Abstract The decoherence of point defect qubits is often governed by the electron spin-nuclear spin hyperfine interaction that can be parameterized by using ab inito calculations in principle. So far most of the theoretical works have focused on the hyperfine interaction of the closest nuclear spins, while the accuracy of the predictions for distinct nuclear spins is barely discussed. Here we demonstrate for the case of the NV center in diamond that the absolute relative error of the computed hyperfine parameters can exceed 100% using an industry standards first-principles code. To overcome this issue, we implement an alternative method and report on significantly improved hyperfine values with $${{{{{{{\mathcal{O}}}}}}}}$$ O (1%) relative mean error at all distances. The provided accurate hyperfine data for the NV center enables high-precision simulation of NV quantum nodes for quantum information processing and positioning of nuclear spins by comparing experimental and theoretical hyperfine data.
Abstract The decoherence of point defect qubits is often governed by the electron spin-nuclear spin hyperfine interaction that can be parameterized by using ab inito calculations in principle. So far most of the theoretical works have focused on the hyperfine interaction of the closest nuclear spins, while the accuracy of the predictions for distinct nuclear spins is barely discussed. Here we demonstrate for the case of the NV center in diamond that the absolute relative error of the computed hyperfine parameters can exceed 100% using an industry standards first-principles code. To overcome this issue, we implement an alternative method and report on significantly improved hyperfine values with O O (1%) relative mean error at all distances. The provided accurate hyperfine data for the NV center enables high-precision simulation of NV quantum nodes for quantum information processing and positioning of nuclear spins by comparing experimental and theoretical hyperfine data.
A negatively-charged nitrogen-vacancy (NV) center in diamond is a promising system for quantum computation and quantum information. It has the diamond structure with a substitutional nitrogen atom and a neighboring vacancy. An electron spin in the NV center has an exceptionally long coherence time at room temperature. Thus the NV center has a potential to realize a room-temperature quantum computer which is more efficient than a classical computer. In this dissertation, we focus on the nitrogen nuclear spin as well as the electron spin in the NV center. Every NV center has the nitrogen nuclear spin. Because of the long coherence time of the nitrogen nuclear spin, it is a good candidate for a quantum memory. Thus it is important to prepare the nitrogen nuclear spin qubit in a given pure state for quantum computation. We provide a theoretical understanding of the popular nuclear spin initialization technique. Furthermore, we propose an optimal condition for the initialization of the nitrogen nuclear spin by including the local strain in the NV center. We expect that this optimal condition can improve the purity of the nuclear spin initialization. We also propose an efficient quantum measurement protocol for the hyperfine interaction between the electron spin and the ¹⁵N nuclear spin in the NV center. A precise knowledge of the hyperfine interaction is important to reduce an error in a coherent control of the ¹⁵N nuclear spin. In this protocol, a sequence of quantum operations with successively increasing duration is utilized to estimate the hyperfine interaction with successively higher precision approaching the quantum metrology limit. Unlike common quantum metrological methods, this protocol does not need the preparation of the nuclear spin in a pure state. In the presence of realistic operation errors and electron spin decoherence, we show the overall precision of our protocol still surpasses the standard quantum limit
Precise characterization of a hyperfine interaction is a prerequisite for high fidelity manipulations of electron and nuclear spins belonging to a hybrid qubit register in diamond. Here, we demonstrate a novel scheme for determining a hyperfine interaction, using single-quantum and zero-quantum Ramsey fringes, by applying it to the system of a Nitrogen Vacancy (NV) center and a 13C nuclear spin in the 1st shell. The zero-quantum Ramsey fringe, analogous to the quantum beat in a Λ-type level structure, particularly enhances the measurement precision for non-secular hyperfine terms. Precisions less than 0.5 MHz in the estimation of all the components in the hyperfine tensor were achieved. Furthermore, for the first time we experimentally determined the principal axes of the hyperfine interaction in the system. Beyond the 1st shell, this method can be universally applied to other 13C nuclear spins interacting with the NV center.
Nitrogen-vacancy (NV) centers in diamond are a solid-state platform for quantum sensing 1 and information processing due to their spin-dependent optical transitions at room temperature 2. Accurate characterization of NV spin dynamics, including hyperfine interactions with nuclear spins, is essential both for optimizing sensing performance and for designing high-fidelity quantum controls. In this work, we use the open-source package/ library Quantum Toolbox in Python (QuTiP) 3, 4 to simulate two readout protocols (continuous-wave ODMR, pulsed ODMR) with and without the hyperfine coupling. By comparing simulated resonance positions and population dynamics against experimental and simulation profiles from the literature, we demonstrate that our QuTiP model reproduces the characteristic profiles present in other works. We analyze the computational cost of including hyperfine terms to the model via execution time averaging and show that built-in parallelization accelerates the no-hyperfine model but provides small returns when the coupling is included. Finally, we illustrate how simulation parameters align with predictions of DC magnetometry 5. We also provide some ideas for extending this framework to GPU-accelerated and/or machine learning assisted parameter estimation and calibration 6, 7. Our soon-to-be open-source code 8 provides a flexible foundation for both quantum sensing characterization and the development of NV-based quantum information protocols.
Abstract Nitrogen-vacancy (NV) centers in diamond have been developed into essential hardware units for a wide range of solid-state-based quantum technology applications. While such applications require the long spin coherence times of the NV centers, they are often limited due to decoherence. In this study, we theoretically investigate the decoherence of NV-spin ensembles induced by nitrogen impurities (P1 centers), which are one of the most dominant and inevitable magnetic field noise sources in diamond. We combined cluster correlation expansion and density functional theory to compute the Hahn-echo spin-coherence time of the NV centers for a broad range of P1 concentrations. Results indicate a clear linear dependence of T2 on P1 concentrations on a log scale with a slope of −1.06, which is in excellent agreement with previous experimental results. The interplay between the Jahn–Teller effect and the hyperfine interaction in the P1 center plays a critical role in determining the bath dynamics and the resulting NV decoherence. Our results provide a theoretical upper bound for the NV-spin T2 over a wide range of P1 densities, serving as a key reference for materials optimization and spin bath characterization to develop highly coherent NV-based devices for quantum information technology.
This work investigates the applicability of the nitrogen-vacancy (NV) defect center in diamond for quantum computation and metrology purposes. The NV center is a molecule like defect in the diamond lattice which is optically active and possesses an electron spin in its ground state. The spin can be used as a quantum bit and as a field sensor. The NV center has three major properties enabling individual control of single defects. Its optical properties depend on the spin state, the spin can be polarized optically and the spin state has an exceptionally long lifetime. Single NV centers can be controlled by optical and microwave radiation. Generally, the research on individually controllable quantum systems is not only motivated by quantum computation and communication. With the ongoing miniaturization nowadays electronic and electro-optic devices will soon reach the limit of single quantum building blocks. While in these applications the full complexity of single quantum systems might not be needed, small sensors based on single atoms or molecules might very well take advantage of the susceptibility of quantum coherences to environmental conditions. Major challenges for all approaches towards single quantum system control are the individual addressing, the measurement of the quantum state and the protection of quantum coherence from environmental noise. Today, there is a variety of systems (including the NV center) that allow control on the single quantum level. These are for example single photons, single ions and atoms in traps, single spins in semiconductors or single molecules in solid state systems. Rather mesoscopic examples are superconducting devices, nanomechanical oscillators or surface plasmon polaritons. Regarding the NV center it has been shown that the magnetic moment of its electron spin allows individual sensing and coupling to other surrounding electron and nuclear spins. Especially single nuclear spins were shown to be exceptional quantum memories. In this work small quantum registers of up to 5 spins have been used to test major requirements for a feasible quantum processor. Therefore, mainly artificially created high purity diamond samples with controlled spin and impurity concentration were used. The NV centers were either grown in or created via ion implantation techniques in a controlled fashion. As a first requirement for quantum computation entanglement among up to three spins has been generated and was verified by quantum state tomography. This proves the access of the full Hilbert space. Especially, entanglement among nuclear spins was very long-living. In further experiments this processor was used for first quantum algorithms like super-dense coding and the Deutsch algorithm. In addition, this work demonstrates new methods to initialize nuclear spin qubits into a desired quantum state. This is particularly important as improper initialization inhibits quantum computation. One of these methods is related to dynamic nuclear spin polarization and the other to measurement based state preparation. Nuclear spins in the diamond lattice originate mainly from the C-13 isotope. By artificially altering its content the influence on the NV center spin was investigated. The coherence times of the NV center were increasing inversely with the nuclear spin density. Even increasing nuclear spin density to offer more nuclear spin qubits to an operational quantum register was possible. As an alternative route of scaling up the quantum register pairs of closely spaced NV centers were investigated. For the first time two qubit gates among two NV centers mediated by magnetic dipolar coupling have been realized. Furthermore the sensing ability was demonstrated by measuring the relative distance of the two centers (10 nm) with sub-nm precision. Eventually, this work contains new insight into the electronically excited state of the NV center which allowed a more advanced control of the electron and nuclear spins. A comparably high magnetic field was used to decouple electron and nuclear spins. Finally, this allowed quantum nondemolition measurements on single nuclear spins which manifests in the observation of quantum jumps. The new insight was used to drastically improve the performance of quantum state readout. Summarizing, it was shown that single NV centers and proximal nuclear spins form versatile small quantum registers which can be interconnected with neighboring such NV quantum registers. Although the number of qubits used in this work is still small the experimental results propose a way of how to proceed when building a quantum computer. Regarding quantum metrology, however, the use of such a small register which can sense fields and store and process the results would already outperform a single NV electron spin by orders of magnitude.
Digital information based on the laws of quantum mechanics promisses powerful new ways of computation and communication. However, quantum information is very fragile; inevitable errors continuously build up and eventually all information is lost. Therefore, realistic large-scale quantum information processing requires the protection of quantum bits (qubits) against errors. In this thesis we present the experimental implementation of quantum error correction protocols based on spins in diamond. In such protocols, a quantum state is protected against errors by encoding in multiple qubits. Errors can be detected and corrected by measurement of correlations, so-called stabilizer-measurements, on these qubits.The experimental work presented in this thesis employs multiple spins in diamond as qubits to explore and implement error correction protocols. The nitrogen-vacancy (NV) centre in diamond is a lattice defect consisting of a nitrogen atom (N) and a vacancy (V) on two adjacent diamond lattice sites. This defect effectively results in an electronic spin that can be addressed as a qubit. The spin state can be manipulated by microwave fields and optically read out. At liquid helium temperatures (cryogenic temperature, ~4 K = -269 C), the NV electron spin provides high-fidelity single-shot readout and long coherence times.The NV centre is surrounded by naturally available (1.1% abundance) nuclear C13 spins. As the number of spins that are close enough to the NV centre to be strongly coupled is limited, we employ the weakly coupled nuclear spins in the spin bath of the NV centre. Using dynamical decoupling techniques these nuclear spins can be detected via the NV electron spin through the hyperfine interaction. The nuclear spins are long-lived and robust against optical excitation of the NV electron spin, which can make these spins a robust quantum register for quantum error correction.In Ch. 4 we demonstrate universal control over multiple of such weakly coupled nuclear C13 spins in the environment of the NV centre at ambient temperatures. We demonstrate initialization, control and read-out of individual nuclear spins. Finally, we implement a quantum error correction protocol by encoding a quantum state in the NV electron spin and two nuclear spins. Errors are detected by un-encoding the quantum state back to the electron spin and correction via a double controlled operation.For universal fault-tolerant quantum computations it is essential that the quantum information remains encoded at all times. In Ch. 5 we present multiple rounds of quantum error correction and active feedback on a continuously encoded qubit at cryogenic temperatures. A quantum state is protected by encoding in three weakly coupled spins. Errors are detected via high-fidelity non-demolition readout of the NV electron spin and actively corrected using fast classical electronics. We demonstrate that an actively error-corrected qubit is robust against phase flip errors and show that a superposition state can live longer than the best physical qubit in the encoding.The presented methods and results can be extended to a range of future experiments. In Ch. 6 we propose the implementation of five-qubit quantum error correction, the smallest code to correct for general single-qubit errors on the physical qubits in the encoding, by extending the experimental methods as developed in Chs. 4&5. Besides the exploration and development of larger error correction protocols and fault-tolerant quantum computing, the presented quantum register based in spins in diamond can be employed as a quantum node and combined with recent advances in the realization of quantum entanglement over large distances to form quantum networks. These networks can be used to study both fundamental questions as well as future applications in quantum information technology.