Using Universal Frame Randomization and Randomized Compilation to Mitigate Errors in Quantum Optimization

TL;DR

This paper demonstrates that universal frame randomization and Randomized Compilation can effectively mitigate errors in quantum optimization algorithms like QAOA on superconducting circuits, improving energy estimation accuracy.

Contribution

The study applies and compares two error mitigation techniques, universal frame randomization and Randomized Compilation, to QAOA, showing their effectiveness in a superconducting quantum system.

Findings

Both methods mitigate errors in QAOA circuits.

Randomized Compilation achieved an extremal energy of 4.08±0.36.

Universal frame randomization achieved an extremal energy of 5.25±0.145.

Abstract

Error mitigation is essential for near-term quantum devices, and two promising techniques are universal frame randomization and Randomized Compilation. These methods insert random twirling gates into a circuit to reduce errors while preserving unitarity and depth. We apply universal frame randomization and Randomized Compilation to the quantum approximate optimization algorithm (QAOA) with $p=1$ on a superconducting quantum circuit system, demonstrating its potential to improve energy calculations. Specifically, we investigate the use of QAOA to calculate the lowest energy state of a frustrated Ising ring system and compare the results of randomized circuits generated using both techniques. Our results show that both methods can mitigate errors, with expected extremal energy values of $5.25\pm0.145$ and $4.08\pm0.36$, for Randomized Compilation and universal frame randomization respectively, compared to $2.63\pm0.068$ without randomization and $5.676\pm0.006$ with a noiseless simulator.