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Title: Quantum counting algorithm and its application in mesoscopic physics

Abstract

We discuss a quantum counting algorithm which transforms a physical particle-number state (and superpositions thereof) into a binary number. The algorithm involves two quantum Fourier transformations. One transformation is in physical space, where a stream of n<N=2{sup K} (charged) particles is coupled to K qubits, rotating their states by prescribed angles. The second transformation is within the Hilbert space of qubits and serves to read out the particle number in a binary form. Applications include a divisibility check characterizing the size of a finite train of particles in a quantum wire and a scheme allowing one to entangle multiparticle wave functions in a Mach-Zehnder interferometer, generating Bell, Greenberger-Horne-Zeilinger, or Dicke states.

Authors:
 [1];  [2];  [3]
  1. L. D. Landau Institute for Theoretical Physics RAS, 117940 Moscow (Russian Federation)
  2. Moscow Institute of Physics and Technology, Institutskii per. 9, 141700 Dolgoprudny, Moscow District (Russian Federation)
  3. Theoretische Physik, ETH-Zurich, CH-8093 Zuerich (Switzerland)
Publication Date:
OSTI Identifier:
21440483
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 82; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.82.012316; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CHARGED PARTICLES; FOURIER TRANSFORMATION; HILBERT SPACE; MACH-ZEHNDER INTERFEROMETER; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM STATES; QUANTUM WIRES; QUBITS; WAVE FUNCTIONS; BANACH SPACE; COMPUTERS; FUNCTIONS; INFORMATION; INTEGRAL TRANSFORMATIONS; INTERFEROMETERS; MATHEMATICAL LOGIC; MATHEMATICAL SPACE; MEASURING INSTRUMENTS; NANOSTRUCTURES; QUANTUM INFORMATION; SPACE; TRANSFORMATIONS

Citation Formats

Lesovik, G B, Theoretische Physik, ETH-Zurich, CH-8093 Zuerich, Suslov, M V, NIX Computer Company, R and D Department, Zvezdniy Boulevard 19, 129085 Moscow, and Blatter, G. Quantum counting algorithm and its application in mesoscopic physics. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.82.012316.
Lesovik, G B, Theoretische Physik, ETH-Zurich, CH-8093 Zuerich, Suslov, M V, NIX Computer Company, R and D Department, Zvezdniy Boulevard 19, 129085 Moscow, & Blatter, G. Quantum counting algorithm and its application in mesoscopic physics. United States. https://doi.org/10.1103/PHYSREVA.82.012316
Lesovik, G B, Theoretische Physik, ETH-Zurich, CH-8093 Zuerich, Suslov, M V, NIX Computer Company, R and D Department, Zvezdniy Boulevard 19, 129085 Moscow, and Blatter, G. 2010. "Quantum counting algorithm and its application in mesoscopic physics". United States. https://doi.org/10.1103/PHYSREVA.82.012316.
@article{osti_21440483,
title = {Quantum counting algorithm and its application in mesoscopic physics},
author = {Lesovik, G B and Theoretische Physik, ETH-Zurich, CH-8093 Zuerich and Suslov, M V and NIX Computer Company, R and D Department, Zvezdniy Boulevard 19, 129085 Moscow and Blatter, G},
abstractNote = {We discuss a quantum counting algorithm which transforms a physical particle-number state (and superpositions thereof) into a binary number. The algorithm involves two quantum Fourier transformations. One transformation is in physical space, where a stream of n<N=2{sup K} (charged) particles is coupled to K qubits, rotating their states by prescribed angles. The second transformation is within the Hilbert space of qubits and serves to read out the particle number in a binary form. Applications include a divisibility check characterizing the size of a finite train of particles in a quantum wire and a scheme allowing one to entangle multiparticle wave functions in a Mach-Zehnder interferometer, generating Bell, Greenberger-Horne-Zeilinger, or Dicke states.},
doi = {10.1103/PHYSREVA.82.012316},
url = {https://www.osti.gov/biblio/21440483}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 82,
place = {United States},
year = {Thu Jul 15 00:00:00 EDT 2010},
month = {Thu Jul 15 00:00:00 EDT 2010}
}