Polyakov, Pis’ma ZhETF 22, 503 (1975) Google ScholarĪlso see: A. Perelomov, Scattering, Reactions and Decay in Nonrelativistic Quantum Mechanics (Israel Program for Scientific Translations, Jerusalem, 1969) Google Scholar Sudarshan, Fundamentals of Quantum Optics (Benjamin, New York, 1968), Chap. Gardinger, Quantum Noise (Springer-Verlag, New York, 1991), Chap. 10, 84 (1963) Google Scholar Crossref, ISI Levitov, “Estimate of minimal noise in a quantum conductor,” preprint cond-mat/9507011. Levitov, “Coherent states of alternating current,” preprint cond-mat/9501040, to appear in Phys. Levitov, “Orthogonality catastrophe in a mesoscopic conductor due to a time-dependent flux,” preprint cond-mat/9312013. Lesovik, “Quantum measurement in electric circuit,” preprint cond-mat/9401004. Mazenko (World Scientific, Singapore, 1986), p. Imry, Directions in Condensed Matter Physics, edited by G. Lenstra (Kluwer Academic, New York, 1990), pp. 38 Google ScholarĪnalogies in Optics and Micro Electronics, edited by W. Bruynsraede (Springer, Heidelberg, 1985), Vol. Landauer, in Localization, Interaction and Transport Phenomena, edited by B. Mesoscopic Phenomena in Solids, edited by B. Demonstrated realisation sets a clear benchmark in the quest for the future quantum speedup in the linear systems of equations solution. A 2 17-dimensional problem is implemented on several IBM quantum computer superconducting quantum processors, a record-breaking result for a linear system solved by a quantum computer. A classification of linear systems based on the entanglement properties of the associated phase-estimation unitary operation is introduced, enabling a highly efficient search for solutions that is facilitated by a straightforward matrix-to-circuit map. Here a hybrid algorithm based on phase estimation and classical optimization of the circuit width and depth is employed for solving a specific class of large linear systems of equations ubiquitous to many areas of science and engineering. However, so far, quantum-enabled large-scale solutions have been realized only for limited set of problems. Today's intermediate-scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers.
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