Fermionic Quantum Approximate Optimization Algorithm

TL;DR

FQAOA is a novel quantum algorithm that preserves fermion particle number to efficiently solve constrained combinatorial optimization problems, outperforming existing methods especially in portfolio optimization.

Contribution

This paper introduces FQAOA, a new approach that intrinsically enforces constraints via fermion number preservation, with a systematic driver Hamiltonian design guideline.

Findings

FQAOA outperforms existing approaches in portfolio optimization.

FQAOA reduces to quantum adiabatic computation at large circuit depth.

The Hamiltonian design guideline benefits multiple quantum algorithms.

Abstract

Quantum computers are expected to accelerate solving combinatorial optimization problems, including algorithms such as Grover adaptive search and quantum approximate optimization algorithm (QAOA). However, many combinatorial optimization problems involve constraints which, when imposed as soft constraints in the cost function, can negatively impact the performance of the optimization algorithm. In this paper, we propose fermionic quantum approximate optimization algorithm (FQAOA) for solving combinatorial optimization problems with constraints. Specifically FQAOA tackle the constrains issue by using fermion particle number preservation to intrinsically impose them throughout QAOA. We provide a systematic guideline for designing the driver Hamiltonian for a given problem Hamiltonian with constraints. The initial state can be chosen to be a superposition of states satisfying the constraint and the ground state of the driver Hamiltonian. This property is important since FQAOA reduced to quantum adiabatic computation in the large limit of circuit depth p and improved performance, even for shallow circuits with optimizing the parameters starting from the fixed-angle determined by Trotterized quantum adiabatic evolution. We perform an extensive numerical simulation and demonstrates that proposed FQAOA provides substantial performance advantage against existing approaches in portfolio optimization problems. Furthermore, the Hamiltonian design guideline is useful not only for QAOA, but also Grover adaptive search and quantum phase estimation to solve combinatorial optimization problems with constraints. Since software tools for fermionic systems have been developed in quantum computational chemistry both for noisy intermediate-scale quantum computers and fault-tolerant quantum computers, FQAOA allows us to apply these tools for constrained combinatorial optimization problems.