This paper introduces a simple alternating-current (AC) control strategy to perform quantum state manipulations under non-Markovian noise. A genetic algorithm is adopted to optimize the parameters of the AC control, which can be further used to fulfil one-qubit quantum operations at a given final time. Theoretical analysis and simulations show that our method works almost equally well for 1/ f noise, ohmic, sub-ohmic and super-ohmic noise, which demonstrates the robustness of our strategy for noise with various spectra. In comparison with the Markovian cases, our method is more suitable to be used to suppress non-Markovian noise.
This paper introduces a simple alternating-current (AC) control strategy to perform quantum state manipulations under non-Markovian noise. A genetic algorithm is adopted to optimize the parameters of the AC control, which can be further used to fulfil one-qubit quantum operations at a given final time. Theoretical analysis and simulations show that our method works almost equally well for 1/ f noise, ohmic, sub-ohmic and super-ohmic noise, which demonstrates the robustness of our strategy for noise with various spectra. In comparison with the Markovian cases, our method is more suitable to be used to suppress non-Markovian noise.
We study the implementation of one-, two- and three-qubit quantum gates for interacting qubits using optimal control. Markovian and non-Markovian environments are compared and efficient optimization algorithms utilizing analytic gradient expressions and quasi-Newton updates are given for both cases. The performance of the algorithms is analysed for a large set of problems in terms of the fidelities attained and the observed convergence behaviour. New notions of success rate and success speed are introduced and density plots are utilized to study the effects of key parameters, such as gate operation times, and random variables such as the initial fields required to start the iterative algorithm. Core characteristics of the optimal fields are analysed statistically. Substantial differences between Markovian and non-Markovian environments in terms of the possibilities for control and the control mechanisms are uncovered. In the non-Markovian case, gate fidelities improve substantially when the details of the system bath coupling are taken into account, although imperfections such as field leakage can be a significant problem. In the Markovian case, computation time is saved if the fields are pre-optimized neglecting the environment, while including the latter generally does not significantly improve gate fidelities.
Resisting diverse noise effects is crucial for the accurate manipulation of quantum systems. For static or slowly varying noises, many efficient noise mitigation strategies have been developed, such as composite pulses and dynamical decoupling. However, for fast fluctuating noise in the Markovian limit, whether and to what extent coherent quantum control can enhance quantum engineering tasks remains unclear and less explored. Here, we propose a robust quantum optimal control method to tackle Markovian noises. The basic idea is that, regarding the Markovian noise channel as perturbation, we quantitatively characterize the noise-induced error evolution by the perturbative expansion term, and then take them as the objective functions to be suppressed. During optimization, the optimal controls are obtained by maximizing the control target function and meanwhile minimizing the perturbative terms due to Markovian noise order by order. As demonstration examples, we first apply our method to quantum state transfer tasks on two-level and three-level $\mathrm{\ensuremath{\Lambda}}$ systems, then use it to design quantum gates in two-level and three-level ladder systems, all under Markovian noises. The simulation results illustrate that our method can notably enhance quantum state transfer fidelities and have very limited improvement on gate fidelities. The method presented here is versatile and can be extended to enhance the performance of various control tasks under Markovian noise in multilevel or multiqubit quantum systems.
An essential action in quantum information processing is the manipulation (control) of a single qubit, ideally a closed two-level system. However, in realistic applications, quantum processes are often under the influence of the external environment, e.g., presenting some degree of dissipation and decoherence. In this paper we address the emerging difficulties in the (tracking) quantum control of a two-level system under the influence of both Markovian and non-Markovian noise. We employ a same framework to treat both situations, a Lindblad-type equation, but considering that for the former (latter) case, the decay rate $\mathrm{\ensuremath{\Gamma}}$ is time independent (dependent). We discuss the conditions leading to a breakdown of the quantum control and eventual ways to overcome the problem, like employing a fast control scheme or controlling the off-diagonal terms of the system density matrix. Surprisingly, for Markovian noise such breakdown time decreases with $\mathrm{\ensuremath{\Gamma}}$ not as an exponential but as a power law. This indicates that the quantum control should be possible for a coupling between the system and the environment stronger than previously expected. Moreover, we find that for non-Markovian noise, the breakdown time is longer when there is backflow, i.e., $\mathrm{\ensuremath{\Gamma}}(t)$ can be negative. The present theoretical results point to certain favorable scenarios to operate qubits even in a noisy medium.
We propose a control approach to transfer the population between selected quantum states in the non-Markovian open quantum system. This transfers, assisted by single qubit phase shift operations can generate universal logic gates for quantum computing. We find that the occupation probability behaves differently for different environmental conditions, such as the temperature and the ratio between the frequency of the quantum system of interest, and the cut-off frequency of Ohmic reservoir. We provide an active control over non-Markovian open quantum system for the quantum state engineering.
We investigate the generation of quantum operations for one-qubit systems under classical Markovian noise with a $1/{f}^{\ensuremath{\alpha}}$ power spectrum, where $2>\ensuremath{\alpha}>0$. We present an efficient way to approximate the noise with a discrete multistate Markovian fluctuator. With this method, the average temporal evolution of the qubit state operator under $1/{f}^{\ensuremath{\alpha}}$ noise can be feasibly determined from recently derived deterministic master equations. We obtain qubit operations such as quantum memory and the NOT gate to high fidelity by a gradient-based optimization algorithm. For the NOT gate, the computed fidelities are qualitatively similar to those obtained earlier for random telegraph noise. In the case of quantum memory, however, we observe a nonmonotonic dependency of the fidelity on the operation time, yielding a natural access rate of the memory.
To suppress decoherence of solid-state qubits induced by non-Markovian noises, we propose a strategy to couple the qubit with a chaotic device, whose broad power distribution in the high-frequency domain can be used to freeze the noises in the similar way of the dynamical decoupling control (DDC) method. Compared with the DDC, high-frequency components can be generated by the chaotic device even driven by a low-frequency field and thus the control fields do not need any optimization. Thus, our method is easier to be realized in experiments. As an application to superconducting circuits, we find that various noises in a broad band, including low-frequency 1/ƒ, high-frequency Ohmic, sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator, and the decoherence rate of the qubit is efficiently decreased by about 100 times in magnitude. Using experimentally realizable parameters, the decoherence time of the superconducting charge qubit can reach 200 µs by our method, which is 10 ∼ 100 times longer in magnitude than that observed in experiments.