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arXiv:2410.07024 · Physical Review Letters

Role of Coherence for Quantum Computational Advantage

Hugo Thomas, Pierre-Emmanuel Emeriau, Rawad Mezher, Elham Kashefi, Harold Ollivier, Ulysse Chabaud

Published Aug 15, 2025• 5 citations
arXivHTMLPDF

Abstract

Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness, and coherence are arguably of great significance. We introduce "path coherence" as a measure of the coherent path interferences arising in a quantum computation. Leveraging the sum-over-paths formalism, we obtain a classical algorithm for estimating quantum transition amplitudes, the complexity of which scales with path coherence. As path coherence relates to the hardness of classical estimation of quantum transition amplitudes, it provides a new perspective on the role of coherence in quantum computational advantage. Beyond their fundamental significance, our results have practical applications for simulating large classes of quantum computations with classical computers.

DOI
10.1103/1csn-x1cx

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Nonstabilizerness describes the distance of a quantum state to its closest stabilizer state. It is—like entanglement—a necessary resource for a quantum advantage over classical computing. We study nonstabilizerness, quantified by stabilizer entropy, in a hybrid quantum circuit with projective measurements and a controlled injection of non-Clifford resources. We discover a phase transition between a power law and constant scaling of nonstabilizerness with system size controlled by the rate of measurements. The same circuit also exhibits a phase transition in entanglement that appears, however, at a different critical measurement rate. This mechanism shows how, from the viewpoint of a quantum advantage, hybrid circuits can host multiple distinct transitions where not only entanglement, but also other nonlinear properties of the density matrix come into play. Published by the American Physical Society 2024
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