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

Ryan Babbush*, Dominic W. Berry, Hartmut Neven

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
17 Downloads (Pure)


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.

Original languageEnglish
Article number040301
Pages (from-to)1-7
Number of pages7
JournalPhysical Review A
Issue number4
Publication statusPublished - 4 Apr 2019

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