Postselection-free learning of measurement-induced quantum dynamics

Abstract

We address how one can empirically infer properties of quantum states generated by dynamics involving measurements. Our focus is on many-body settings where the number of measurements is extensive, making brute-force approaches based on postselection intractable due to their exponential sample complexity. We introduce a general-purpose scheme that can be used to infer any property of the post-measurement ensemble of states (e.g. the average entanglement entropy, or frame potential) using a scalable number of experimental repetitions. We first identify a general class of estimable properties that can be directly extracted from experimental data. Then, based on empirical observations of such quantities, we show how one can indirectly infer information about any particular given non-estimable quantity of interest through classical post-processing. Our approach is based on an optimization task, where one asks what are the minimum and maximum values that the desired quantity could possibly take, while ensuring consistency with observations. The true value of this quantity must then lie within a feasible range between these extrema, resulting in two-sided bounds. Narrow feasible ranges can be obtained by using a classical simulation of the device to determine which estimable properties one should measure. Even in cases where this simulation is inaccurate, unambiguous information about the true value of a given quantity realised on the quantum device can be learned. As an immediate application, we show that our method can be used to verify the emergence of quantum state designs in experiments. We identify some fundamental obstructions that in some cases prevent sharp knowledge of a given quantity from being inferred, and discuss what can be learned in cases where classical simulation is too computationally demanding to be feasible.

23 + 7 pages, 7 figures

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• Quantum criticality under imperfect teleportation
• Deep thermalization under charge-conserving quantum dynamics
• Dynamics of Pseudoentanglement
• Entanglement swapping in critical quantum spin chains
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Protect Measurement-Induced Phase Transition from Noise
• Boundary transitions from a single round of measurements on gapless quantum states
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Matchgate circuits deeply thermalize
• Hardness of observing strong-to-weak symmetry breaking
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Post-measurement Quantum Monte Carlo
• Deterministic quantum trajectory via imaginary time evolution