Quantum Computing and Second Quantization

Makaruk, Hanna Ewa

doi:10.1142/S0218216517410061

Title: Quantum Computing and Second Quantization

Abstract

Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

Authors:

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Fri Feb 10 00:00:00 EST 2017

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1352444

Report Number(s):: LA-UR-15-29479
Journal ID: ISSN 0218-2165; TRN: US1700866

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Knot Theory and Its Ramifications

Additional Journal Information:: Journal Volume: 26; Journal Issue: 03; Journal ID: ISSN 0218-2165

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; second quantization, multi particles quantum theory, quantum computing

Citation Formats


                    Makaruk, Hanna Ewa. Quantum Computing and Second Quantization.  United States: N. p., 2017. 
Web.  doi:10.1142/S0218216517410061.

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                    Makaruk, Hanna Ewa. Quantum Computing and Second Quantization.  United States.  https://doi.org/10.1142/S0218216517410061

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                    Makaruk, Hanna Ewa. Fri .  
"Quantum Computing and Second Quantization".  United States.  https://doi.org/10.1142/S0218216517410061.  https://www.osti.gov/servlets/purl/1352444.

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@article{osti_1352444,

  title        = {Quantum Computing and Second Quantization},

  author       = {Makaruk, Hanna Ewa},

  abstractNote = {Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.},

  doi          = {10.1142/S0218216517410061},

  journal      = {Journal of Knot Theory and Its Ramifications},

  number       = 03,

  volume       = 26,

  place        = {United States},

  year         = {Fri Feb 10 00:00:00 EST 2017},

  month        = {Fri Feb 10 00:00:00 EST 2017}

}

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Works referenced in this record:

An algebraic approach to linear-optical schemes for deterministic quantum computing
journal, November 2005

Aniello, Paolo; Cagli, Ruben Coen
Journal of Optics B: Quantum and Semiclassical Optics, Vol. 7, Issue 12
DOI: 10.1088/1464-4266/7/12/038

Embedding qubits into fermionic Fock space: Peculiarities of the four-qubit case
journal, June 2015

Lévay, Péter; Holweck, Frédéric
Physical Review D, Vol. 91, Issue 12
DOI: 10.1103/PhysRevD.91.125029

Qubits as parafermions
journal, September 2002

Wu, L. -A.; Lidar, D. A.
Journal of Mathematical Physics, Vol. 43, Issue 9
DOI: 10.1063/1.1499208

Generalized pure spinors
journal, December 1994

Trautman, Andrzej; Trautman, Krzysztof
Journal of Geometry and Physics, Vol. 15, Issue 1
DOI: 10.1016/0393-0440(94)90045-0

Generalized noiseless quantum codes utilizing quantum enveloping algebras
journal, February 2001

Durdevich, Micho; Makaruk, Hanna E.; Owczarek, Robert
Journal of Physics A: Mathematical and General, Vol. 34, Issue 7
DOI: 10.1088/0305-4470/34/7/314

Inefficiency of classically simulating linear optical quantum computing with Fock-state inputs
journal, February 2014

Gard, Bryan T.; Olson, Jonathan P.; Cross, Robert M.
Physical Review A, Vol. 89, Issue 2
DOI: 10.1103/PhysRevA.89.022328

Exchange gate on the qudit space and Fock space
journal, October 2003

Fujii, Kazuyuki
Journal of Optics B: Quantum and Semiclassical Optics, Vol. 5, Issue 6
DOI: 10.1088/1464-4266/5/6/011

Entanglement in fermionic Fock space
journal, February 2014

Sárosi, Gábor; Lévay, Péter
Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 11
DOI: 10.1088/1751-8113/47/11/115304

Noiseless Quantum Codes
journal, October 1997

Zanardi, P.; Rasetti, M.
Physical Review Letters, Vol. 79, Issue 17
DOI: 10.1103/PhysRevLett.79.3306

Quantum computing with parafermions
journal, March 2016

Hutter, Adrian; Loss, Daniel
Physical Review B, Vol. 93, Issue 12
DOI: 10.1103/PhysRevB.93.125105

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Similar Records

Title: Quantum Computing and Second Quantization

Abstract

Citation Formats

An algebraic approach to linear-optical schemes for deterministic quantum computing journal, November 2005

Embedding qubits into fermionic Fock space: Peculiarities of the four-qubit case journal, June 2015

Qubits as parafermions journal, September 2002

Generalized pure spinors journal, December 1994

Generalized noiseless quantum codes utilizing quantum enveloping algebras journal, February 2001

Inefficiency of classically simulating linear optical quantum computing with Fock-state inputs journal, February 2014

Exchange gate on the qudit space and Fock space journal, October 2003

Entanglement in fermionic Fock space journal, February 2014

Noiseless Quantum Codes journal, October 1997

Quantum computing with parafermions journal, March 2016

An algebraic approach to linear-optical schemes for deterministic quantum computing
journal, November 2005

Embedding qubits into fermionic Fock space: Peculiarities of the four-qubit case
journal, June 2015

Qubits as parafermions
journal, September 2002

Generalized pure spinors
journal, December 1994

Generalized noiseless quantum codes utilizing quantum enveloping algebras
journal, February 2001

Inefficiency of classically simulating linear optical quantum computing with Fock-state inputs
journal, February 2014

Exchange gate on the qudit space and Fock space
journal, October 2003

Entanglement in fermionic Fock space
journal, February 2014

Noiseless Quantum Codes
journal, October 1997

Quantum computing with parafermions
journal, March 2016