Error-Mitigated Simulation of Quantum Many-Body Scars on Quantum Computers with Pulse-Level Control

Abstract: Quantum many-body scars are an intriguing dynamical regime in which quantum systems exhibit coherent dynamics and long-range correlations when prepared in certain initial states. We use this combination of coherence and many-body correlations to benchmark the performance of present-day quantum computing devices by using them to simulate the dynamics of an antiferromagnetic initial state in mixed-field Ising chains of up to 19 sites. In addition to calculating the dynamics of local observables, we also calculate the Loschmidt echo and a nontrivial connected correlation function that witnesses long-range many-body correlations in the scarred dynamics. We find coherent dynamics to persist over up to 40 Trotter steps even in the presence of various sources of error. To obtain these results, we leverage a variety of error mitigation techniques including noise tailoring, zero-noise extrapolation, dynamical decoupling, and physically motivated postselection of measurement results. Crucially, we also find that using pulse-level control to implement the Ising interaction yields a substantial improvement over the standard CNOT-based compilation of this interaction. Our results demonstrate the power of error mitigation techniques and pulse-level control to probe many-body coherence and correlation effects on present-day quantum hardware.