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

TL;DR

This work addresses error mitigation for quantum optimization on NISQ devices by applying two twirling techniques—universal frame randomization and Randomized Compilation—to a QAOA circuit with $p=1$ solving a frustrated Ising ring. By implementing these methods on IBM superconducting hardware (with TKET for universal frame randomization and True-Q for randomized compilation) and comparing to simulators, the study demonstrates that both approaches can shift energy estimates closer to the noiseless baseline, achieving extremal energies of $5.25 \pm 0.145$ and $4.08 \pm 0.36$ respectively, versus $2.63 \pm 0.068$ without mitigation and $5.676 \pm 0.006$ for the noiseless case. The experimental setup maps a 12-node ring to 12 qubits and samples a 289-point parameter grid ($17 \times 17$) with $5000$ shots per circuit to build an energy landscape. Overall, the results indicate that universal frame randomization and Randomized Compilation are effective, practical error-mitigation strategies for QAOA on current quantum hardware, and motivate further exploration of combining techniques and tuning compilation counts for improved performance.

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.

Figures (11)

• Figure 1: Circuit and cycles for randomized compilation on a simple quantum circuit. Each cycle is circled with a dashed line.
• Figure 2: Circuit with randomized frames around each cycle. Arbitrary random gates are inserted before and after each cycle to "frame" the cycle.
• Figure 3: Frustrated Ising ring Roberts_2020. Nodes are connected by coupling terms denoted $J$, $J_L$, and $-J_R$. The negative coupling term causes frustration. Red nodes are in one state (spin up) and the blue node is in the other state (spin down).
• Figure 4: Circuit diagram for QAOA. Gates parameterized by $\beta$ and $\gamma$ are iterated over the length of the circuit. The first complete layer of the circuit is circled with a dashed line.
• Figure 5: Energy Landscape generated by running QAOA on a closed IBM quantum simulator with no noise model (Fall 2022).