Using Frame Randomization to Mitigate Errors in Quantum Optimization

Abstract: Error mitigation is essential for near-term quantum devices, and one promising technique is frame randomization. This method inserts random twirling gates into a circuit to reduce errors while preserving unitarity and depth. We apply frame randomization 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 two different randomized 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 Pauli frame randomization respectively, compared to $2.63\pm0.068$ without randomization and $5.676\pm0.006$ with a noiseless simulator.