Freedom of the mixer rotation axis improves performance in the quantum approximate optimization algorithm

Abstract

Variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA) are particularly attractive candidates for implementation on near-term quantum processors. As hardware realities such as error and qubit connectivity will constrain achievable circuit depth in the near future, new ways to achieve high-performance at low depth are of great interest. In this work, we present a modification to QAOA that adds additional variational parameters in the form of freedom of the rotation-axis in the XY -plane of the mixer Hamiltonian. Via numerical simulation, we show that this leads to a drastic performance improvement over standard QAOA at finding solutions to the MAXCUT problem on graphs of up to 7 qubits. Furthermore, we explore the Z-phase error mitigation properties of our modified ansatz, its performance under a realistic error model for a neutral atom quantum processor, and the class of problems it can solve in a single round.

Modular Parity Quantum Approximate Optimization

“…While the present work focuses on improving the quantum implementation part of the parity QAOA, there are additional opportunities to improve its performance via the classical part, for example different decoding strategies that result in smarter cost functions. More generally, further improvements of the parity QAOA might also involve exploiting recently investigated phenomena regarding QAOA parameters [35][36][37] and utilizing other types of mixing Hamiltonians [38]. The case where a physical qubit is involved in multiple driver lines has to be treated with care.…”

Amplitude amplification-inspired QAOA: improving the success probability for solving 3SAT

“…To tackle the problem of variational quantum algorithms amplifying suboptimal solutions, Bennett and Wang [18] employ a similar adaption to Variant 1 to the more general framework of the QWOA. They Transverse-field Grover search [19] MAOA [18] ma-QAOA [55] GM-QAOA [16] Th-QAOA [17] GM-Th-QAOA [17] XY-QAOA [56] XQAOA [57] FAM-QAOA [58] RQAOA [59] present the maximum amplification optimization algorithm (MAOA) and apply it to combinatorial optimization problems. They use a similar distinction between good and bad solutions to classify the elements in the set of feasible solutions into ones meeting a certain threshold for the cost function and those that do not.…”

“…ma-QAOA [55]) or that adapt the mixer Hamiltonian to increase the reachable solutions (e.g. X-QAOA [57], FAM-QAOA [58]).…”

Error Mitigation for Quantum Approximate Optimization

“…There are several adaptions to the simple p-level QAOA method described in the main text in Sec. II A [38,42,[66][67][68][69][70][71][72][73]. For instance, the Quantum Alternation Operator Ansatz [38] (QAOA+) provides a more expressive variational state by modifying the definitions of U x (β) and U p (γ).…”