Optimizing Robust Quantum Gates in Open Quantum Systems

Vaibhav Bhutoria, Andy Koswara, Raj Chakrabarti

Abstract In recent work, we introduced the asymptotic theory of quantum robust control, which enables control of moments of quantum observables and gates in the presence of Hamiltonian uncertainty or field noise. In this paper, we extend this theory of quantum robust control to encompass two of the most important generalizations: robust control of arbitrary quantum observables and robust control of quantum systems sustaining environmental decoherence. In addition, we present deterministic Pareto optimization algorithms that can be applied in conjunction with either asymptotic or leading order measures of robustness. This enables robust control of any observable in quantum systems with any initial density matrix, and for which the entropy can change arbitrarily during the time evolution. Methods for robust optimal control of open quantum systems are presented that maximize the expected value of a quantum control objective while minimizing the expected environmentally induced decoherence.

Hyeong-Jin Kim

Luke S. Baker, Syed Ali Raza Shah, Anatoly V. Zlotnik +1 more

We develop an optimal control algorithm for robust quantum gate preparation in open environments with the state of the quantum system represented using the Lindblad master equation. The algorithm is based on adaptive linearization and iterative quadratic programming to progressively shape the control signal into an optimal form. Robustness is achieved with exponential rates of convergence by introducing uncertain parameters into the master equation and expanding the parameterized state over the basis of Legendre polynomials. We prove that the proposed control algorithm reduces to GRadient Ascent Pulse Engineering (GRAPE) [1] when the robustness portion of the algorithm is bypassed and signal restrictions are relaxed. The control algorithm is applied to prepare Controlled NOT and SWAP gates with high precision. Using only second order Legendre polynomials, the examples showcase unprecedented robustness to 100% parameter uncertainty in the interaction strength between the qubits, while simultaneously compensating for 20% uncertainty in signal intensity. The results could enable new capabilities for robust implementation of quantum gates and circuits subject to harsh environments and hardware limitations.

Li Ran, Frank Gaitan

Matthew Grace, Jason Dominy, Wayne M. Witzel +1 more

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 $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ 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 $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ 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, postfacto 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.

Guang Hao Low, Theodore J. Yoder, Isaac L. Chuang