Unconditional quantum advantage from a two-round CHSH problem in one dimension

Abstract:We introduce a relation problem constructed from the Clauser--Horne--Shimony--Holt (CHSH) game, which we call the two-round one-dimensional CHSH problem. Its two-round structure ensures that the CHSH questions are supplied only after the relevant Pauli-frame data have been fixed, thereby ruling out a simple classical strategy that solves the corresponding problem perfectly when all inputs are supplied simultaneously. We construct a quantum circuit on $2N$ qubits that uses only adjacent two-qubit gates, has operational depth at most eight, and achieves the optimal quantum success probability of CHSH, which is strictly smaller than one. We prove that, for every fixed $0\leq\delta<(\sqrt{2}-1)/4$, any randomized classical circuit with fixed wiring and bounded gate fan-in that achieves an average success probability of at least $(2+\sqrt{2})/4-\delta$ requires depth $\Omega(\log N)$ after the questions of the second round are supplied. This yields an unconditional separation even though the quantum circuit is restricted to a one-dimensional geometry, whereas the classical circuit has no geometric locality restriction. The result shows that perfect quantum success is not necessary for unconditional quantum advantage with shallow circuits.

arXiv:2609.21237 [quant-ph]

(or arXiv:2609.21237v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.21237 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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