Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization

Ryan Babbush, Dominic W. Berry, Hartmut Neven

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with N Majorana modes for time t to precision ϵ with gate complexity O(N⁷⁄²t+N⁵⁄²t polylog(N/ϵ)). In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in 1/ϵ and large polynomial improvement in N and t over prior state-of-the-art algorithms which scale as O(N¹⁰t²/ϵ). Our approach involves a variant of the qubitization technique in which we encode the Hamiltonian H as an asymmetric projection of a signal oracle U onto two different signal states prepared by state oracles, A|0)→|A) and B|0)→|B), such that H=⟨B|U|A⟩. Our strategy for applying this method to the Sachdev-Ye-Kitaev model involves realizing B using only Hadamard gates and realizing A as a random quantum circuit.

LanguageEnglish
Article number040301
Pages1-7
Number of pages7
JournalPhysical Review A
Volume99
Issue number4
DOIs
Publication statusPublished - 4 Apr 2019

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simulation
polynomials
projection
scaling

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Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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title = "Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization",
abstract = "We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with N Majorana modes for time t to precision ϵ with gate complexity O(N⁷⁄²t+N⁵⁄²t polylog(N/ϵ)). In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in 1/ϵ and large polynomial improvement in N and t over prior state-of-the-art algorithms which scale as O(N¹⁰t²/ϵ). Our approach involves a variant of the qubitization technique in which we encode the Hamiltonian H as an asymmetric projection of a signal oracle U onto two different signal states prepared by state oracles, A|0)→|A) and B|0)→|B), such that H=⟨B|U|A⟩. Our strategy for applying this method to the Sachdev-Ye-Kitaev model involves realizing B using only Hadamard gates and realizing A as a random quantum circuit.",
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Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization. / Babbush, Ryan; Berry, Dominic W.; Neven, Hartmut.

In: Physical Review A, Vol. 99, No. 4, 040301, 04.04.2019, p. 1-7.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Babbush, Ryan

AU - Berry, Dominic W.

AU - Neven, Hartmut

N1 - Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2019/4/4

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N2 - We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with N Majorana modes for time t to precision ϵ with gate complexity O(N⁷⁄²t+N⁵⁄²t polylog(N/ϵ)). In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in 1/ϵ and large polynomial improvement in N and t over prior state-of-the-art algorithms which scale as O(N¹⁰t²/ϵ). Our approach involves a variant of the qubitization technique in which we encode the Hamiltonian H as an asymmetric projection of a signal oracle U onto two different signal states prepared by state oracles, A|0)→|A) and B|0)→|B), such that H=⟨B|U|A⟩. Our strategy for applying this method to the Sachdev-Ye-Kitaev model involves realizing B using only Hadamard gates and realizing A as a random quantum circuit.

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