A model of quantum gravity on a noisy quantum computer

Abstract

We study the Sachdev-Ye-Kitaev (SYK) model -- an important toy model for quantum gravity on IBM's superconducting qubit quantum computers. By using a graph-coloring algorithm to minimize the number of commuting clusters of terms in the qubitized Hamiltonian, we find the circuit complexity of the time evolution using the first-order Lie product formula for \(N\) Majorana fermions is \(\mathcal{O}(N^5 J^{2}t^2/\epsilon)\) where \(J\) is the dimensionful coupling parameter, \(t\) is the evolution time, and \(\epsilon\) is the desired accuracy. This complexity is a significant improvement over existing result in the literature. With this improved resource requirement, we perform the time evolution for \(N=6, 8\) using up to 300 two-qubit gates and perform different error mitigation schemes on the noisy hardware results. We find good agreement with the results obtained using exact diagonalization on classical computers and noiseless simulators. In particular, we compute the return probability to the vacuum state after time \(t\) and out-of-time order correlators (OTOC) which is a standard method of quantifying the chaotic nature of quantum many-body systems.