Sachdev-Ye-Kitaev model on a noisy quantum computer
We study the 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 gate complexity of the time evolution using the
first-order 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 precision. With this improved
resource requirement, we perform the time evolution for $N=6, 8$ with maximum
two-qubit circuit depth of 343. We perform different error mitigation schemes
on the noisy hardware results and find good agreement with the exact
diagonalization results on classical computers and noiseless simulators. In
particular, we compute return probability after time $t$ and out-of-time order
correlators (OTOC) which is a standard observable of quantifying the chaotic
nature of quantum systems.
Muhammad Asaduzzaman Raghav G. Jha Bharath Sambasivam