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Physical Review A

Optimizing quantum gates within decoherence-free subspaces

Xiaoxiao Hu, Feihao Zhang, Yansong Li, Guilu Long

Published Dec 15, 2021• 9 citations
Publisher

Abstract

A scheme for optimizing quantum gates in quantum computation on decoherence-free subspaces using optimal control theory is presented. Compared with the previous scheme, this scheme possesses the following properties: (i) efficiency in finding control sequences, specifically in a system without controllable exchange interaction where the previous method is difficult to handle; (ii) robustness against control errors; and (iii) showing better performance than the robust GRAPE method under stochastic noise. As an application, we work out the control sequences for the not, quantum phase, and cnot gates.

DOI
10.1103/physreva.104.062612

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A scheme for optimizing quantum gates in quantum computation on decoherence-free subspaces using optimal control theory is presented. Compared with the previous scheme, this scheme possesses the following properties: (i) efficiency in finding control sequences, specifically in a system without controllable exchange interaction where the previous method is difficult to handle; (ii) robustness against control errors; and (iii) showing better performance than the robust GRAPE method under stochastic noise. As an application, we work out the control sequences for the not, quantum phase, and cnot gates.
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Nonadiabatic holonomic quantum computation (NHQC) offers a way to realize geometric quantum gates beyond the adiabatic regime. To extend the flexibility and control robustness, many NHQC schemes have been proposed. Here, we propose to use quantum optimal control theory to search control sequences that can realize holonomic gates. Given a target gate and the corresponding computational subspace, our optimization algorithm can find the control sequence automatically. Furthermore, by defining an averaged target function, our method can improve the robustness of the holonomic gates against the errors such as thermal noises and amplitude errors. As an application, we search the control sequences for the Hadamard, not, and cnot gates in a nitrogen-vacancy-center system.
A general formulation of optimal control theory for open quantum systems (quantum subsystems) based on a superoperator method is presented. This approach is applied to a computation of optimized time-dependent fields for solid-state-based realizations of quantum gates. Decoherence is incorporated within the spin-boson model and treated within, essentially, the Bloch-Redfield formalism. Generating a ``decoherence-free subspace'' for the superoperator dynamically, we identify optimal trajectories in the phase space of the dynamical system for one- and two-qubit subsystems. Numerical analysis shows that, for the ideal case where one has full control over the subsystem's Hamiltonian, any gate operation can be realized with arbitrary small loss of coherence due to dephasing and optimal solutions exist which are independent of both spectral density and the temperature of the environment. At the example of a Josephson charge quantum gate we study the more realistic situation where one has a restricted number of control fields which, while providing a universal gate, cannot completely eliminate dephasing.
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This study optimizes qubit control protocols using optimal control theory, machine learning, and stochastic modeling to enhance quantum computing performance. Quantum computing represents a transformative leap in computational power, with qubits serving as the fundamental building blocks of quantum information processing. However, the efficient control and manipulation of qubits remain significant challenges due to decoherence, noise, and imperfect control pulses. This study focuses on optimizing qubit control protocols using advanced applied mathematical techniques, including optimal control theory, machine learning, and stochastic modeling, to enhance quantum computing performance. By leveraging these techniques, we develop robust control strategies that minimize errors, improve gate fidelity, and extend coherence times. Our methodology integrates numerical simulations with experimental validation, demonstrating significant improvements in qubit control accuracy and reliability. The results highlight the potential of these optimized protocols to enable scalable and fault-tolerant quantum computing. This work contributes to the ongoing efforts to realize practical quantum technologies, offering insights into the interplay between mathematical optimization and quantum system dynamics.