Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization
Year: 2019
Type: article
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 $\ensuremath{\epsilon}$ with gate complexity $O({N}^{7/2}t+{N}^{5/2}t\phantom{\rule{0.16em}{0ex}}\mathrm{polylog}(N/\ensuremath{\epsilon}))$. In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in $1/\ensuremath{\epsilon}$ and large polynomial improvement in $N$ and $t$ over prior state-of-the-art algorithms which scale as $O({N}^{10}{t}^{2}/\ensuremath{\epsilon})$. 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, $A|0\ensuremath{\rangle}\ensuremath{\mapsto}|A\ensuremath{\rangle}$ and $B|0\ensuremath{\rangle}\ensuremath{\mapsto}|B\ensuremath{\rangle}$, such that $H=\ensuremath{\langle}B|U|A\ensuremath{\rangle}$. 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.
Source: Physical Review A
Authors: Ryan Babbush, Dominic W. Berry, Hartmut Neven
Institutions: Google (United States), Macquarie University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,675
Funder: Australian Research Council
OpenAlex ID: W2805699655