TL;DR
This paper establishes a quantum Tsirelson-type inequality for random quantum circuits, showing that polynomial-time quantum algorithms require exponentially many queries to outperform average-case output probabilities, thus providing evidence for quantum supremacy.
Contribution
It introduces a Tsirelson inequality analogue for quantum circuits, quantifies query complexity bounds, and analyzes optimality of naive sampling algorithms in various random circuit models.
Findings
Quantum algorithms need exponentially many queries to surpass average output probabilities.
For Haar-random unitaries, lower and upper bounds on query complexity are established.
Naive sampling is optimal for Fourier distribution of random Boolean functions.
Abstract
A leading proposal for verifying near-term quantum supremacy experiments on noisy random quantum circuits is linear cross-entropy benchmarking. For a quantum circuit on qubits and a sample , the benchmark involves computing , i.e. the probability of measuring from the output distribution of on the all zeros input. Under a strong conjecture about the classical hardness of estimating output probabilities of quantum circuits, no polynomial-time classical algorithm given can output a string such that is substantially larger than (Aaronson and Gunn, 2019). On the other hand, for a random quantum circuit , sampling from the output distribution of achieves on average (Arute et al., 2019). In analogy with the Tsirelson…
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Videos
The Quantum Supremacy Tsirelson Inequality· youtube
