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arXiv:2411.05078 · Physical Review Applied

Efficiency of optimal control for noisy spin qubits in diamond

Hendry M. Lim, Genko T. Genov, Roberto Sailer, Alfaiz Fahrurrachman, Muhammad Aziz Majidi, Fedor Jelezko, Ressa S. Said

Published Nov 20, 2025• 3 citations
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Abstract

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.

DOI
10.1103/3hnz-bysr

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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.
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Abstract Owing to its remarkable optical properties and its ability to be controlled by microwave fields at room temperature, nitrogen-vacancy (NV) centre in diamond has been a promising platform for various nanotechnological applications, e.g. quantum sensing and magnetic resonance spectroscopy. The qubit associated with the NV centre ground state spin has been the key element for the realisation of such applications. Its coherence time determines the application performances, e.g. the sensitivity of the NV-qubit based quantum sensor. Due to unwanted and unavoidable interactions with noisy environment, the qubit undergoes decoherence that shortens its coherence time and hence reduces its application performance. Therefore, the investigation and mitigation of the decoherence of the NV qubit are of the utmost importance. Here, we simulate the qubit decoherence using Ornstein-Uhlenbeck process that is essential for designing a set of modulating control pulses to mitigate the effect.
Robust and high-fidelity control of electron spins in solids is the cornerstone for facilitating applications of solid-state spins in quantum information processing and quantum sensing. However, precise control of spin systems is always challenging due to the presence of various noises originating from the thermal environment and control fields. Here, noise-resilient quantum gates, designed with robust optimal control (ROC) algorithms, are demonstrated experimentally with nitrogen-vacancy centers in diamond to realize tailored robustness against detunings and Rabi errors simultaneously. In the presence of both 10% off-resonance detuning and 10% deviation of a Rabi frequency, we achieve an average single-qubit gate fidelity of up to 99.89%. Our experiments also show that, ROC-based multipulse quantum sensing sequences can suppress spurious responses resulting from finite widths and imperfections of microwave pulses, which provides an efficient strategy for enhancing the performance of existing multipulse quantum sensing sequences.
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.
Quantum computing holds the potential to outperform classical computing in certain complicated tasks by leveraging qubits and their manipulation through quantum gates. A compelling platform to physically realize qubits and their control is the Nitrogen-Vacancy (NV) center in diamond, where Rabi oscillation of spin qubit enables effective quantum operations. However, a significant challenge lies in mitigating qubit decoherence caused by external factors. Hence, this paper reports on the experimental demonstration of Rabi oscillation of spin qubit in NV center in diamond, focusing on investigating the impact of magnetic field and noises. Experiments conducted using CIQTEK Diamond Quantum Computer for Education (CIQTEK is a China quantum company) reveal that the magnetic field significantly impacts the resonant frequency which must align with the microwave pulse to observe clear Rabi oscillations. However, despite careful frequency tuning, noises from several sources lead to qubit decoherence, disrupting Rabi oscillations and causing them to decay over time. These results provide insights into key factors affecting qubit performance, paving the way in developing strategies to minimize decoherence.
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.