Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm

The trading of fidelity for scale enables approximate classical simulators such as matrix product states (MPSs) to run quantum circuits beyond exact methods. A control parameter, the so-called bond dimension χ MPSs, governs allocated computational resources and output fidelity. Here, we characterize optimization algorithm by expectation value cost function that it seeks minimize find follows a scaling law F(lnχ/N), where N is number qubits. With lnχ amounting entanglement MPS can encode, show relevant variable investigating per qubit. Importantly, our results calibrate power required achieve desired benchmark performance hardware in realistic setup. For instance, quantify hardness performing better classically than noisy superconducting processor readily matching its function. Moreover, relate global individual operations establish relationship with N. We sharpen requirements computers outperform techniques at running speed, size, fidelity.4 MoreReceived 17 June 2022Revised 2 November 2022Accepted 28 2022DOI:https://doi.org/10.1103/PRXQuantum.3.040339Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasOptimization problemsQuantum algorithmsQuantum benchmarkingQuantum entanglementQuantum simulationTechniquesMatrix statesNumerical techniquesTensor network methodsQuantum Information