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.
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.
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.
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.
Diamond based quantum technology is a fast emerging field with both scientific and technological importance. With the growing knowledge and experience concerning diamond based quantum systems comes an increased demand for performance. Quantum optimal control (QOC) provides a direct solution to a number of existing challenges as well as a basis for proposed future applications. Together with a swift review of QOC strategies, quantum sensing, and other relevant quantum technology applications of nitrogen-vacancy (NV) centers in diamond, the authors give the necessary background to summarize recent advancements in the field of QOC assisted quantum applications with NV centers in diamond.
The thesis focuses on one of the most promising experimental platforms for quantum technologies: Single nitrogen-vacancy (NV) centers in diamond. This quantum system is composed by the spins of the valence electrons of the crystalline point defects and their nearby nuclei. Quite generally, a fundamental requirement to exploit the potentialities of the quantum nature of a system is its precise control. However, this always involves new challenges, related to the need to protect the quantum system from the environment (i.e. preserving the quantum nature of the system itself) and the desire to develop measurement protocols that can enhance its performance for quantum applications. Therefore, I focused my Ph.D. work to find novel solutions to these challenges.
Decoherence is a major challenge for quantum technologies, whose negative effects can be mitigated by quantum optimal control. The decoherence dynamics significantly varies depending on the characteristics of the system’s environment, consequently affecting the optimization outcomes. In this work, we investigate the optimization of a negatively charged nitrogen-vacancy ( NV − ) center qubit-spin-inversion control pulse, and observe two error-compensation mechanisms, depending on how long the correlation time is compared to the pulse duration. Additionally, we analyze the effects of control space constraints and optimization options to identify a strategy to improve the optimization performance. Finally, we present experimental realizations of the optimized pulses, exhibiting the applicability of the procedure. Our work serves as a generic yet essential guide to implementing optimal control in the presence of realistic noise.
Quantum-system characterization techniques represent the front line in the identification and mitigation of noise in quantum computing but can be expensive in terms of quantum resources and time to repeatedly employ. Another challenging aspect is that the parameters governing the performance of various operations tend to drift over time and monitoring these is hence a difficult task. One of the most promising characterization techniques, gate-set tomography (GST), provides a self-consistent estimate of the completely positive trace-preserving (CPTP) maps for a complete set of gates, as well as preparation and measurement operators. We develop a method for performance optimization seeded by tomography (POST), which couples the power of GST with a classical optimization routine to achieve a consistent gate improvement in just a short number of steps within a given calibration cycle. By construction, the POST procedure finds the best available gate operation given the hardware and is therefore robust to the effects of drift. Further, in comparison to other quantum error-mitigation techniques, it builds upon a one-time application of GST. To demonstrate the performance of this method on a real quantum computer, we map out the operations of six qubit pairs on the superconducting ibmq_poughkeepsie quantum device. Under the restriction of logical-only control, we monitor the performance of the POST approach on a chosen controlled-not (cnot) gate over a period of six weeks. In this time, we achieve a consistent improvement in gate fidelity, averaging a fidelity increase of 21.1% as measured by randomized benchmarking. The POST approach should find wide applicability as it is hardware agnostic and can be applied at the upper logical level or at a deeper pulse-control level.