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.

arXiv comment7+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 (45)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Improved Simulation of Stabilizer Circuits
• Characterizing Quantum Supremacy in Near-Term Devices
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Measurement-driven entanglement transition in hybrid quantum circuits
• Theory of the phase transition in random unitary circuits with measurements
• Measurement-induced criticality in random quantum circuits
• Unitary-projective entanglement dynamics
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Dynamical purification phase transitions induced by quantum measurements
• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Improved classical simulation of quantum circuits dominated by Clifford gates
• Entanglement in a fermion chain under continuous monitoring
• Scalable probes of measurement-induced criticality
• Entanglement transition from variable-strength weak measurements
• Emergent statistical mechanics of entanglement in random unitary circuits
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Entanglement phase transitions in measurement-only dynamics
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• Statistical mechanics of quantum error correcting codes
• Measurement Protected Quantum Phases
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Postselection-free entanglement dynamics via spacetime duality
• Measurement-induced quantum criticality under continuous monitoring
• Self-Organized Error Correction in Random Unitary Circuits with Measurement
• Measurement-induced criticality in (2+1)-d hybrid quantum circuits
• Measurement-induced phase transition: A case study in the non-integrable model by density-matrix renormalization group calculations
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Symmetry enriched phases of quantum circuits
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Measurement-induced entanglement transitions in many-body localized systems
• Spacetime duality between localization transitions and measurement-induced transitions
• Efficient classical simulation of noisy random quantum circuits in one dimension
• How Dynamical Quantum Memories Forget
• Measurements conspire nonlocally to restructure critical quantum states
• Mean-field entanglement transitions in random tree tensor networks
• Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
• Transitions in the learnability of global charges from local measurements
• Tight bounds on the convergence of noisy random circuits to the uniform distribution
• Neural-Network Decoders for Measurement Induced Phase Transitions

Cited by in corpus (60)

• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Experimental Realization of a Measurement-Induced Entanglement Phase Transition on a Superconducting Quantum Processor
• Universality in driven open quantum matter
• Disordered monitored free fermions
• Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Scrambling Transition in a Radiative Random Unitary Circuit
• Probing post-measurement entanglement without post-selection
• Measurement-altered Ising quantum criticality
• Localization properties in disordered quantum many-body dynamics under continuous measurement
• Triviality of quantum trajectories close to a directed percolation transition
• Nonlocality and entanglement in measured critical quantum Ising chains
• Entanglement and Absorbing-State Transitions in Interactive Quantum Dynamics
• Many-body Dynamics in Monitored Atomic Gases Without Post-Selection Barrier
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Postselection-free learning of measurement-induced quantum dynamics
• System-environment entanglement phase transitions
• Boundary transfer matrix spectrum of measurement-induced transitions
• Experimental demonstration of scalable cross-entropy benchmarking to detect measurement-induced phase transitions on a superconducting quantum processor
• Random-matrix models of monitored quantum circuits
• Field theory of monitored, interacting fermion dynamics with charge conservation
• Quantum criticality under imperfect teleportation
• Measurement induced criticality in quasiperiodic modulated random hybrid circuits
• Measurement-induced phase transitions in monitored infinite-range interacting systems
• Monitored long-range interacting systems: spin-wave theory for quantum trajectories
• Entanglement Transition due to particle losses in a monitored fermionic chain
• A Dyson Brownian motion model for weak measurements in chaotic quantum systems
• Steering-induced phase transition in measurement-only quantum circuits
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Protect Measurement-Induced Phase Transition from Noise
• Entanglement transitions induced by quantum-data collection
• A Solvable Model of Quantum Darwinism-Encoding Transitions
• Local and nonlocal stochastic control of quantum chaos: Measurement- and control-induced criticality
• Learning a quantum channel from its steady-state
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Measurement-induced phase transitions in systems with diffusive dynamics
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Probing prethermal nonergodicity through measurement outcomes of monitored quantum dynamics
• Multipartite entanglement structure of monitored quantum circuits
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Random Quantum Circuits with Time-Reversal Symmetry
• Monitored Fluctuating Hydrodynamics
• Noise resilience in adaptive and symmetric monitored quantum circuits
• Quantum Darwinism-encoding transitions on expanding trees
• Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information
• Observable Measurement-Induced Transitions
• Elusive phase transition in the replica limit of monitored systems
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Competing automorphisms and disordered Floquet codes
• Ultralight Dark Matter from the Edge of Field Space
• Post-measurement Quantum Monte Carlo
• Neural network enhanced cross entropy benchmark for monitored circuits
• Measurement and feedforward induced entanglement negativity transition
• Deterministic quantum trajectory via imaginary time evolution
• Diagnosing chaos with projected ensembles of process tensors
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics