Quantum counting algorithm and its application in mesoscopic physics

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.012316· OSTI ID:21440483

Lesovik, G B ^[1]; Suslov, M V ^[2]; Blatter, G ^[3]

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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)

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.

• OSTI ID: 21440483
• Journal Information: Physical Review. A, Vol. 82, Issue 1; Other Information: DOI: 10.1103/PhysRevA.82.012316; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

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