Quantum simulation of the SachdevYeKitaev model by asymmetric qubitization
Abstract
We show that one can quantum simulate the dynamics of a SachdevYeKitaev model with N Majorana modes for time t to precision ɛ with gate complexity O (N^{7 /2}t +N^{5 /2}t polylog (N /ɛ ) ) . In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in 1 /ɛ and large polynomial improvement in N and t over prior stateoftheart algorithms which scale as O (N^{10}t^{2}/ɛ ) . 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 SachdevYeKitaev model involves realizing B using only Hadamard gates and realizing A as a random quantum circuit.
 Publication:

Physical Review A
 Pub Date:
 April 2019
 DOI:
 10.1103/PhysRevA.99.040301
 arXiv:
 arXiv:1806.02793
 Bibcode:
 2019PhRvA..99d0301B
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 8 pages, 1 figure. This version adds a more complete analysis in appendix