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arXiv:2208.07008 · Physical Review A

Robust quantum control with disorder-dressed evolution

Tenzan Araki, Franco Nori, Clemens Gneiting

Published Mar 17, 2023• 13 citations
arXivHTMLPDF

Abstract

Quantum control pulses, used to produce desired states in quantum technology applications, can be problematically sensitive to disorder. Here, the authors develop a systematic approach to finding quantum control pulses that are robust in realistic scenarios by translating disorder into a quantum master equation and maximizing the purity of the resulting density matrix.

DOI
10.1103/physreva.107.032609

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Quantum control pulses, used to produce desired states in quantum technology applications, can be problematically sensitive to disorder. Here, the authors develop a systematic approach to finding quantum control pulses that are robust in realistic scenarios by translating disorder into a quantum master equation and maximizing the purity of the resulting density matrix.
The active harnessing of quantum resources in engineered quantum devices poses unprecedented requirements on device control. Besides the residual interaction with the environment, causing environment-induced decoherence, uncontrolled parameters in the system itself---disorder---remain as a substantial factor limiting the precision and thus the performance of devices. These perturbations may arise, for instance, due to imperfect sample production, stray fields, or finite accuracy of control electronics. Disorder-dressed quantum evolution means a unifying framework, based on quantum master equations, to analyze how these detrimental influences cause deviations from the desired system dynamics. This description may thus contribute to unveiling and mitigating disorder effects towards robust schemes. To demonstrate the broad scope of this framework, we evaluate two distinct scenarios: a central spin immersed in an isotropic spin bath and a random mass Dirac particle. In the former scenario, we demonstrate how the disorder average reflects purity oscillations, indicating the time- and state-dependent severity of the disorder impact. In the latter scenario, we discuss disorder-induced backscattering and disorder-induced Zitterbewegung as consequences of the breakup of spin-momentum locking.
Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles, it is now timely to zoom out and take the whole picture: concerning applications that require user-driven evolutions, qubits should be assessed within the desired algorithm. This means to test qubits under external control while relaxation is active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit algorithms subject to relaxation. It is handled via a code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio computation. We calculate fidelities against relaxation and imperfections, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-qubit systems driven under relaxation and imperfections in quantum algorithms.
Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles, it is now timely to zoom out and take the whole picture: concerning applications that require user-driven evolutions, qubits should be assessed within the desired algorithm. This means to test qubits under external control while relaxation is active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit algorithms subject to relaxation. It is handled via a code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio computation. We calculate fidelities against relaxation and imperfections, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-qubit systems driven under relaxation and imperfections in quantum algorithms.
Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles at a mature stage, it is now timely to widen the scope and take the whole picture: concerning applications that require user-driven coherent evolutions, qubits should be assessed operating within the desired algorithm. This means to test qubits under external control while relaxation and imperfections are active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit gate-based algorithms subject to relaxation. It is handled via a home-made code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio\textit{ab initio}ab initio computation. We evaluate the impact of relaxation and potential experimental imperfections in the calculated fidelities, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-spin-qubit systems in quantum algorithms, and will serve as a help to design robust spin qubits against decoherence and to perform better-characterized experiments.
Referring to a Fano-type model qualitative analogy we develop a comprehensive basic mechanism for the laser control of the non-Markovian bath response and fully implement it in a realistic control scheme, in strongly coupled open quantum systems. Converged hierarchical equations of motion are worked out to numerically solve the master equation of a spin-boson Hamiltonian to reach the reduced electronic density matrix of a heterojunction in the presence of strong terahertz laser pulses. Robust and efficient control is achieved increasing by a factor of 2 the non-Markovianity measured by the time evolution of the volume of accessible states. The consequences of such fields on the central system populations and coherence are examined, putting the emphasis on the relation between the increase of non-Markovianity and the slowing down of decoherence processes.
Progress in quantum physics has made it possible to perform experiments in which individual quantum systems are monitored and manipulated in real time. The advent of such new technical capabilities provides strong motivation for the development of theoretical and experimental methodologies for quantum feedback control. The availability of such methods would enable radically new approaches to experimental physics in the quantum realm. Likewise, the investigation of quantum feedback control will introduce crucial new considerations to control theory, such as the uniquely quantum phenomena of entanglement and measurement back-action. The extension of established analysis techniques from control theory into the quantum domain may also provide new insight into the dynamics of complex quantum systems. We anticipate that the successful formulation of an input-output approach to the analysis and reduction of large quantum systems could have very general applications in nonequilibrium quantum statistical mechanics and in the nascent field of quantum information theory.