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.
| Language | English |
|---|---|
| Article number | 040301 |
| Pages | 1-7 |
| Number of pages | 7 |
| Journal | Physical Review A |
| Volume | 99 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 4 Apr 2019 |
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Bibliographical note
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.Cite this
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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 journal › Article › Research › peer-review
TY - JOUR
T1 - Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization
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
Y1 - 2019/4/4
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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85064042104&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.99.040301
DO - 10.1103/PhysRevA.99.040301
M3 - Article
VL - 99
SP - 1
EP - 7
JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information
T2 - Physical Review A: covering atomic, molecular, and optical physics and quantum information
JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information
SN - 2469-9926
IS - 4
M1 - 040301
ER -