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.
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.
Precise and efficient control of quantum systems is essential to perform quantum information-processing tasks. In terms of adiabatic speedup via leakage elimination operator approach, for a closed system, the ideal pulse control conditions have been theoretically derived by P-Q partitioning technique. However, it is a challenge to design the corresponding control pulses for an open system, which requires noisy environments to be addressed. In this paper, we apply the stochastic search procedures to an open qutrit system and successfully obtain the optimal control pulses for significant adiabatic speedup. The calculation results show that these optimal pulses allow us to acquire higher fidelities than the ideal pulses. The improvement of fidelity is large for relatively strong system-bath coupling strength and high bath temperature. For certain coupling strength and bath temperature, the maximal improvement can be achieved for a critical characteristic frequency which represents the memory time of the environment. Our investigation indicates that the stochastic search procedures are powerful tools to design control pulses for combating the detrimental effects of the environment.
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.
The efficient implementation of quantum computing is contingent upon high-fidelity quantum operations. Nevertheless, the fidelity of these operations is constrained by the precision of quantum system evolution control. The optimization of quantum control pulses is essential for improving the manipulation accuracy of superconducting qubits. Traditional optimization methods, including gradient descent and the gradient ascent pulse engineering algorithm, frequently encounter challenges such as slow convergence and susceptibility to local optima in pulse optimization problems. This study introduces an adaptive open-loop optimization algorithm based on the adaptive moment estimation (Adam) optimizer, capitalizing on the benefits of momentum and adaptive learning rate adjustments inherent in Adam. We conduct experimental analysis on the algorithm’s hyperparameters to achieve optimal solutions with a higher fidelity range at a faster convergence speed, effectively improving the fidelity and optimization efficiency of quantum gate operations. Through numerical simulations on the QuTiP platform, we validate the excellent performance of the Adam algorithm in quantum gate optimization. In optimizing the X and SWAP gates, its fidelity improved by 0.03% and 0.0016%, respectively, compared to the GRAPE algorithm. Compared to the CRAB method, the initial convergence speed of the Adam method increased fivefold, enabling it to achieve the target fidelity more rapidly. Future research will investigate closed-loop optimization strategies, utilizing feedback derived from the fidelity results of actual quantum computers to further augment quantum control performance
Accurate and precise quantum control is crucial for quantum information processing. Zero-area pulse control, originally developed for closed systems, has played a significant role in driving quantum systems toward desired states. However, its effectiveness is often compromised by environmental noise. Traditional methods can find optimal pulses for fixed environmental parameters, and they need to be recalculated again once the environmental parameters change. Here, we propose a supervised learning (SL)-based protocol to design optimal zero-area pulses in noisy environments. By including environmental parameters as input during training, the neural network (NN) learns to generate effective controls for various environmental parameters. We demonstrate the protocol using quantum state transmission through a spin chain governed by a non-Markovian master equation. The SL-optimized pulses significantly enhance transmission fidelity compared to ideal pulses, with greater improvements observed at higher system-bath coupling and temperature, where more optimization space exists. Interestingly, fidelity first increases and then decreases with stronger Markovianity, suggesting that highly Markovian environments limit control performance. We also compare the SL method with a genetic algorithm, and the similar results confirm the accuracy and generalization ability of the NN-based approach.
We investigate the influence of environment noise on the control cost and the quantum speed limit time (QSLT) in the process of almost-exact state transmission (AEST) through a spin chain under pulse control. The chain is immersed in its surrounding non-Markovian, finite-temperature heat baths. We find that AEST can be realized in weak system-bath coupling, low temperature, and strong non-Markovian baths under effective external control. Correspondingly, the control cost and QSLT increase with increasing bath temperature and coupling strength. It is noticeable that non-Markovianity from the baths can be helpful to reduce the control cost and shorten the QSLT. Furthermore, we find that there exists a trade-off between the control cost and transmission fidelity and that higher fidelity requires higher cost. In addition, the minimum control cost has been found to obtain certain transmission fidelity.
Quantum control techniques are employed to perform adiabatic quantum computing in the presence of noise. First, we analyze the adiabatic entanglement protocol (AEP) for two qubits. In this case, we found that this protocol is very robust against noise. The reason behind this fact is related to the chosen Hamiltonians, where the ground state of the initial Hamiltonian is not affected by the noise. The optimal control solution, in this case, is to leave the system in its ground state and apply a fast pulse to entangle the qubits at the end of the time evolution. Secondly, we probe a system composed of three qubits, where the goal is to teleport the first qubit to the third qubit. In this case, the ground state of the system does not share the same robustness against noise as in the case of AEP. To improve the robustness against noise, we propose the inclusion of a local control field that can drive the system to an intermediate state, which is more robust against noise in comparison to other states. The target state is also achieved by a fast pulse at the final time. We found that this approach provides a significant gain in the fidelity and can improve the adiabatic quantum computing in the so-called Noisy Intermediate-Scale Quantum (NISQ) devices in a near future.