Chopped random-basis quantum optimization

Abstract

In this work we describe in detail the Chopped RAndom Basis (CRAB) optimal control technique recently introduced to optimize t-DMRG simulations [1]. Here we study the efficiency of this control technique in optimizing different quantum processes and we show that in the considered cases we obtain results equivalent to those obtained via different optimal control methods while using less resources. We propose the CRAB optimization as a general and versatile optimal control technique. PACS numbers:Realizing artificial, controllable quantum systems has represented one of the most promising challenge in physics for the last thirty years [2]. On one side such systems could unveil unexplored features of Nature, when employed as universal quantum simulators [3]; on the other side this technology could be exploited to realize a new generation of extremely powerful devices, like quantum computers [4]. Along with the impressive progress marked recently in the construction of tunable quantum systems [5,6], there is a renewed and increasing interest in quantum optimal control (OC) theory, the study of the optimization techniques aimed at improving the outcome of a quantum process [2]. Indeed OC can prove to be crucial under several respects for the development of quantum devices: first, it can be generally employed to speed up a quantum process to make it less prone to decoherence or noise effects induced by the unavoidable interaction with the external environment. Second, considering a realistic experimental setup in which just few parameters are tunable or, in the most difficult situations, only partially tunable, OC can provide an answer about the optimal use of the available resources.Traditionally OC has been exploited in atomic and molecular physics [7][8][9]. More recently, with the advent of quantum information, the requirement of accurate control of quantum systems has become unavoidable to build quantum information processors [10][11][12][13][14][15][16]. However, the above mentioned methods often result in optimal driving fields that require a level of tunability incompatible with current experimental capabilities and in general, the calculation of the optimal fields requires an exact description of the system (either analytical or numerical). The field of application of these methods is severely limited also by the need to have access to huge amount of information about the system, e.g. computing gradients of the control fields, expectation values of observables as a function of time. Moreover, standard OC algorithms define a set of Euler-Lagrange equations that have to be solved to find the optimal control pulse [2], where the equation for the correction to the driving field is highly dependent on the constraints imposed on the system and on the figures of merit considered. This implies that considering different figures of merit and/or constraints on the system needs a redefinition of the corresponding Euler-Lagrange equations, hindering a straightforward adaptation of the optimization procedure to different s...

Exploring the quantum speed limit with computer games

“…This method locates an ostensible QSL at T num QSL = 0.29 after approximately 7.4 · 10 8 trials. This KASS optimization formed our most successful bare computer optimization method, outperforming also the acclaimed CRAB algorithm [27].KASS and CRAB fit the prevalent paradigm of multistarting of local optimizers, while global optimizers are rarely used in quantum optimal control. To investigate the BHW problem using a global optimizer we chose the so-called differential evolution algorithm (DE) due to its demonstrated success in quantum problems [28].…”

“…This method locates an ostensible QSL at T num QSL = 0.29 after approximately 7.4 · 10 8 trials. This KASS optimization formed our most successful bare computer optimization method, outperforming also the acclaimed CRAB algorithm [27].…”

Noise-resistant optimal spin squeezing via quantum control

“…This makes adiabatic evolution significantly exposed to external noise: typically in many-body systems the gap closes with increasing system size N , which implies a dramatic increase of the time required for adiabatic evolutions for large N . Previous studies have demonstrated that optimal control is a powerful tool to drastically reduce the time needed to perform a many-body quantum evolution [15,19]. In particular the Chopped Random Basis (CRAB) technique offers an efficient way to implement optimal control, based on an expansion of the control field onto a truncated basis [14,15].…”

“…Previous studies have demonstrated that optimal control is a powerful tool to drastically reduce the time needed to perform a many-body quantum evolution [15,19]. In particular the Chopped Random Basis (CRAB) technique offers an efficient way to implement optimal control, based on an expansion of the control field onto a truncated basis [14,15]. Recently it has been shown that optimal control allows for reaching the Quantum Speed Limit (QSL), the minimal time required by physical constraints to perform a given transformation, in spin chains [19,20], cold atoms in optical lattices [21], Bose-Einstein condensates in atom chip experiments and in crossing of quantum phase transitions [23].…”

“…Other approaches applied control techniques creating spin squeezing as a succession of unitary pulses of a constant Hamiltonian [11][12][13]. We employ the Chopped Random Basis (CRAB) technique [14,15] to optimally control the evolution of a collection of N two-level systems mutually coupled through a time-dependent non linear (i.e. quadratic) interaction.…”