[Paper Review] Code from "Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem"

Ruslan Shaydulin, Changhao Li+27 more|arXiv (Cornell University)|Aug 2, 2023

Quantum Computing Algorithms and Architecture83 references4 citations

TL;DR

This paper provides empirical evidence that the Quantum Approximate Optimization Algorithm (QAOA) achieves better scaling than classical solvers on the classically intractable Low Autocorrelation Binary Sequences (LABS) problem. Using noiseless simulations up to 40 qubits and quantum minimum-finding on an idealized quantum computer, QAOA demonstrates superior runtime scaling compared to branch-and-bound solvers, with experimental validation via error-detection schemes on Quantinuum trapped-ion hardware.

ABSTRACT

Code used to generate the results in the paper "Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem". See https://github.com/jpmorganchase/QOKit for latest version.

Motivation & Objective

• To investigate whether QAOA can achieve a scaling advantage over classical solvers on a classically intractable optimization problem.
• To evaluate the performance of QAOA with fixed parameters and constant depth on the Low Autocorrelation Binary Sequences (LABS) problem.
• To benchmark QAOA against state-of-the-art classical exact solvers like branch-and-bound for the LABS problem.
• To demonstrate experimental feasibility of QAOA on trapped-ion hardware using algorithm-specific error detection.
• To assess the combined performance of QAOA with quantum minimum-finding for improved empirical scaling.

Proposed method

• Conducted noiseless simulations of QAOA on the LABS problem using a distributed quantum simulator on the Polaris supercomputer with 256 nodes and 1024 GPUs.
• Simulated full statevector propagation, leveraging diagonal cost Hamiltonian structure to apply phase-separation via elementwise multiplication with precomputed cost values.
• Implemented mixing operations using parallelized 2x2 unitary rotations applied to qubit pairs, optimized via index grouping analogous to fast Walsh–Hadamard transforms.
• Used a hybrid CPU-GPU architecture where GPUs managed statevector chunks and CPUs coordinated communication and result aggregation.
• Applied quantum minimum-finding to QAOA to enhance success probability and improve empirical scaling performance.
• Executed QAOA circuits on Quantinuum trapped-ion processors using a custom error detection scheme to validate experimental feasibility.

Experimental results

Research questions

• RQ1 Does QAOA exhibit better asymptotic scaling than classical exact solvers like branch-and-bound for the LABS problem?
• RQ2 Can QAOA with fixed parameters and constant depth outperform classical heuristics on classically intractable instances of LABS?
• RQ3 How does the combination of QAOA with quantum minimum-finding affect the time-to-solution scaling for LABS?
• RQ4 What is the experimental feasibility of implementing QAOA for LABS on near-term trapped-ion quantum hardware?
• RQ5 Can error-detection schemes improve the reliability of QAOA execution on noisy intermediate-scale quantum devices?

Key findings

• QAOA with fixed parameters and constant depth demonstrated better runtime scaling than branch-and-bound solvers up to 40 qubits on the LABS problem.
• The time-to-solution (TTS) of QAOA with fixed parameters scaled as approximately 1.23^N, outperforming the classical heuristic TTS of 1.25^N observed in prior studies.
• When enhanced with quantum minimum-finding, QAOA achieved the best empirical scaling of any algorithm for the LABS problem in the studied range.
• Noiseless simulations confirmed that the success probability p^opt, though exponentially small, could be accurately estimated using full statevector simulation.
• Experimental execution on Quantinuum trapped-ion hardware with error-detection schemes demonstrated progress toward fault-tolerant QAOA execution on real hardware.
• The distributed QAOA simulator achieved high performance by leveraging GPU parallelization and efficient memory management across 256 nodes on the Polaris supercomputer.