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arXiv:1310.2109 · Quantum Information Processing

Various methods of optimizing control pulses for quantum systems with decoherence

Łukasz Pawela, Przemysław Sadowski

Published Jan 25, 2016• 12 citations
arXivHTMLPDF

Abstract

We design control setting that allows the implementation of an approximation of an unitary operation of a quantum system under decoherence using various quantum system layouts and numerical algorithms. We focus our attention on the possibility of adding ancillary qubits which help to achieve a desired quantum map on the initial system. Furthermore, we use three methods of optimizing the control pulses: genetic optimization, approximate evolution method and approximate gradient method. To model the noise in the system we use the Lindblad equation. We obtain results showing that applying the control pulses to the ancilla allows one to successfully implement unitary operation on a target system in the presence of noise, which is not possible which control field applied to the system qubits.

DOI
10.1007/s11128-016-1242-y

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We design control setting that allows the implementation of an approximation of an unitary operation of a quantum system under decoherence using various quantum system layouts and numerical algorithms. We focus our attention on the possibility of adding ancillary qubits which help to achieve a desired quantum map on the initial system. Furthermore, we use three methods of optimizing the control pulses: genetic optimization, approximate evolution method and approximate gradient method. To model the noise in the system we use the Lindblad equation. We obtain results showing that applying the control pulses to the ancilla allows one to successfully implement unitary operation on a target system in the presence of noise, which is not possible which control field applied to the system qubits.
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental effect of decoherence. One set of particles functions as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one- and two-qubit unitary gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. The quantum-gate fidelity, expressed in terms of a novel state-independent distance measure, is maximized with respect to the control field using combined genetic and gradient algorithms. The resulting high-fidelity gates demonstrate the feasibility of precisely guiding the quantum evolution via optimal control, even when the system complexity is exacerbated by environmental coupling. It is found that the gate duration has an important effect on the control mechanism and resulting fidelity. An analysis of the sensitivity of the gate performance to random variations in the system parameters reveals a significant degree of robustness attained by the optimal control solutions.
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental effect of decoherence. One set of particles functions as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one- and two-qubit unitary gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. The quantum-gate fidelity, expressed in terms of a novel state-independent distance measure, is maximized with respect to the control field using combined genetic and gradient algorithms. The resulting high-fidelity gates demonstrate the feasibility of precisely guiding the quantum evolution via the optimal control, even when the system complexity is exacerbated by environmental coupling. It is found that the gate duration has an important effect on the control mechanism and resulting fidelity. An analysis of the sensitivity of the gate performance to random variations in the system parameters reveals a significant degree of robustness attained by the optimal control solutions.
Superconducting nanoelectrical circuits are promising candidates for the physical implementation of the basic building block of a quantum computer, the qubit. We investigate how optimal control theory can be applied to optimize the dynamics of Josephson qubits. For the example of the charge qubit, several numerical methods are employed to search for external control fields which, by current technology, are realistic and induce the desired unitary time evolution within the system (i.e. the desired gate operation) as faithfully as possible in presence of dissipation, decoherence and leakage. Associated calculations which model the environment microscopically are time-intensive so that parallel computing methods are beneficial in the sampling over control fields. In particular, we discuss the performance of differential-evolution-algorithm based optimizations on a cluster. Using a simpler Lindblad model for environmental effects, we compare the performance of a conjugate-gradient approach to that of a genetic algorithm.
Realizing coherent quantum computation requires precise and robust manipulation of quantum systems through quantum control protocols. Most quantum control techniques rely on heuristic methods for designing the driving pulses that steer the system towards a target state. Such methods are often based on brute-force optimization and offer limited understanding of the solution landscape. In contrast, quantum algorithms offer a rich body of analytical methods with rigorous error guarantees for implementing unitary and non-unitary transformations, which suggests a promising direction for developing new approaches to quantum control. Among various such algorithms, quantum signal processing (QSP) has emerged as a powerful framework for quantum algorithm design, implementation, and optimization. However, its potential for quantum control remains largely unexplored. In this work, we establish QSP-Control, an analytical framework for quantum control of qubit-oscillator dynamics. We focus on dispersively coupled qubit-oscillator systems and employ the QSP formalism to mitigate unwanted nonlinear effects arising from cross-Kerr interactions. In addition, we develop constructions for precise manipulation of Fock states by designing Fock-state-selective operators, based on structural parallels between the Jaynes-Cummings interaction and QSP. These findings demonstrate how several practically relevant problems in quantum control can be mapped to forms amenable to QSP, offering both a systematic design framework and an interpretable perspective on quantum control.
Abstract Quantum optimal control theory (QOCT) can be used to design the shape of electromagnetic pulses that implement operations on quantum devices. By using non-trivially shaped waveforms, gates can be made significantly faster than those built by concatenating monochromatic pulses. Recently, we applied this idea to the control of molecular spin qudits modeled with Schrödinger’s equation and showed it can speed up operations, helping mitigate the effects of decoherence (Castro et al 2022 Phys. Rev. Appl. 17 064028). However, short gate times require large optimal pulse amplitudes, which may not be experimentally accessible. Introducing bounds to the amplitudes then unavoidably leads to longer operation times, for which decoherence can no longer be neglected. Here, we study how to improve this procedure by applying QOCT on top of Lindblad’s equation, to design control pulses accounting for decoherence already in the optimization process. We define the control signal in terms of generic parameters, which permits the introduction of bounds and constraints. This is convenient, as amplitude and frequency limitations are inherent to waveform generators. The pulses that we obtain consistently enhance operation fidelities compared to those achieved with the optimization based on Schrödinger’s equation, demonstrating the flexibility and robustness of our method. The improvement is larger the shorter the spin coherence time T 2.