Loading [MathJax]/extensions/tex2jax.js

Efficient quantum pseudorandomness with nearly time-independent hamiltonian dynamics

Research output: Contribution to journalReview articleResearchpeer review

Authors

  • Yoshifumi Nakata
  • Christoph Hirche
  • Masato Koashi
  • Andreas Winter

External Research Organisations

  • University of Tokyo
  • Autonomous University of Barcelona (UAB)
  • Catalan Institution for Research and Advanced Studies (ICREA)

Details

Original languageEnglish
Article number021006
JournalPhysical Review X
Volume7
Issue number2
Publication statusPublished - 10 Apr 2017
Externally publishedYes

Abstract

Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.

Keywords

    Quantum information, Quantum physics, Statistical physics

ASJC Scopus subject areas

Cite this

Efficient quantum pseudorandomness with nearly time-independent hamiltonian dynamics. / Nakata, Yoshifumi; Hirche, Christoph; Koashi, Masato et al.
In: Physical Review X, Vol. 7, No. 2, 021006, 10.04.2017.

Research output: Contribution to journalReview articleResearchpeer review

Nakata Y, Hirche C, Koashi M, Winter A. Efficient quantum pseudorandomness with nearly time-independent hamiltonian dynamics. Physical Review X. 2017 Apr 10;7(2):021006. doi: 10.1103/PhysRevX.7.021006
Nakata, Yoshifumi ; Hirche, Christoph ; Koashi, Masato et al. / Efficient quantum pseudorandomness with nearly time-independent hamiltonian dynamics. In: Physical Review X. 2017 ; Vol. 7, No. 2.
Download
@article{529681af2ef844aa8b1f136c684257b6,
title = "Efficient quantum pseudorandomness with nearly time-independent hamiltonian dynamics",
abstract = "Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.",
keywords = "Quantum information, Quantum physics, Statistical physics",
author = "Yoshifumi Nakata and Christoph Hirche and Masato Koashi and Andreas Winter",
year = "2017",
month = apr,
day = "10",
doi = "10.1103/PhysRevX.7.021006",
language = "English",
volume = "7",
journal = "Physical Review X",
issn = "2160-3308",
publisher = "American Physical Society",
number = "2",

}

Download

TY - JOUR

T1 - Efficient quantum pseudorandomness with nearly time-independent hamiltonian dynamics

AU - Nakata, Yoshifumi

AU - Hirche, Christoph

AU - Koashi, Masato

AU - Winter, Andreas

PY - 2017/4/10

Y1 - 2017/4/10

N2 - Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.

AB - Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.

KW - Quantum information

KW - Quantum physics

KW - Statistical physics

UR - http://www.scopus.com/inward/record.url?scp=85021312671&partnerID=8YFLogxK

U2 - 10.1103/PhysRevX.7.021006

DO - 10.1103/PhysRevX.7.021006

M3 - Review article

AN - SCOPUS:85021312671

VL - 7

JO - Physical Review X

JF - Physical Review X

SN - 2160-3308

IS - 2

M1 - 021006

ER -