Non-adiabatic Fast Control of Mixed States Based on Lewis–Riesenfeld Invariant

Abstract

We apply the inversely-engineered control method based on Lewis-Riesenfeld invariants to control mixed states of a two-level quantum system. We show that the inversely-engineered control passages of mixed states -and pure states as special cases -can be made significantly faster than the conventional adiabatic control passages, which renders the method applicable to quantum computation. We devise a new type of inversely-engineered control passages, to be coined the antedated control passages, which further speed up the control significantly. We also demonstrate that by carefully tuning the control parameters, the inversely-engineered control passages can be optimized in terms of speed and energy cost.

Spin-selective electron transfer in a quantum dot array

“…The STA protocols have been utilized for manipulations of, e.g., isolated atoms and molecules [36,[68][69][70][71], spin systems [72][73][74][75], Bose-Einstein condensates [76][77][78][79][80][81][82][83], and electron spin of a single nitrogen-vacancy center in diamond [84,85]. Several STA protocols have been applied to STIRAP systems, for example, Loop STIRAP [86], counterdiabatic [36,68], fast-forward [87], and invariant-based engineering protocols [36,88].…”

Dynamical invariants for quantum control of four-level systems

“…A major problem in adiabatic quantum control is that in many cases the evolution is so slow that the system may start decohering. Evolution in the eigenstates of I, however, is not restricted by the adiabaticity condition and can be made to be fast, a feature which caused a recent surge of applications [8][9][10][11][12][13][14][15][16]. DIs have been used in the context of quantum field theory [17].…”

“…Note that in the case of two-level, however, a classification of Hamiltonians and their DIs does exist [29]. Consequently, insofar the quantum control and computation models based on DIs are nigh limited to two-level systems [8][9][10][11][12][13][14][15][16]. Special cases in four-level systems have also been studied [28].…”

“…Besides partially causing the first limitation, this third difficulty circumscribes how and how much one can control a quantum system based on the DIs of the system. In fact, because of this limitation, in order to gain the control of a quantum system via a DI of the system, a special method -the inversely engineered control (IEC)-is needed, which was invented in [13] for pure states and extended to mixed states in [8].…”

Analytical approach to swift nonleaky entangling gates in superconducting qubits

“…We accomplish this in two ways: by adapting a recently developed reverseengineering approach to solving the Schrödinger equation, and by employing analytically solvable pulse shapes with special properties. For the harmful transition we are essentially devising transitionless driving, which is in itself an interesting topic 33 that has found applications recently in different contexts of quantum control [34][35][36][37] . We first focus on the most well-known entangling gate, the two-qubit CN OT gate, in which the state of one qubit is either flipped or left alone depending on the state of the other qubit.…”