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arXiv:2304.10748 · Physical Review A

Optimized control for high-fidelity state transmission in open systems

Yang-Yang Xie, Feng-Hua Ren, Arapat Ablimit, Xiang-Han Liang, Zhao-Ming Wang

Published Sep 1, 2023• 5 citations
arXivHTMLPDF

Abstract

Quantum state transfer through spin chains has been extensively investigated. Two schemes, the coupling set for perfect state transfer (PST) or adding a leakage elimination operator (LEO) Hamiltonian have been proposed to boost the transmission fidelity. However, these ideal schemes are only suitable for closed systems and will lose their effectiveness in open ones. In this work, we invoke a well-explored optimization algorithm, Adam, to expand the applicable range of PST couplings and LEO to the open systems. Our results show that, although the transmission fidelity decreases with increasing system-bath coupling strength, Markovianity and temperature for both ideal and optimized cases, the fidelities obtained by the optimized schemes always outweigh the ideal cases. The enhancement becomes bigger for a stronger bath, indicating a stronger bath provides more space for the Adam to optimize. This method will be useful for the realization of high-fidelity information transfer in the presence of environment.

DOI
10.1103/physreva.108.032401

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Quantum state transfer through spin chains has been extensively investigated. Two schemes, the coupling set for perfect state transfer (PST) or adding a leakage elimination operator (LEO) Hamiltonian have been proposed to boost the transmission fidelity. However, these ideal schemes are only suitable for closed systems and will lose their effectiveness in open ones. In this work, we invoke a well-explored optimization algorithm, Adam, to expand the applicable range of PST couplings and LEO to the open systems. Our results show that, although the transmission fidelity decreases with increasing system-bath coupling strength, Markovianity and temperature for both ideal and optimized cases, the fidelities obtained by the optimized schemes always outweigh the ideal cases. The enhancement becomes bigger for a stronger bath, indicating a stronger bath provides more space for the Adam to optimize. This method will be useful for the realization of high-fidelity information transfer in the presence of environment.
Pulse-controlled non-adiabatic quantum state transmission (QST) was proposed many years ago. However, in practice environmental noise inevitably damages communication quality in the proposal. In this paper, we study the optimally controlled non-adiabatic QST in the presence of quantum noise. By using the Adam algorithm, we find that the optimal pulse sequence can dramatically enhance the transmission fidelity of such an open system. In comparison with the idealized pulse sequence in a closed system, it is interesting to note that the improvement of the fidelity obtained by the Adam algorithm can even be better for a bath strongly coupled to the system. Furthermore, we find that the Adam algorithm remains powerful for different numbers of sites and different types of Lindblad operators, showing its universality in performing optimal control of quantum information processing tasks.
Existing optimal control methods of open quantum systems rely on extensive numerical simulations of the dynamics in the presence of a bath, or alternatively ignore the exact bath dynamics. If the bath effects are to be treated properly on both Markovian and non-Markovian timescales using numerical simulations, the number of bath modes cannot be large. This may affect the ability to simulate realistic scenarios. Even if realistic, such simulations are hard to interpret physically. An alternative approach advocated here is to resort to a perturbative analysis provided the system–bath coupling is weak. This analysis would allow for the effects of any given bath (finite or infinite, Markovian or non-Markovian) and any control at our disposal. This poses the challenge of constructing a method for the optimization of various operations requiring proper manipulation of the system, based on a general perturbative treatment to second order in the system–bath coupling. This proposed treatment yields a universal tool for optimizing the fidelity of a given operation. It involves a fidelity-control matrix: a construct that allows us to prioritize the use of available control resources so as to maximize the operation fidelity in any given bath. As an analytically solvable example of this general method, we analyse quantum state-transfer optimization, from a ‘noisy’ (write-in) qubit to its ‘quiet’ counterpart (storage qubit). Intriguing interplay is revealed between our ability to avoid bath-induced errors that profoundly depend on the bath-memory time and the limitations imposed by leakage out of the operational subspace. Counterintuitively, under no circumstances is the fastest transfer optimal (for a given transfer energy).
We consider the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations-a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.
Abstract Transmission of a quantum state is essential for performing quantum information processing tasks. The communication channel will be inevitably immersed in its surrounding environment under realistic conditions. In this paper, we investigate the influence of environment noise on the transmission fidelity when transferring a quantum state through a spin chain. The non-Markovian open system dynamics is systematically analyzed by using the quantum state diffusion equation method. With each spin immersed in its own finite temperature and non-Markovian heat bath, we consider three types of system–bath interaction: dephasing, dissipation and spin-boson. The transmission fidelity is found to decrease with the increasing bath temperature and system–bath coupling strength. Interestingly, we find that the bath non-Markovianity can help enhancing the transmission fidelity.
We investigate the most general conditions under which a finite ferromagnetic long-range interacting spin chain achieves unitary fidelity and the shortest transfer time in transmitting an unknown input qubit. A deeper insight into system dynamics, allows us to identify an ideal system involving sender and receiver only. However, this two-spin ideal chain is unpractical due to the rapid decrease of the coupling strength with the distance. Therefore, we propose an optimization scheme for approaching the ideal behavior, while keeping the interaction strength still reasonably high. The procedure is scalable with the size of the system and straightforward to implement.
Effective quantum control is essential for quantum computing and information processing, yet level leakage remains a bottleneck limiting control fidelity. The leakage elimination operator (LEO) approach is highly effective at suppressing leakage from a target subspace to other subspaces. Analytical control conditions under the high-frequency driving limit have been derived via the Feshbach PQ partitioning technique. However, the driving intensity is subject to fundamental physical bounds, and low-frequency driving is experimentally more feasible. In this work, we reformulate LEO within the Magnus framework and extend it beyond the high-frequency limit. We show that the analytical control conditions obtained from the Feshbach PQ partitioning technique are equivalent to the zeroth-order Magnus expansion. We then analyze the higher-order Magnus corrections. By minimizing the leakage, we obtain a modified pulse condition suitable for the low-frequency regime. As an illustrative example, we study near-perfect state transfer through a one-dimensional spin chain under LEO control. We find that the second-order Magnus correction improves the transmission fidelity at low-frequency driving, while the improvement becomes negligible at high frequencies. Our results provide an effective route for designing control pulses in the low-frequency regime, with potential applications in superconducting qubits, trapped ions, and solid-state spin systems.