High-fidelity gate implementation requires sophisticated control pulses that steer the quantum system to undergo the desired transformation. Quantum Optimal Control allows to derive these control pulses in an open-loop fashion based on numerical simulations. However, their precision can be limited by incomplete knowledge of the system. Closed-loop optimization overcomes this limitation by incorporating feedback from measurements, provided a suitable and efficient measure of the gate performance can be defined. In this article, we present an efficient method to evaluate the performance of a two-qubit gate by preparation and measurement of only two quantum states, enabling experimental closed-loop optimization with a metric previously believed to be limited to open-loop control. We tailor the approach to nitrogen-vacancy centers in diamond and, through numerical simulations, demonstrate how the method can optimize a two-qubit gate while reducing the number of required measurements by two orders of magnitude compared to standard process tomography under realistic experimental settings.
High-fidelity gate implementation requires sophisticated control pulses that steer the quantum system to undergo the desired transformation. Quantum Optimal Control allows to derive these control pulses in an open-loop fashion based on numerical simulations. However, their precision can be limited by incomplete knowledge of the system. Closed-loop optimization overcomes this limitation by incorporating feedback from measurements, provided a suitable and efficient measure of the gate performance can be defined. In this article, we present an efficient method to evaluate the performance of a two-qubit gate by preparation and measurement of only two quantum states, enabling experimental closed-loop optimization with a metric previously believed to be limited to open-loop control. We tailor the approach to nitrogen-vacancy centers in diamond and, through numerical simulations, demonstrate how the method can optimize a two-qubit gate while reducing the number of required measurements by two orders of magnitude compared to standard process tomography under realistic experimental settings.
A recurring challenge in quantum science and technology is the precise control of their underlying dynamics that lead to the desired quantum operations, often described by a set of quantum gates. These gates can be subject to application-specific errors, leading to a dependence of their controls on the chosen circuit, the quality measure and the gate-set itself. A natural solution would be to apply quantum optimal control in an application-oriented fashion. In turn, this requires the definition of a meaningful measure of the contextual gate-set performance. Therefore, we explore and compare the applicability of quantum process tomography, linear inversion gate-set tomography, randomized linear gate-set tomography, and randomized benchmarking as measures for closed-loop quantum optimal control experiments, using a macroscopic ensemble of nitrogen-vacancy centers in diamond as a test-bed. Our work demonstrates the relative trade-offs between those measures and how to significantly enhance the gate-set performance, leading to an improvement across all investigated methods.
Quantum optimal control can play a crucial role in realizing a set of universal quantum logic gates with error rates below the threshold required for fault tolerance. Open-loop quantum optimal control relies on accurate modeling of the quantum system under control and does not scale efficiently with system size. These problems can be avoided in closed-loop quantum optimal control, which utilizes feedback from the system to improve control fidelity. In this paper, two gradient-based closed-loop quantum optimal control algorithms, the hybrid quantum-classical approach (HQCA) described by Li et al. [Phys. Rev. Lett. 118, 150503 (2017)] and the finite-difference (FD) method, are experimentally investigated and compared to the open-loop quantum optimal control utilizing the gradient ascent method. We employ a solid-state ensemble of coupled electron-nuclear spins serving as a two-qubit system. Specific single-qubit and two-qubit state preparation gates are optimized using the closed-loop and open-loop methods. The experimental results demonstrate the implemented closed-loop quantum control outperforms the open-loop control in our system. Furthermore, simulations reveal that HQCA is more robust than the FD method to gradient noise which originates from measurement noise in this experimental setting. On the other hand, the FD method is more robust to control field distortions coming from nonideal hardware.
A negatively charged nitrogen-vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits, and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.
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
Quantum technologies are transitioning from proof-of-principle experiments to practical everyday applications. As this transition unfolds, it remains unclear which quantum system will offer the most suitable platform for specific tasks. While many candidate systems offer excellent control and demonstrate rapid progress, they often require demanding operating conditions such as cryogenic temperatures down to the millikelvin range. The nitrogen-vacancy (N-V) center in diamond is a notable exception. This optically active defect allows full control of its electronic spin state at room temperature and maintains long coherence times under ambient conditions, a prerequisite for many applications. This accessibility makes the N-V center uniquely suited for translating fundamental quantum concepts into deployable technologies. The applicability of N-V centers in quantum sensing, quantum control, and quantum simulation is the central focus of this thesis. After an introductory overview of the field, the thesis introduces the experimental and theoretical concepts that are necessary to understand the presented results. It proceeds to show how the operating regime of N-V centers as sensors for AC magnetic fields and nuclear spins can be extended to low and zero magnetic bias fields. Many commonly used sensing protocols require a magnetic bias field, which can alter the investigated dynamics or may be infeasible to apply due to experimental constraints. This work describes how established sensing protocols can be adjusted for operation under these conditions, and presents novel sensing protocols that enable the detection of AC magnetic fields and nuclear spins in a regime where conventional protocols fail. These results highlight that precise control of the underlying quantum system is a must. Such control can be optimized using quantum optimal control, which allows one to improve the underlying gate operations in a closed-loop, black-box manner, provided a figure of merit can be found which reliably evaluates the gate-set's performance. As this performance can depend on the specific application, the following part of this thesis defines and benchmarks several figures of merit for closed-loop optimal control using an ensemble of N-V centers. The strengths and limitations of these figures of merit are discussed, and the dependence of the optimization performance on several control and experimental parameters is analyzed. The achieved results are applicable to a broad range of other physical platforms, and can serve as a reference for experimental groups that aim to optimize their gate operations using optimal control. Building upon these insights into quantum control, the next part of this thesis presents the fabrication, control, and application of a room-temperature quantum simulator based on thin nuclear spin layers in diamond. A detailed assessment of the growth process is provided, and the dynamics that allow nearby N-V centers to initialize and read out the nuclear spins are thoroughly investigated. Furthermore, the nuclear spin layer is employed to create and study discrete time-crystalline order. The results demonstrate a scalable route for exploring quantum many-body phenomena under ambient conditions. The thesis concludes with a summary and discussion of all results and provides an outlook on future work based on these findings. In conclusion, this thesis demonstrates and expands the versatile use of N-V centers in diamond for quantum sensing, control, and simulation, highlighting their potential as a practical platform for future quantum technologies.
Nitrogen-vacancy (NV) centers in diamond are a promising platform for ambient, high-spatial resolution magnetometry relevant to biological signals such as cardiac and muscle activity. One of the challenges is the development of pulse sequences tailored to biological signals in the near DC-range. The spatial environment of NV centers within the diamond lattice is highly complex, e.g. due to magnetic field inhomogeneities, limiting the sensors performance. To overcome these experimental constraints, quantum optimal control (QOC) aims at a precise manipulation of the systems dynamics via optimally shaped microwave pulses increasing the overall robustness of spin-based quantum sensors.