Optimized fermionic SWAP networks with equivalent circuit averaging for QAOA

TL;DR

This paper presents optimized fermionic SWAP networks combined with Equivalent Circuit Averaging to improve QAOA performance on superconducting qubits, achieving significant error reduction through gate decomposition and randomized compilation techniques.

Contribution

It introduces a novel optimization of fermionic SWAP networks and a new error mitigation method called Equivalent Circuit Averaging for QAOA.

Findings

Achieved ~60% error reduction in QAOA circuits on four qubits.

Validated techniques experimentally on the Advanced Quantum Testbed.

Demonstrated improved circuit fidelity with optimized gate decomposition.

Abstract

The fermionic SWAP network is a qubit routing sequence that can be used to efficiently execute the Quantum Approximate Optimization Algorithm (QAOA). Even with a minimally-connected topology on an n-qubit processor, this routing sequence enables O(n^2) operations to execute in O(n) steps. In this work, we optimize the execution of fermionic SWAP networks for QAOA through two techniques. First, we take advantage of an overcomplete set of native hardware operations [including 150 ns controlled-pi/2 phase gates with up to 99.67(1)% fidelity] in order to decompose the relevant quantum gates and SWAP networks in a manner which minimizes circuit depth and maximizes gate cancellation. Second, we introduce Equivalent Circuit Averaging, which randomizes over degrees of freedom in the quantum circuit compilation to reduce the impact of systematic coherent errors. Our techniques are experimentally validated on the Advanced Quantum Testbed through the execution of QAOA circuits for finding the ground state of two- and four-node Sherrington-Kirkpatrick spin-glass models with various randomly sampled parameters. We observe a ~60% average reduction in error (total variation distance) for QAOA of depth p = 1 on four transmon qubits on a superconducting quantum processor.