Quantum Approximate Optimization Algorithm with Fixed Number of Parameters

TL;DR

The paper proposes FPC-QAOA, a scalable quantum optimization method with fixed parameters, reducing classical complexity and improving performance on near-term quantum hardware.

Contribution

It introduces FPC-QAOA, a variational algorithm with fixed parameters that scales efficiently and mitigates overparameterization issues in quantum optimization.

Findings

Achieves comparable or better performance than standard QAOA.

Requires minimal classical effort and fewer quantum evaluations.

Demonstrates robustness on IBM quantum hardware with up to 50 qubits.

Abstract

We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless of the number of qubits, Hamiltonian complexity, or circuit depth. By separating schedule function optimization from circuit digitization, FPC-QAOA enables accurate schedule approximations with minimal parameters while supporting arbitrarily deep digitized adiabatic evolutions, constrained only by NISQ hardware capabilities. This separation allows depth to scale without expanding the classical search space, mitigating overparameterization and optimization challenges typical of deep QAOA circuits, such as barren plateaus-like behaviors. We benchmark FPC-QAOA on random MaxCut instances and the Tail Assignment Problem, achieving performance comparable to or better than standard QAOA with nearly constant classical effort and significantly fewer quantum circuit evaluations. Experiments on the IBM Kingston superconducting processor with up to 50 qubits confirm robustness and hardware efficiency under realistic noise. These results position FPC-QAOA as a practical and scalable paradigm for variational quantum optimization on near-term quantum devices.