Quantum control is an essential tool for the operation of quantum technologies such as quantum computers, simulators, and sensors. Although there are sophisticated theoretical tools for developing quantum control protocols, formulating optimal protocols while incorporating experimental conditions remains a challenge. In this paper, motivated by recent advances in realization of real-time feedback control in circuit quantum electrodynamics systems, we study the effect of experimental imperfections on the optimality of qubit purification protocols. Specifically, we find that the optimal control solutions in the presence of detector inefficiency and non-negligible decoherence can be significantly different from the known solutions to idealized dynamical models. In addition, we present a simplified form of the verification theorem to examine the global optimality of a control protocol.
Quantum control is an essential tool for the operation of quantum technologies such as quantum computers, simulators, and sensors. Although there are sophisticated theoretical tools for developing quantum control protocols, formulating optimal protocols while incorporating experimental conditions remains a challenge. In this paper, motivated by recent advances in realization of real-time feedback control in circuit quantum electrodynamics systems, we study the effect of experimental imperfections on the optimality of qubit purification protocols. Specifically, we find that the optimal control solutions in the presence of detector inefficiency and non-negligible decoherence can be significantly different from the known solutions to idealized dynamical models. In addition, we present a simplified form of the verification theorem to examine the global optimality of a control protocol.
Quantum feedback control protocols can improve the operation of quantum devices. Here we examine the performance of a purification protocol when there are imperfections in the controls. The ideal feedback protocol produces an x -eigenstate from a mixed state in the minimum time, and is known as rapid state preparation. The imperfections we examine include time delays in the feedback loop, finite strength feedback, calibration errors and inefficient detection. We analyse these imperfections using the Wiseman–Milburn feedback master equation and related formalism. We find that the protocol is most sensitive to time delays in the feedback loop. For systems with slow dynamics, however, our analysis suggests that inefficient detection would be the bigger problem. We also show how system imperfections, such as dephasing and damping, can be included in a model via the feedback master equation.
Recent advancements in quantum technologies have highlighted the importance of mitigating system imperfections, including parameter uncertainties and decoherence effects, to improve the performance of experimental platforms. However, most of the previous efforts in quantum control are devoted to the realization of arbitrary unitary operations in a closed quantum system. Here, we improve the algorithm that suppresses system imperfections and noises, providing notably enhanced scalability for robust and optimal control of open quantum systems. Through experimental validation in a superconducting quantum circuit, we demonstrate that our approach outperforms its conventional counterpart for closed quantum systems with an ultra-low infidelity of about 0.60%, while the complexity of this algorithm exhibits the same scaling, with only a modest increase in the prefactor. This work represents a notable advancement in quantum optimal control techniques, paving the way for realizing quantum-enhanced technologies in practical applications.
This study optimizes qubit control protocols using optimal control theory, machine learning, and stochastic modeling to enhance quantum computing performance. Quantum computing represents a transformative leap in computational power, with qubits serving as the fundamental building blocks of quantum information processing. However, the efficient control and manipulation of qubits remain significant challenges due to decoherence, noise, and imperfect control pulses. This study focuses on optimizing qubit control protocols using advanced applied mathematical techniques, including optimal control theory, machine learning, and stochastic modeling, to enhance quantum computing performance. By leveraging these techniques, we develop robust control strategies that minimize errors, improve gate fidelity, and extend coherence times. Our methodology integrates numerical simulations with experimental validation, demonstrating significant improvements in qubit control accuracy and reliability. The results highlight the potential of these optimized protocols to enable scalable and fault-tolerant quantum computing. This work contributes to the ongoing efforts to realize practical quantum technologies, offering insights into the interplay between mathematical optimization and quantum system dynamics.
A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However, the existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally. We address the task of finding the global optimal feedback control for purifying a single qubit in the presence of measurement inefficiency. We use the Bloch vector length, a more physical and practical quantity than purity, to assess the quality of the state, and employ a backward-iteration algorithm to find the globally optimal strategy. Our results show that a speedup is available for quantum efficiencies well below 0.5, which opens the possibility of experimental implementation in existing systems.
Quantum networks rely on the efficient distribution of entanglement to enable long-distance quantum communication and information processing. A key challenge in these networks is the design of routing protocols capable of maintaining high quality entanglement in the presence of noise, decoherence, and imperfect operations, which progressively degrade the fidelity of entangled states through entanglement swapping. Entanglement purification provides an effective mechanism to mitigate this degradation at the cost of additional resources. In this work, we study purification-aware quantum routing and formulate the problem of selecting optimal purification strategies as an optimization task. By employing dynamic programming techniques, we identify strategies that optimally balance resource consumption and end-to-end fidelity, demonstrating the effectiveness of our approach across different scenarios.
It was first shown by Jacobs, in 2003, that the process of qubit state purification by continuous measurement of one observable can be enhanced, on average, by unitary feedback control. Here, we quantify this by the reduction in any one of the family of Rényi entropies , with , at some terminal time, revealing the rich structure of stochastic quantum control even for this simple problem. We generalize Jacobs' original argument, which was for the (unique) impurity measure with a linear evolution map under his protocol, by replacing linearity with convexity, thereby making it applicable to Rényi entropies for α in a finite interval about one. Even with this generalization, Jacobs' argument fails to identify the surprising fact, which we prove by Bellmanʼs principle of dynamic programming, that his protocol is globally optimal for all Rényi entropies whose decrease is locally maximized by that protocol. Also surprisingly, even though there is a range of Rényi entropies whose decrease is always locally maximized by the null-control protocol, that null-control protocol cannot be shown to be globally optimal in any instance. These results highlight the non-intuitive relation between local and global optimality in stochastic quantum control.