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.
20 pages, 11 figures
References in corpus (19)
- The density-matrix renormalization group in the age of matrix product states
- Probing many-body dynamics on a 51-atom quantum simulator
- Noisy intermediate-scale quantum (NISQ) algorithms
- Phenomenology of fully many-body-localized systems
- Many-body localization in periodically driven systems
- Digital quantum simulation of fermionic models with a superconducting circuit
- Modeling and Control of Quantum Systems: An Introduction
- A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
- Interferometric probes of many-body localization
- Influence matrix approach to many-body Floquet dynamics
- Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving
- Constructing Tensor Network Influence Functionals for General Quantum Dynamics
- Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks
- Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
- Localization of phonons in ion traps with controlled quantum disorder
- 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