Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
arXiv:2410.00953 · doi:10.22331/q-2025-04-01-1681
Abstract
We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process,we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions,and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit's gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics.
arXiv comment14 pages,12 figures
References in corpus (73)
- Efficient simulation of one-dimensional quantum many-body systems
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Time-dependent variational principle for quantum lattices
- Unifying time evolution and optimization with matrix product states
- Power of data in quantum machine learning
- Operator Spreading in Random Unitary Circuits
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Quantum advantage in learning from experiments
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Instantaneous non-local computation of low T-depth quantum circuits
- The Heisenberg Representation of Quantum Computers
- Random Quantum Circuits
- Holographic duality from random tensor networks
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- A Universal Operator Growth Hypothesis
- Mixed-state entanglement from local randomized measurements
- Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
- Solution of a minimal model for many-body quantum chaos
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Emergent statistical mechanics of entanglement in random unitary circuits
- Information-theoretic bounds on quantum advantage in machine learning
- Scrambling and thermalization in a diffusive quantum many-body system
- Efficient estimation of Pauli observables by derandomization
- Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
- Weak Quantum Chaos
- Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Average Symmetry-Protected Topological Phases
- Locality, Quantum Fluctuations, and Scrambling
- Entanglement dynamics in quantum many-body systems
- Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
- Krylov Complexity in Open Quantum Systems
- Scaling of entanglement entropy at deconfined quantum criticality
- Efficient and feasible state tomography of quantum many-body systems
- Operator Dynamics in Brownian Quantum Circuit
- Quantum entanglement in random physical states
- Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
- Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
- Entanglement entropy from nonequilibrium work
- Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
- Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors
- Scalable and Flexible Classical Shadow Tomography with Tensor Networks
- Shallow shadows: Expectation estimation using low-depth random Clifford circuits
- Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
- Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
- Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers
- Quantum vs. classical information: operator negativity as a probe of scrambling
- Operator backflow and the classical simulation of quantum transport
- Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution
- Operator relaxation and the optimal depth of classical shadows
- Signature of quantum chaos in operator entanglement in 2d CFTs
- Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
- Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows
- Extracting subleading corrections in entanglement entropy at quantum phase transitions
- Evolution of entanglement entropy at SU() deconfined quantum critical points
- Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
- Operator growth in random quantum circuits with symmetry
- Classical shadows of fermions with particle number symmetry
- An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
- Real-time correlators in chaotic quantum many-body systems
- Classical shadows based on locally-entangled measurements
- Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo
- Measuring operator size growth in quantum quench experiments
- Deep thermalization under charge-conserving quantum dynamics
- Operator Size Distribution in Large Quantum Mechanics of Majorana Fermions
- Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
- Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
- Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
- Operator Growth in Open Quantum Systems
- Efficient Measurement-Driven Eigenenergy Estimation with Classical Shadows
- Predicting Arbitrary State Properties from Single Hamiltonian Quench Dynamics
- Optimal tradeoffs for estimating Pauli observables