The name comes from the English word "bracket". Quantum mechanics In quantum mechanics and quantum computing, bra–ket notation is used ubiquitously to denote quantum states. The notation uses angle brackets, and , and a vertical bar , to construct "bras" and "kets". A ket is of the form , v \rangle. Mathematically it denotes a vector, \boldsymbol v, in an abstract (complex) vector space V, and physicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Distribution
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q = 1-p. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcome (probability), outcomes that are Boolean-valued function, Boolean-valued: a single bit whose value is success/yes and no, yes/Truth value, true/Binary code, one with probability ''p'' and failure/no/false (logic), false/Binary code, zero with probability ''q''. It can be used to represent a (possibly biased) coin toss where 1 and 0 would represent "heads" and "tails", respectively, and ''p'' would be the probability of the coin landing on heads (or vice versa where 1 would represent tails and ''p'' would be the probability of tails). In particular, unfair co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Machine Learning
Quantum machine learning is the integration of quantum algorithms within machine learning programs. The most common use of the term refers to machine learning algorithms for the analysis of classical data executed on a quantum computer, i.e. quantum-enhanced machine learning. While machine learning algorithms are used to compute immense quantities of data, quantum machine learning utilizes qubits and quantum operations or specialized quantum systems to improve computational speed and data storage done by algorithms in a program. This includes hybrid methods that involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device. These routines can be more complex in nature and executed faster on a quantum computer. Furthermore, quantum algorithms can be used to analyze quantum states instead of classical data. Beyond quantum computing, the term "quantum machine learning" is also associated with classical machine learning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ronald De Wolf
Ronald Michiel de Wolf (born 1973) is a Dutch Computer Scientist, currently a Senior Researcher at Centrum Wiskunde & Informatica (CWI) and a professor at the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam (UvA). His research interests are on Quantum computing, Quantum information, Coding theory, and Computational complexity theory. His scientific contributions include the first exponential separation between one-way quantum and classical communication protocols for a partial Boolean function, and a proof that a locally decodable code (LDC) with 2 classical queries need exponential length. This suggested the use of techniques from quantum computing to prove results in "classical" computer science. De Wolf and his coauthors received the Best Paper Award at the Annual ACM Symposium on Theory of Computing (STOC) in 2012. For the same article, they also received the 2022 STOC 10-year test of time award and the 2023 Gödel Prize.https://eatcs.o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Cleve
Richard Erwin Cleve is a Canadian professor of computer science at the David R. Cheriton School of Computer Science at the University of Waterloo, where he holds the Institute for Quantum Computing Chair in quantum computing, and an associate member of the Perimeter Institute for Theoretical Physics.Richard Cleve at the IQC directory. Education He obtained his BMath and from the University of Waterloo, and his Ph.D. in 1989 at the |
Quantum Computation
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of 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 exponentially faster than any modern "classical" computer. Theoretically a large-scale quantum computer could break some widely used encryption schemes and aid physicists in performing 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 one of two states (a binary), a qubit can exist in a superposition of its two "bas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harry Buhrman
Harry Buhrman (born 1966) is a Dutch computer scientist, currently Chief Scientist Quantum Algorithms & Innovation at Quantinuum. He previously was ''Professor of algorithms, complexity theory, and quantum computing'' at the University of Amsterdam (UvA), group leader of the Quantum Computing Group at the Centrum Wiskunde & Informatica (CWI), and executive director of QuSoft, the Dutch research center for quantum software. Buhrman research interests are on Quantum Computing, Quantum Information, Quantum Cryptography, Computational complexity theory, Kolmogorov Complexity, and Computational Biology. Buhrman contributed substantially to the quantum analogue of Communication complexity, exhibiting an advantage of the use of qubits in distributed information-processing tasks. Although quantum entanglement cannot be used to replace communication, can be used to reduce the communication exponentially. Buhrman was elected a member of the Royal Netherlands Academy of Arts and Sciences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
