A unified picture of decoherence control

Ilya Grigorenko, Dmitri V. Khveshchenko

Igor Ermakov, Oleg Valentinovich Lychkovskiy, Tim Byrnes

Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure that allows these circuits to be efficiently simulatable. The approach involves analyzing the transformation of operators in the Heisenberg picture, and viewing this as a spread within a network of basis operators. The operator amplitudes are found to follow a single variable Porter-Thomas distribution for random universal quantum circuits. The number of operators with amplitude above a threshold value is shown to have a characteristic form involving an initial exponential growth, saturation, then exponential decay in the presence of decoherence. We show the number of significant operators can be used to estimate the complexity of a numerical algorithm where errors can be consistently controlled as a function of the complexity of the simulation.

Yu-Qiu Zhou, Shuang Cong, Fangfang Meng

A Lyapunov-based unified control method for quantum state trajectory tracking control is proposed in this paper. By inducing the error between the controlled state and the target state as error state, the trajectory tracking control problem of the quantum system is transformed into the regular control problem of systematic error state. Through an interaction picture transformation, the spin effect is eliminated. The unified control method is designed in the trajectory tracking control for the quantum system which can also solve the problems caused by the non-ideal quantum systems, where the free Hamiltonian of the system is not strongly regular and (or) not commutes with the target state, and (or) the control Hamiltonian is not fully connected. The unified trajectory tracking control proposed can drive the system from an arbitrary initial state to an arbitrary target state and achieve the purpose of tracking. The numerical simulation experiments and results analyses are given.

Sebastián Fortín, Olímpia Lombardi

Gershon Kurizki, G. Gordon, N. Erez

A physical picture -is presented of decoherence and its dynamical control on non-Markovian time scales. The Nakajima-Zwanzig master-equation formalism , combined with optimal-control theory , is used to obtain universal recipes for driving fields capable of optimally suppressing decoherence or maximizing fidelity in multipartite quantum computing or storage .This approach also allows ultrafast control of thermodynamic properties.

Felix Cheung