Kavli Affiliate: Joel E. Moore
| First 5 Authors: Maxime Dupont, Nicolas Didier, Mark J. Hodson, Joel E. Moore, Matthew J. Reagor
| Summary:
Trading fidelity for scale enables approximate classical simulators such as
matrix product states (MPS) to run quantum circuits beyond exact methods. A
control parameter, the so-called bond dimension $chi$ for MPS, governs the
allocated computational resources and the output fidelity. Here, we
characterize the fidelity for the quantum approximate optimization algorithm by
the expectation value of the cost function it seeks to minimize and find that
it follows a scaling law $mathcal{F}bigl(lnchibigr/Nbigr)$ with $N$ the
number of qubits. With $lnchi$ amounting to the entanglement that an MPS can
encode, we show that the relevant variable for investigating the fidelity is
the entanglement per qubit. Importantly, our results calibrate the classical
computational power required to achieve the desired fidelity and benchmark the
performance of quantum hardware in a realistic setup. For instance, we quantify
the hardness of performing better classically than a noisy superconducting
quantum processor by readily matching its output to the scaling function.
Moreover, we relate the global fidelity to that of individual operations and
establish its relationship with $chi$ and $N$. We pave the way for noisy
quantum computers to outperform classical techniques at running a quantum
optimization algorithm in speed, size, and fidelity.
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