Polynomially restricted operator growth in dynamically integrable models
arXiv:2406.13026 · doi:10.1103/PhysRevB.111.094314
Abstract
We provide a framework to determine the upper bound to the complexity of a computing a given observable with respect to a Hamiltonian. By considering the Heisenberg evolution of the observable, we show that each Hamiltonian defines an equivalence relation, causing the operator space to be partitioned into equivalence classes. Any operator within a specific class never leaves its equivalence class during the evolution. We provide a method to determine the dimension of the equivalence classes and evaluate it for various models, such as the chain and Kitaev model on trees. Our findings reveal that the complexity of operator evolution in the model grows from the edge to the bulk, which is physically manifested as suppressed relaxation of qubits near the boundary. Our methods are used to reveal several new cases of simulable quantum dynamics, including a - model which cannot be reduced to free fermions.
10 pages, 7 figures
References in corpus (51)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Characterizing Quantum Supremacy in Near-Term Devices
- Strong quantum computational advantage using a superconducting quantum processor
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Operator Spreading in Random Unitary Circuits
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
- A Universal Operator Growth Hypothesis
- Parafermionic edge zero modes in Z_n-invariant spin chains
- Simulating quantum many-body dynamics on a current digital quantum computer
- Emulating many-body localization with a superconducting quantum processor
- Matchgates and classical simulation of quantum circuits
- Exactly solvable Kitaev model in three dimensions
- Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
- Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
- Classification of gapless Z2 spin liquids in three-dimensional Kitaev models
- Dissipative Dynamics and Phase Transitions in Fermionic Systems
- Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
- Dissipative spin chain as a non-Hermitian Kitaev ladder
- Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
- Disentangling Scrambling and Decoherence via Quantum Teleportation
- Noise-resilient Edge Modes on a Chain of Superconducting Qubits
- Integrable Floquet dynamics
- Transport in a disordered tight-binding chain with dephasing
- Non-Gaussian correlations imprinted by local dephasing in fermionic wires
- Integrability of Lindbladians from operator-space fragmentation
- Information scrambling in chaotic systems with dissipation
- Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model
- Efficient classical simulation of matchgate circuits with generalized inputs and measurements
- A solvable family of driven-dissipative many-body systems
- Information scrambling vs. decoherence -- two competing sinks for entropy
- Operator and entanglement growth in non-thermalizing systems: many-body localization and the random singlet phase
- Basis-independent quantum coherence and its distribution
- Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid
- Extending matchgates into universal quantum computation
- Closed hierarchy of correlations in Markovian open quantum systems
- Exact description of transport and non-reciprocity in monitored quantum devices
- Analytical solutions for a boundary driven XY chain
- Nonequilibrium phase transition in transport through a driven quantum point contact
- Quantum dynamics in one and two dimensions via recursion method
- Generalised Onsager Algebra in Quantum Lattice Models
- Exact dynamics of quantum dissipative models: Wannier-Stark localization in the fragmented operator space
- Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
- Quantum many-body simulations with PauliStrings.jl
- A solvable class of non-Markovian quantum multipartite dynamics
- Stochastic Sampling of Operator Growth Dynamics
- Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
- Relaxation of imbalance in a disordered XX model with on-site dephasing
- Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
- Effect of dephasing on the current through a periodically driven quantum point contact