Quantum-state preparation with universal gate decompositions

Plesch, Martin; Brukner, Caslav

doi:10.1103/PHYSREVA.83.032302

Title: Quantum-state preparation with universal gate decompositions

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Abstract

In quantum computation every unitary operation can be decomposed into quantum circuits--a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-not(cnot) gates. Two measures are important when judging the complexity of the circuit: the total number of cnot gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of 2. It also reduces the total number of cnot gates from 2{sup n} to (23/24)2{sup n} in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from 11 cnot gates to 9 and the depth from 11 to 5 steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.

Authors:

Plesch, Martin ^[1]; Brukner, Caslav ^[1]

Faculty of Physics, University of Vienna, Vienna (Austria)

Publication Date:: Tue Mar 15 00:00:00 EDT 2011

OSTI Identifier:: 21537398

Resource Type:: Journal Article

Journal Name:: Physical Review. A

Additional Journal Information:: Journal Volume: 83; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.83.032302; (c) 2011 American Institute of Physics; Journal ID: ISSN 1050-2947

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; QUANTUM COMPUTERS; QUANTUM STATES; QUBITS; ROTATION; COMPUTERS; INFORMATION; MOTION; QUANTUM INFORMATION

Citation Formats


                    Plesch, Martin, Faculty of Informatics, Masaryk University, Brno, Institute of Physics, Slovak Academy of Sciences, Bratislava, Brukner, Caslav, and Institute of Quantum Optics and Quantum Information. Quantum-state preparation with universal gate decompositions.  United States: N. p., 2011. 
        Web.  doi:10.1103/PHYSREVA.83.032302.

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                    Plesch, Martin, Faculty of Informatics, Masaryk University, Brno, Institute of Physics, Slovak Academy of Sciences, Bratislava, Brukner, Caslav, & Institute of Quantum Optics and Quantum Information. Quantum-state preparation with universal gate decompositions.  United States.  https://doi.org/10.1103/PHYSREVA.83.032302

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                    Plesch, Martin, Faculty of Informatics, Masaryk University, Brno, Institute of Physics, Slovak Academy of Sciences, Bratislava, Brukner, Caslav, and Institute of Quantum Optics and Quantum Information. 2011.  
        "Quantum-state preparation with universal gate decompositions".  United States.  https://doi.org/10.1103/PHYSREVA.83.032302.

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@article{osti_21537398,

  title        = {Quantum-state preparation with universal gate decompositions},

  author       = {Plesch, Martin and Faculty of Informatics, Masaryk University, Brno and Institute of Physics, Slovak Academy of Sciences, Bratislava and Brukner, Caslav and Institute of Quantum Optics and Quantum Information},

  abstractNote = {In quantum computation every unitary operation can be decomposed into quantum circuits--a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-not(cnot) gates. Two measures are important when judging the complexity of the circuit: the total number of cnot gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of 2. It also reduces the total number of cnot gates from 2{sup n} to (23/24)2{sup n} in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from 11 cnot gates to 9 and the depth from 11 to 5 steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.},

  doi          = {10.1103/PHYSREVA.83.032302},

  url          = {https://www.osti.gov/biblio/21537398},
  journal      = {Physical Review. A},

  issn         = {1050-2947},

  number       = 3,

  volume       = 83,

  place        = {United States},

  year         = {Tue Mar 15 00:00:00 EDT 2011},

  month        = {Tue Mar 15 00:00:00 EDT 2011}

}

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