Controlling quantum many-body systems using reduced-order modelling
arXiv:2211.00467 · doi:10.1103/PhysRevResearch.6.013161
Abstract
Quantum many-body control is among most challenging problems in quantum science, due to computational complexity of related underlying problems. We propose an efficient approach for solving a class of control problems for many-body quantum systems, where time-dependent controls are applied to a sufficiently small subsystem. The approach is based on a tensor-networks-based scheme to build a low-dimensional reduced-order model of the subsystem's non-Markovian dynamics. Simulating dynamics of such a reduced-order model, viewed as a ``digital twin" of the original subsystem, is significantly more efficient, which enables the use of gradient-based optimization toolbox in the control parameter space. We validate the proposed method by solving control problems for quantum spin chains. In particular, the approach automatically identifies sequences for exciting the quasiparticles and guiding their dynamics to recover and transmit information. Additionally, when disorder is induced and the system is in the many body localized phase, we find generalized spin-echo sequences for dynamics inversion, which show improved performance compared to standard ones. Our approach by design takes advantage of non-Markovian dynamics of a subsystem to make control protocols more efficient, and, under certain conditions can store information in the rest of the many-body system and subsequently retrieve it at a desired moment of time. We expect that our results will find direct applications in the study of many-body systems, in probing non-trivial quasiparticle properties, as well as in development control tools for quantum computing devices.
arXiv comment20 pages, 11 figures
References in corpus (53)
- Quantum Computing in the NISQ era and beyond
- The density-matrix renormalization group in the age of matrix product states
- The nitrogen-vacancy colour centre in diamond
- Probing many-body dynamics on a 51-atom quantum simulator
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Many-body localization, thermalization, and entanglement
- Noisy intermediate-scale quantum (NISQ) algorithms
- Efficient simulation of one-dimensional quantum many-body systems
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Phenomenology of fully many-body-localized systems
- A phenomenology of certain many-body-localized systems
- Local conservation laws and the structure of the many-body localized states
- Control of quantum phenomena: Past, present, and future
- Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
- The capacity of the noisy quantum channel
- Training Schrödinger's cat: quantum optimal control
- Quantum control theory and applications: A survey
- Tensor networks for complex quantum systems
- Many-body localization in periodically driven systems
- Optimal control technique for Many Body Quantum Systems dynamics
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Chopped random-basis quantum optimization
- Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
- Coarse-graining renormalization by higher-order singular value decomposition
- Tensor Network Renormalization
- Digital quantum simulation of fermionic models with a superconducting circuit
- Modeling and Control of Quantum Systems: An Introduction
- Differentiable Programming Tensor Networks
- A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
- Interferometric probes of many-body localization
- Disordered insulator in an optical lattice
- Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
- Controllability properties for finite dimensional quantum Markovian master equations
- Optimal control of complex atomic quantum systems
- Renormalization of tensor networks using graph independent local truncations
- Influence matrix approach to many-body Floquet dynamics
- Optimized auxiliary oscillators for the simulation of general open quantum systems
- Anisotropic Tensor Renormalization Group
- Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving
- Riemannian optimization of isometric tensor networks
- Constructing Tensor Network Influence Functionals for General Quantum Dynamics
- Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks
- Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
- Quantum diffusion with disorder, noise and interaction
- Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
- Localization of phonons in ion traps with controlled quantum disorder
- On the complexity of controlling quantum many-body dynamics
- Entanglement branching operator
- QGOpt: Riemannian optimization for quantum technologies
- Fermionic Models with Superconducting Circuits
- Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models
- Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group