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Annalen der Physik

Optimal Control for Robust Photon State Transfer in Optomechanical Systems

Yan Wang, Jin‐Lei Wu, Yu‐Kun Feng, Jin‐Xuan Han, Yan Xia, Yongyuan Jiang, Jie Song

Published Mar 9, 2021• 11 citations
Publisher

Abstract

Abstract Cavity optomechanical systems converting quantum state between photons facilitate the development of scalable quantum information processors. The control of state transfer in such systems require producing fast and robust transfer to the target state with high fidelity. Shortcuts to adiabaticity (STA) has recently been proved a powerful method for performing fast quantum state conversion in optomechanical systems, which is, however, not robust enough against deviations in control parameters. Here a scheme to realize robust photon state transfer in a universal cavity optomechanical system by combining STA with optimal control technique (OCT) is proposed. Minimizing systematic error sensitivities with adjustable optimization parameters allows to control simultaneously the transfer speed, fidelity, and robustness against errors. Numerical results show that the optimized scheme is insensitive to deviations in optomechanical coupling and frequency detuning over a broad range. The effects of dissipation on the transfer fidelity are also examined for practical implementation of the scheme in realistic scenarios.

DOI
10.1002/andp.202000608

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Abstract Cavity optomechanical systems converting quantum state between photons facilitate the development of scalable quantum information processors. The control of state transfer in such systems require producing fast and robust transfer to the target state with high fidelity. Shortcuts to adiabaticity (STA) has recently been proved a powerful method for performing fast quantum state conversion in optomechanical systems, which is, however, not robust enough against deviations in control parameters. Here a scheme to realize robust photon state transfer in a universal cavity optomechanical system by combining STA with optimal control technique (OCT) is proposed. Minimizing systematic error sensitivities with adjustable optimization parameters allows to control simultaneously the transfer speed, fidelity, and robustness against errors. Numerical results show that the optimized scheme is insensitive to deviations in optomechanical coupling and frequency detuning over a broad range. The effects of dissipation on the transfer fidelity are also examined for practical implementation of the scheme in realistic scenarios.
Shortening the operation time of implementing scheme and reducing the influence of harmful factors have always been the research objectives pursued by people. Based on invariant-based reverse engineering, we present a general scheme for implementing robust population transfer in a three-level system via optimal shortcut to adiabatic passage. The systematic error sensitivity is introduced to measure the robustness of the process. The smooth Rabi frequencies are expressed with some coefficients, which are also related to the systematic error sensitivity and the population of intermediate state. When the amplitude of control field is given, the transfer can be optimized within as small systematic error sensitivity as possible, i.e., the robustness against systematic errors is further improved by choosing suitable correlation coefficient. Additionally, we apply the technique to achieve robust excitation fluctuation transfer between two membranes in an optomechanical system. The relation between the fidelity of excitation fluctuation transfer and variation of effective optomechanical coupling strengths is analysed. Numerical result shows that the fidelity keeps over 0.95 even if the coupling strengths deviates from 20% of the theoretical value. Moreover, comparison with existing literature [Opt. Express29, 7998 (2021)10.1364/OE.417343], the proposed scheme possesses stronger robustness against variations of effective optomechanical coupling strengths and lower population of unwanted states. The idea may provide a promising approach for quantum information processing.
Abstract Adiabatic state conversion in optomechanical systems requires the evolution process to be very slow, which limits its application in quantum information processing. In this paper, we explicitly show that speeding up adiabatic state conversion in optomechanical systems can be implemented. For the case that each cavity is driven far from the red-detuned mechanical sideband, the high-efficiency population transfer between cavity modes is achieved via an additional Hamiltonian  a ( t ) , whereas the population of the mechanical resonator can be effectively inhibited. In the meanwhile, in the case of each cavity driven near the red-detuned mechanical sideband, the population transfers can be realized by varying the modified optomechanical couplings without an additional Hamiltonian. Numerical simulation demonstrates that the transfer is robust to the system decays.
Cat-state qubits formed by photonic coherent states are a promising candidate for realizing fault-tolerant quantum computing. Such logic qubits have a biased noise channel where the bit-flip error dominates over all the other errors. In this manuscript, we propose an optimally robust protocol using the control method of shortcuts to adiabaticity to realize a high-fidelity state transfer in a cat-state qubit. We construct a shortcut based on the Lewis-Riesenfeld invariant and examine the stability versus different types of perturbations for the fast and robust bit flipping. Numerical simulations demonstrate that the bit flipping can be robust against systematic errors in our protocol. Even when the parameter imperfection rate for bit-flip control is 20%, the final population of the target state can still reach ≥ 99%. The optimally robust control provides a feasible method for fault-tolerant and scalable quantum computation.
Abstract For the past few years, shortcuts to adiabaticity have attracted great attention since they can avoid the necessity of slow driving for adiabatic method while inheriting the partial robustness of the adiabatic dynamics. In this paper, a universal approach to implement quantum state transfer in a three‐state system via optimal transitionless quantum driving is presented. The fast path is optimized for great robustness against uncontrolled systematic error by selecting appropriate experimental parameters. The robustness of the protocol is discussed via numerical simulations. Compared with conventional transitionless quantum driving and adiabatic passage, the protocol via optimized transitionless quantum driving possesses more robustness against the systematic error. Furthermore, decoherence arising from atomic spontaneous emission and dephasing only has a slight impact on the fidelity of quantum state transfer. This work opens up a new avenue for high‐fidelity quantum state transfer in the case of the uncontrolled errors.
Adiabatic quantum control is a very important approach for quantum physics and quantum information processing (QIP). It holds the advantage with robustness to experimental imperfections but accumulates more decoherence due to the long evolution time. Here, we propose a universal protocol for fast and robust quantum control in multimode interactions of a quantum system by using shortcuts to adiabaticity. The results show this protocol can speed up the evolution of a multimode quantum system effectively, and it can also keep the robustness very good while adiabatic quantum control processes cannot. We apply this protocol for the quantum state transfer in QIP in the photon-phonon interactions in an optomechanical system, showing a perfect result. These good features make this protocol have the capability of improving effectively the feasibility of the practical applications of multimode interactions in QIP in experiment.
Abstract The multistate stimulated Raman adiabatic passage (STIRAP) is an efficient technique to achieve a selective and accurate population transfer in a chainwise-linked system. However, their efficiency is imperfect due to the nonadiabatic losses from the long runtime of the adiabatic evolution. Here, we focus on realizing a perfect and robust coherent control of the quantum states with optimal shortcut to adiabaticity in a realistic five-state hybrid quantum system. In particular, the optimal shortcut field requires minimal additional coupling (only one coupling strength) to accelerate the adiabatic evolution in this five-state system. Compared to the original STIRAP, the optimal shortcut shows the ultra-high fidelity of quantum state manipulations even though the control parameters of the Hamiltonians are changed in different ways. Furthermore, we study the efficiency of the optimal shortcut field technique in the presence of various experimental errors, such as systematic error, Rabi frequency error, and coupling strength error, and it features a broad range of high efficiencies above 99.9%, showing its robustness against the above errors. The results might shed insight on the further applications of shortcuts to adiabaticity on robust quantum information processing in multi-level quantum systems.