Unifying methods for optimal control in non-Markovian quantum systems via process tensors

Abstract

The large dimensionality of environments is the limiting factor in applying optimal control to open quantum systems beyond Markovian approximations. Multiple methods exist to simulate non-Markovian open systems which effectively reduce the environment to a number of active degrees of freedom. Here we show that several of these methods can be expressed in terms of a process tensor in the form of a matrix-product-operator, which serves as a unifying framework to show how they can be used in optimal control, and to compare their performance. The matrix-product-operator form provides a general scheme for computing gradients using back propagation, and allows the efficiency of the different methods to be compared via the bond dimensions of their respective process tensors.

14 pages, 9 figures

References in corpus (63)

• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Training Schrödinger's cat: quantum optimal control
• Time-evolution methods for matrix-product states
• Quantum Metrology in Non-Markovian Environments
• Quantum control theory and applications: A survey
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Chopped random-basis quantum optimization
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Quantum control of molecular rotation
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Controlling open quantum systems: Tools, achievements, and limitations
• Non-Markovian quantum dynamics: local versus non-local
• Exact c-number Representation of Non-Markovian Quantum Dissipation
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories
• Monotonically convergent optimization in quantum control using Krotov's method
• Decoherence in Solid State Qubits
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Quantum stochastic processes and quantum non-Markovian phenomena
• Optimal control of open quantum systems: cooperative effects of driving and dissipation
• A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems
• Numerically exact open quantum systems simulations for arbitrary environments using automated compression of environments
• Quantum Semi-Markov Processes
• A variational description of the quantum phase transition in the sub-Ohmic spin-boson model
• Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution
• Krotov: A Python implementation of Krotov's method for quantum optimal control
• One decade of quantum optimal control in the chopped random basis
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
• Geometry of variational methods: dynamics of closed quantum systems
• Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
• Efficient simulation of non-Markovian system-environment interaction
• A generalized multi-polaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system
• Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes
• Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
• Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov ${\mathrm{D}}_1$ states
• Generalized master equations leading to completely positive dynamics
• Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
• Quantum heat statistics with time-evolving matrix product operators
• Tomographically reconstructed master equations for any open quantum dynamics
• Tree tensor network state approach for solving hierarchical equations of motion
• Using the Environment to Understand non-Markovian Open Quantum Systems
• Open Quantum System Dynamics from Infinite Tensor Network Contraction
• Tensor network simulation of chains of non-Markovian open quantum systems
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls
• Reservoir Engineering using Quantum Optimal Control for Qubit Reset
• OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors
• Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion
• A discrete memory-kernel for multi-time correlations in non-Markovian quantum processes
• HierarchicalEOM.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems
• Non-Markovian effects in the spin-boson model at zero temperature
• Survey of the Hierarchical Equations of Motion in Tensor-Train format for non-Markovian quantum dynamics
• A simple improved low temperature correction for the hierarchical equations of motion
• Problem-free time-dependent variational principle for open quantum systems
• Realization of hierarchical equations of motion from stochastic perspectives
• The problem of coherent control in non-Markovian open quantum systems
• On stability issues of the HEOM method
• Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?
• Transfer-tensor description of memory effects in open-system dynamics and multi-time statistics
• Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials
• A Universal Framework for Quantum Dissipation:Minimally Extended State Space and Exact Time-Local Dynamics
• Splitting the local Hilbert space: MPS-based approach to large local dimensions

Cited by in corpus (4)

• Semi-group influence matrices for non-equilibrium quantum impurity models
• Universal bounds for quantum metrology in the presence of correlated noise
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
• Process Tensor Approaches to Non-Markovian Quantum Dynamics