Provable Quantum Advantage for Dynamical Phase Transition

• URL: http://arxiv.org/abs/2606.30396v1
• Date: Mon, 29 Jun 2026 14:46:22 GMT
• Title: Provable Quantum Advantage for Dynamical Phase Transition
• Abstract summary: We show that estimating quantum phase transitions to a certain precision is intractable even for quantum computers.<n>We also show a quadratically faster quantum algorithm that estimates observables of Hamiltonian dynamics at multiple time points.<n>Our framework enables broader quantum speedups for detecting anomalous phenomena in classical systems.
• Score: 13.052070073253448
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The universal scaling of critical behavior in phase transitions is a cornerstone of physics. Dynamical quantum phase transitions (DQPTs) are their nonequilibrium analogues: abrupt nonanalyticities that emerge as a quantum system evolves in time. Yet the hardness and cost of detecting this phenomenon remain largely unexplored. We prove that estimating DQPT to a certain precision is intractable even for quantum computers, whereas deciding a subsystem variant of DQPT is as hard as simulating generic quantum circuits, implying a provable exponential quantum advantage. Furthermore, to search for critical times of local DQPTs, we show a quadratically faster quantum algorithm that estimates observables of Hamiltonian dynamics at multiple time points with Heisenberg-limited precision and sublinear scaling in the number of time points. Moreover, through encoding classical evolution into quantum dynamics, our framework enables broader quantum speedups for detecting anomalous phenomena in classical systems.

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