EQE-QAOA: An Equivalence-Preserving Qubit Efficient Framework for Combinatorial Optimization

TL;DR

EQE-QAOA is a novel framework that reduces qubit requirements in QAOA for large-scale combinatorial optimization without performance loss by leveraging symmetries and invariant subspaces.

Contribution

It introduces an equivalence-preserving, qubit-efficient approach that maintains QAOA performance while significantly lowering qubit needs using symmetry-based encoding.

Findings

Reduces qubit requirements without degrading QAOA performance

Proves evolution within an invariant subspace is equivalent to full system

Numerical simulations validate resource savings on Max-Cut instances

Abstract

The limited number of qubits is a major bottleneck in Quantum Approximate Optimization Algorithm (QAOA) for large-scale combinatorial optimization in the Noisy Intermediate-Scale Quantum (NISQ) era. To make progress, existing techniques rely on qubit reduction at the cost of information loss, hence leading to degraded computational performance. As a remedy, we propose the Equivalence-preserving Qubit Efficient QAOA (EQE-QAOA), which significantly reduces the required number of qubits without degrading the performance of QAOA. By exploiting intrinsic symmetries and conserved quantities, we first demonstrate that the QAOA dynamics are strictly confined to an invariant subspace of the Hilbert space. We subsequently prove that the evolution within this subspace is exactly equivalent to that of the full-scale system, achieving the same optimal solution as the original QAOA. Moreover, to reduce the number of qubits, we propose an isometric mapping that re-encodes the subspace into a space relying on fewer qubits. Furthermore, we derive the applicability conditions of EQE-QAOA and show that it is broadly applicable to large-scale combinatorial optimization problems, excluding only unconstrained problems with completely independent variables. Numerical simulations based on Max-Cut instances validate that EQE-QAOA significantly reduces qubit requirements and computational resources, while preserving exact optimization performance.