Cross Entropy Benchmark for Measurement-Induced Phase Transitions

Abstract

We investigate the prospects of employing the linear cross-entropy to experimentally access measurement-induced phase transitions (MIPT) without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with different initial states, the linear cross-entropy $\chi$ between the bulk measurement outcome distributions in the two circuits acts as a boundary order parameter, and can be used to distinguish the volume law from area law phases. In the volume law phase (and in the thermodynamic limit) the bulk measurements cannot distinguish between the two different initial states, and $\chi =1$. In the area law phase $\chi <1$. For circuits with Clifford gates, we provide numerical evidence that $\chi$ can be sampled to accuracy $\epsilon$ from $O(1/{\epsilon }^2)$ trajectories, by running the first circuit on a quantum simulator without postselection, aided by a classical simulation of the second. We also find that for weak depolarizing noise the signature of the MIPT is still present for intermediate system sizes. In our protocol we have the freedom of choosing initial states such that the "classical" side can be simulated efficiently, while simulating the "quantum" side is still classically hard.

7+8 pages, 6 figures. v2: 7+9 pages, 3+3 figures. Updated discussions on sample size (Fig. 2d, 2e), and new results from random Haar circuits (Fig. 3b). Accepted version

References in corpus (5)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Postselection-free entanglement dynamics via spacetime duality
• Measurements conspire nonlocally to restructure critical quantum states
• Transitions in the learnability of global charges from local measurements
• Neural-Network Decoders for Measurement Induced Phase Transitions

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