Quantum Lyapunov control with machine learning

Abstract

Quantum state engineering is a central task in Lyapunov-based quantum control. Given different initial states, better performance may be achieved if the control parameters, such as the Lyapunov function, are individually optimized for each initial state, however, at the expense of computing resources. To tackle this issue, we propose an initial-state-adaptive Lyapunov control strategy with machine learning, specifically, artificial neural networks trained through supervised learning. Two designs are presented and illustrated where the feedforward neural network and the general regression neural network are used to select control schemes and design Lyapunov functions, respectively. Since the sample generation and the training of neural networks are carried out in advance, the initial-state-adaptive Lyapunov control can be implemented without much increase of computational resources.

GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls

“…Here matrices S k and e Λ k ω∆t k are determined by control (u k , w k ) and have one of the three possible forms ( 41), (42), and ( 43) which correspond to the cases 1, 2, 3, depending on the values of the coefficients ∆, p, and q for the control (u k , w k ). The derivatives in the formulae ( 49) and ( 50) are…”

“…Sometimes a solution for the optimal shape of the control can be obtained analytically. However, generally it is not the case and various numerical optimization methods are used, including GRadient Ascent Pulse Engineering (GRAPE) numerical optimization algorithm [30], gradient flows [31], Krotov method [32,33], genetic algorithms for coherent control of closed systems [34] and incoherent control of open quantum systems in [13], gradient free CRAB optimization algorithm [35], Hessian based optimization as in the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm and combined approaches [36,37], machine learning such as quantum reinforcement learning with incoherent control [38], deep reinforcement learning [39], autoencoders [40], speed gradient algorithm [41], Lyapunov control [42] and various schemes [43,44,45,46,47]. Monotonically convergent optimization in quantum control using Krotov's method was obtained for a large class of quantum control problems [48].…”

Quantum control based on three forms of Lyapunov functions

“…The idea of quantum Lyapunov control is to construct a suitable Lyapunov function and design the corresponding control law by ensuring that the first-order partial derivative of the Lyapunov function with respect to time is not greater than zero. Various Lyapunov control methods [21][22][23] have been developed for quantum systems described by the Schrödinger equation or the Liuvile-von Neumann equation. This paper introduces the design of control laws under three classes of Lyapunov function in Ref.…”

Multistability of equilibrium points and periodic solutions for Clifford‐valued memristive Cohen–Grossberg neural networks with mixed delays

“…However, due to its long learning time and reliance on large sample data, it cannot truly adapt to the functions of the brain network. The traditional neural network (NN) model can describe the information transmission function of neurons from the perspective of the change of membrane potential caused by the ingress and egress of ions inside and outside the cell membrane through dynamic systems, which is widely used in automatic control, quantum engineering, and other fields [2,3].…”