We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with N Majorana modes for time t to precision ɛ with gate complexity O (N7 /2t +N5 /2t 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 state-of-the-art algorithms which scale as O (N10t2/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 Sachdev-Ye-Kitaev model involves realizing B using only Hadamard gates and realizing A as a random quantum circuit.
Physical Review A
- Pub Date:
- April 2019
- Quantum Physics;
- Condensed Matter - Strongly Correlated Electrons;
- High Energy Physics - Theory
- 8 pages, 1 figure. This version adds a more complete analysis in appendix