One decade of quantum optimal control in the chopped random basis

Abstract

The Chopped RAndom Basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications, quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraintswhile maintaining an access to the usually trap-free control landscape -and to switch from open-loop to closed-loop optimization (including with remote accessor RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.

Optimal Control in Disordered Quantum Systems

“…Due to the use of backpropagation (widely used in deep learning [31]), the gradient can be obtained very efficiently, with similar computational complexity as forward evaluation of the infidelity [32,33]. This allows us to use many different control parameters which usually presents a bottle neck for previous numerical quantum control studies [14][15][16] and also to have flexibility in the design of the cost functional, for example allowing for the addition of penalty terms and the use of neural networks [20,22]. The gradient can be used in specific optimization algorithms, which we will also refer to as update schemes.…”

“…The final ansatz for the optimal protocols that we use we term "∂P-Fourier" where aim to combine differentiable programming with optimal control based on a Fourier basis and inspired by the CRAB method [16]. Specifically, to fulfill the boundary conditions X 0 (0) = x A and X 0 (τ ) = x B , we define the Fourier ansatz to be the family of protocols parameterized as…”

“…However, a notable drawback is that such adiabatic protocols are inherently Luuk Coopmans: luuk.coopmans@cambridgequantum.com slow and hence susceptible to noise from the environment. This observation precipitated the development of non-adiabatic protocols such as analytically derived shortcuts to adiabaticity (STA) [13] and numerical quantum optimal control methods [14][15][16].…”

“…Shortcuts to adiabaticity approaches, such as the one employed in Ref. [13], rely on simple model descriptions and/or approximations, while standard numerical optimal control is limited in the number of free parameters that can be optimized in a timely fashion [14][15][16]. In this work we circumvent these issues by instead using differentiable programming (∂P) [17,18].…”

“…We combine ∂P with several other traditional quantum control methods, specifically the shortcut to adiabaticity protocol [13] and the Chopped Random Basis (CRAB) Fourier protocol ansatz [16]. A common difficulty which must be overcome is the inevitability of noise or imperfections in experimentally realised systems in form of spatial heterogeneities, i.e.…”