Core Concepts
There exists an efficient classical algorithm that can spoof the System Linear Cross-Entropy Score (sXES) benchmark for noisy quantum Hamiltonian simulation experiments, even when the noise level is above a certain threshold. This result also shows that the complexity-theoretic assumption underlying the hardness of spoofing sXES, called the System Linear Cross-Entropy Quantum Threshold Assumption (sXQUATH), does not hold for sublinear depth quantum circuits.
Abstract
The content discusses the challenges in verifying claims of quantum supremacy, particularly in the context of quantum Hamiltonian simulation experiments. It focuses on a benchmarking metric called the System Linear Cross-Entropy Score (sXES), which has been proposed as a more robust alternative to the Linear Cross-Entropy Benchmarking (Linear XEB) used in previous quantum supremacy experiments.
The key insights are:
The authors show that there exists an efficient classical algorithm that can approximate the output probability distribution of a family of quantum circuits known as the Minimal Quantum Singular Value Transform (mQSVT) circuits, which sXES is assessed upon. This result refutes the complexity-theoretic assumption called the System Linear Cross-Entropy Quantum Threshold Assumption (sXQUATH), which the hardness of spoofing sXES relies on.
The authors further show that their classical algorithm can spoof the sXES benchmark for noisy mQSVT circuits, even when the noise level is above a certain threshold. This suggests that sXES is not a robust benchmarking metric for future quantum supremacy claims.
The authors' approach builds upon the Pauli path algorithm, which has been used to classically simulate quantum circuits in previous works. However, the authors note that the existing Pauli path algorithms cannot be directly applied to mQSVT circuits due to the presence of multiple copies of random unitaries in the circuit.
The analysis of the authors' classical algorithm relies on a detailed study of the higher-order moments of Haar-random unitary expectations, which is more involved than the second-moment analysis used in previous Pauli path algorithms.
Overall, the content highlights the need for a more robust benchmarking method with stronger complexity-theoretic guarantees to verify future claims of quantum supremacy.
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