Experimental Demonstration of Scalable Cross-Entropy Benchmarking to Detect Measurement-Induced Phase Transitions on a Superconducting Quantum Processor
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Kamakari, Hirsh (ORCID:0000000253779631)↗
Engineering topics
Fisher, Matthew P. A.
Publications and source records attributed to Fisher, Matthew P. A..
Cross Entropy Benchmark for Measurement-Induced Phase Transitions
Here, we investigate prospects of employing the linear cross entropy to experimentally access measurement-induced phase transitions 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 χ between the bulk measurement outcome distributions in the two circuits acts as an 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 χ = 1. In the area law phase χ < 1. For circuits with Clifford gates, we provide numerical evidence that χ can be sampled to accuracy ϵ from O(1/ϵ 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 measurement-induced phase transitions 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.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Random Quantum Circuits
Quantum circuits—built from local unitary gates and local measurements—are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far from equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as dynamical phase transitions in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗