A competitive NISQ and qubit-efficient solver for the LABS problem

TL;DR

This paper introduces an extension of the Pauli Correlation Encoding (PCE) method to efficiently solve the LABS problem, demonstrating improved scaling and resource efficiency over classical and quantum approaches through simulations and quantum processor experiments.

Contribution

The paper extends PCE to solve the LABS problem, showing improved scalability and resource efficiency, and demonstrates its resilience to noise on a quantum processor.

Findings

Outperforms classical heuristics in scaling and resource use

Simulations of up to 45 variables with minimal qubits

Proof-of-principle on IonQ's quantum processor shows noise resilience

Abstract

Pauli Correlation Encoding (PCE) is as a qubit-efficient variational approach to combinatorial optimization problems. The method offers a polynomial reduction in qubit count and a super-polynomial suppression of barren plateaus. Here, we extend the PCE-based framework to solve the Low Autocorrelation Binary Sequences (LABS) problem, a notoriously hard problem often used as a benchmark for classical and quantum solvers. To illustrate this,we simulate two variants of the PCE quantum solver for LABS instances of up to $N=45$ binary variables: one with commuting and one with maximally non-commuting sets of Pauli operators. The simulations use $4$ qubits and a circuit Ansatz with a total of $30$ two-qubit gates. We benchmark our method against the state-of-the-art classical solver and other quantum schemes. We observe improved scaling in the total time to reach the exact solution, outperforming the best-performing classical heuristic while using only a fraction of the quantum resources required by other quantum approaches. In addition, we perform proof-of-principle demonstrations on IonQ's Forte quantum processor, showing that the final solution is resilient to noise. Our findings point at PCE-based solvers as a promising quantum-inspired classical heuristic for hard problems as well as a tool to reduce the resource requirements for actual quantum algorithms.