Optimal steering of matrix product states and quantum many-body scars
arXiv:2204.02899 · doi:10.1103/PRXQuantum.3.030343
Abstract
Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of non-trivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states~(MPS). We compare counter-diabatic and leakage minimization approaches to the so-called local steering problem, that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS state in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counter-diabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally we apply our leakage minimization approach to construct quantum scars in the periodically driven non-integrable Ising model.
arXiv comment24 pages, 9 figures
References in corpus (44)
- Many-Body Physics with Ultracold Gases
- 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
- NMR Techniques for Quantum Control and Computation
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Quantum many-body scars
- Classical simulation of infinite-size quantum lattice systems in one spatial dimension
- Time-dependent variational principle for quantum lattices
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
- Lieb-Schultz-Mattis in Higher Dimensions
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Shortcuts to adiabaticity by counter-diabatic driving
- Optimal control technique for Many Body Quantum Systems dynamics
- Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
- Chopped random-basis quantum optimization
- Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
- Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
- Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
- Reinforcement Learning in Different Phases of Quantum Control
- Exact Excited States of Non-Integrable Models
- Classical and quantum shortcuts to adiabaticity for scale-invariant driving
- Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
- Minimizing irreversible losses in quantum systems by local counter-diabatic driving
- Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system
- Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
- Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
- Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
- Many-body spin interactions and the ground state of a dense Rydberg lattice gas
- Collapse and revival of quantum many-body scars via Floquet engineering
- Adiabatic tracking of quantum many-body dynamics
- Optimal control of complex atomic quantum systems
- Large Classes of Quantum Scarred Hamiltonians from Matrix Product States
- Slow quantum thermalization and many-body revivals from mixed phase space
- Discrete time-crystalline order enabled by quantum many-body scars: entanglement steering via periodic driving
- Creating quantum many-body scars through topological pumping of a 1D dipolar gas
- Exact Floquet quantum many-body scars under Rydberg blockade
- Liquid ground state, gap and excited states of a strongly correlated spin chain
- Fast adiabatic evolution by oscillating initial Hamiltonians
- Superadiabatic quantum state transfer in spin chains
- Homogeneous Floquet time crystal from weak ergodicity breaking
- Approximate Dynamics Lead to More Optimal Control: Efficient Exact Derivatives
- Superadiabatic driving of a three-level quantum system
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- Bridging quantum criticality via many-body scarring
- Efficient Paths for Local Counterdiabatic Driving
- Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
- Geometric Floquet theory
- Variational adiabatic transport of tensor networks
- Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
- Controlling Many-Body Quantum Chaos: Bose-Hubbard systems
- Counterdiabatic Route to Entanglement Steering and Dynamical Freezing in the Floquet Lipkin-Meshkov-Glick Model
- Adiabatic time evolution of highly excited states
- Tangent space generators of matrix product states and exact Floquet quantum scars
- Embedding semiclassical periodic orbits into chaotic many-body Hamiltonians
- Controlling nonergodicity in quantum many-body systems by reinforcement learning
- Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices
- Machine-learning-inspired quantum control in many-body dynamics
- Non-onsite symmetries and quantum teleportation in split-index matrix product states
- Classical periodic trajectories and quantum scars in many-spin systems
- Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes
- Dipolar optimal control of entangled current states