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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 leverages 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. In particular, a large-scale quantum computer could break 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.
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is generally reserved for algorithms that seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement.
A quantum Turing machine (QTM) or universal quantum computer is an abstract machine used to model the effects of a quantum computer. It provides a simple model that captures all of the power of quantum computation—that is, any quantum algorithm can be expressed formally as a particular quantum Turing machine. However, the computationally equivalent quantum circuit is a more common model.
Nuclear magnetic resonance quantum computing (NMRQC) is one of the several proposed approaches for constructing a quantum computer, that uses the spin states of nuclei within molecules as qubits. The quantum states are probed through the nuclear magnetic resonances, allowing the system to be implemented as a variation of nuclear magnetic resonance spectroscopy. NMR differs from other implementations of quantum computers in that it uses an ensemble of systems, in this case molecules, rather than a single pure state.
Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions, by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete with many local minima; such as finding the ground state of a spin glass or the traveling salesman problem. The term "quantum annealing" was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm. It was formulated in its present form by T. Kadowaki and H. Nishimori in 1998 though an imaginary-time variant without quantum coherence had been discussed by A. B. Finnila, M. A. Gomez, C. Sebenik and J. D. Doll in 1994.
Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to perform calculations and is closely related to quantum annealing.
In computational complexity theory, QMA, which stands for Quantum Merlin Arthur, is the set of languages for which, when a string is in the language, there is a polynomial-size quantum proof that convinces a polynomial time quantum verifier of this fact with high probability. Moreover, when the string is not in the language, every polynomial-size quantum state is rejected by the verifier with high probability.
Vladimir E. Korepin is a professor at the C. N. Yang Institute of Theoretical Physics of the Stony Brook University. Korepin made research contributions in several areas of mathematics and physics.
Alexei Yurievich Kitaev is a Russian–American professor of physics at the California Institute of Technology and permanent member of the Kavli Institute for Theoretical Physics. He is best known for introducing the quantum phase estimation algorithm and the concept of the topological quantum computer while working at the Landau Institute for Theoretical Physics. He is also known for introducing the complexity class QMA and showing the 2-local Hamiltonian problem is QMA-complete, the most complete result for k-local Hamiltonians. Kitaev is also known for contributions to research on a model relevant to researchers of the AdS/CFT correspondence started by Subir Sachdev and Jinwu Ye; this model is known as the Sachdev–Ye–Kitaev (SYK) model.
Frank Verstraete is a Belgian quantum physicist who is working on the interface between quantum information theory and quantum many-body physics. He pioneered the use of tensor networks and entanglement theory in quantum many body systems. He holds the Leigh Trapnell Professorship of Quantum Physics at the Faculty of Mathematics, University of Cambridge, and is professor at the Faculty of Physics at Ghent University.
The Skolkovo Institute of Science and Technology, or Skoltech, is a private institute located in Moscow, Russia. Skoltech was established in 2011 as part of a multi-year partnership with the Massachusetts Institute of Technology (MIT) Globally, the university in 2023 was ranked # 702 in the world by US News & World Report. It was among the number 65 young university in the world according to Nature Index in 2021. That same year Skoltech entered the subject ranking in physics among young universities for the first time, and named a rapidly rising university. In February 2022 MIT ended its partnership with Skoltech in protest of the Russian invasion of Ukraine.
Quantum simulators permit the study of a quantum system in a programmable fashion. In this instance, simulators are special purpose devices designed to provide insight about specific physics problems. Quantum simulators may be contrasted with generally programmable "digital" quantum computers, which would be capable of solving a wider class of quantum problems.
Quantum machine learning is the integration of quantum algorithms within machine learning programs.
Andrew MacGregor Childs is an American computer scientist and physicist known for his work on quantum computing. He is currently a professor in the department of computer science and Institute for Advanced Computer Studies at the University of Maryland. He also co-directs the Joint Center for Quantum Information and Computer Science, a partnership between the University of Maryland and the National Institute of Standards and Technology.
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the best solution to a problem from a set of possible solutions. Mostly, the optimization problem is formulated as a minimization problem, where one tries to minimize an error which depends on the solution: the optimal solution has the minimal error. Different optimization techniques are applied in various fields such as mechanics, economics and engineering, and as the complexity and amount of data involved rise, more efficient ways of solving optimization problems are needed. Quantum computing may allow problems which are not practically feasible on classical computers to be solved, or suggest a considerable speed up with respect to the best known classical algorithm.
Applying classical methods of machine learning to the study of quantum systems is the focus of an emergent area of physics research. A basic example of this is quantum state tomography, where a quantum state is learned from measurement. Other examples include learning Hamiltonians, learning quantum phase transitions, and automatically generating new quantum experiments. Classical machine learning is effective at processing large amounts of experimental or calculated data in order to characterize an unknown quantum system, making its application useful in contexts including quantum information theory, quantum technologies development, and computational materials design. In this context, it can be used for example as a tool to interpolate pre-calculated interatomic potentials or directly solving the Schrödinger equation with a variational method.
Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems and fluids. Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties.
Ivan Oseledets is a Russian computer scientist and mathematician and professor at the Skolkovo Institute of Science and Technology. He is best known for the tensor train decomposition, which is more commonly called a matrix product state in the area of tensor networks.
Germán Sierra is a Spanish theoretical physicist, author, and academic. He is Professor of Research at the Institute of Theoretical Physics Autonomous University of Madrid-Spanish National Research Council.
Zhenghan Wang is a Chinese-American mathematician. He is a principal researcher at Microsoft Station Q, as well as a professor of mathematics at the University of California, Santa Barbara.
References
- ↑ "Faculty Profile at the Skolkovo Institute of Science and Technology". skoltech.ru. Retrieved May 9, 2022.
- ↑ Biamonte, Jacob (2021). "Universal variational quantum computation". Physical Review A. 103 (3): L030401. arXiv: 1903.04500 . doi: 10.1103/PhysRevA.103.L030401 .
- ↑ Biamonte, Jacob; Wittek, Peter; Nicola, Pancotti; Rebentrost, Patrick; Wiebe, Nathan; Lloyd, Seth (2017). "Quantum machine learning". Nature. 549 (7671): 195–202. arXiv: 1611.09347 . doi:10.1038/nature23474. PMID 28905917. S2CID 64536201.
- ↑ "Jacob Biamonte". Simons Institute for the Theory of Computing. Retrieved 2024-08-08.
- ↑ "Mathematics Genealogy Project". genealogy.math.ndsu.nodak.edu. Retrieved May 9, 2022.
- ↑ "Moscow Institute of Physics and Technology Dissertation Council". mipt.ru. Retrieved May 9, 2022.
- ↑ Biamonte, Jacob (2022). On the mathematical structure of quantum models of computation based on Hamiltonian minimisation (DSc). Moscow Institute of Physics and Technology. p. 242. arXiv: 2009.10088 .
- ↑ "The 2018 USERN Prize Ceremony in Reggio Calabria". usern.tums.ac.ir. Retrieved May 12, 2022.
- ↑ "Awarded Projects Announcements". fqxi.org. Retrieved May 12, 2022.
- ↑ "Six Degrees to the Emergence of Reality, FQXi interview, by Carinne Piekema". fqxi.org. Retrieved May 12, 2022.
