A game of quantum advantage: linking verification and simulation
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We present a formalism that captures the process of proving quantum superiority to skeptics as an interactive game between two agents, supervised by a referee. The model captures most of the currently existing quantum advantage verification techniques. In this formalism, Bob samples from a distribution on a quantum device that is supposed to demonstrate a quantum advantage. The other player, the skeptical Alice, is then allowed to propose mock distributions supposed to reproduce Bob's device's statistics. Bob then needs to provide witness functions to prove that Alice's proposed mock distributions cannot properly approximate his device. Within this framework, we establish three results. First, for random quantum circuits, Bob being able to efficiently distinguish his distribution from Alice's implies efficient approximate simulation of the distribution. Secondly, finding a polynomial time function to distinguish the output of random circuits from the uniform distribution can also spoof the heavy output generation problem in polynomial time. This pinpoints that exponential resources may be unavoidable for even the most basic verification tasks in the setting of random quantum circuits. Finally, by employing strong data processing inequalities, our framework allows us to analyse the effect of noise on classical simulability and verification of more general near-term quantum advantage proposals.
Originalsprog | Engelsk |
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Artikelnummer | 753 |
Tidsskrift | Quantum |
Vol/bind | 6 |
Sider (fra-til) | 1-44 |
ISSN | 2521-327X |
DOI | |
Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
DSF was supported by VILLUM FONDEN via the QMATH Centre of Excellence under Grant No. 10059. RGP was supported by the Quantum Computing and Simulation Hub, an EPSRC-funded project, part of the UK National Quantum Technologies Programme. We thank Anthony Leverrier and Juani Bermejo-Vega for helpful comments and discussions.
Publisher Copyright:
© 2022 Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. All right reserved.
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