Optimized pulses for the control of uncertain qubits

Abstract

Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for π/2-and π-pulses, and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian.Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from π/2-and π-pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter, to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, post facto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.

Robustness of controlled quantum dynamics

“…For example, [16] considered robustness of pulses for quantum gate operations in the presence of Hamiltonian parameter uncertainty and input field disturbances using an approach based on second order perturbation theory. [17] analyzed the Hessian curvature of the quantum control landscape for population transfer at its extrema and its effect on robustness of optimal quantum control to field disturbances.…”

“…Most quantum robust control strategies typically apply leading order approximations to quantify the robustness of the control fidelity to system parameter uncertainty or field disturbances [16][17][18]. For example, [16] considered robustness of pulses for quantum gate operations in the presence of Hamiltonian parameter uncertainty and input field disturbances using an approach based on second order perturbation theory.…”

“…When designing the profile of a control field for optimizing a quantum performance criterion, such factors must be taken into account in order to ensure quantum control robustness. Control of quantum dynamics that maintains high fidelity in the presence of these types of uncertainty is referred to as robust quantum control [15,16,[22][23][24].…”

“…molecular ro-vibrational states) more challenging [11]. Model-based control of quantum dynamics has been studied in the presence of various types of uncertainty in both the system Hamiltonian and the manipulated control field [12][13][14][15][16][17][18]. In particular, it is infeasible to perfectly model the Hamiltonian of a large quantum sys-tem since ab initio methods become computationally intractable without some approximation and because laboratory measurements are not readily accessible.…”

“…Another study [31] examined the inherent degree of robustness in an optimal control field due to the bilinearity of quantum observable expectation values in the evolution operator and its adjoint. More recent studies on quantum robust control have introduced several types of numerical approximations such as leading order expansions in order to quantify robustness [15][16][17][18]32].…”