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Physica Scripta

Quantum neural network-inspired variational quantum circuit for simulating diamond 14 NV center Hamiltonian with a proximal 13 C isotope

Chisomo Daka, Somnath Bhattacharyya

Published Jan 3, 2025• 4 citations
Publisher

Abstract

Abstract We present a variational quantum circuit (VQC) that utilizes the architecture of a quantum neural network (QNN) to simulate hyperfine interactions in diamond nitrogen vacancy (NV) centers, which is typically a challenging task for traditional computation methods. Isotopes of 13 C, though naturally rare, possess a nuclear spin ( l = 1 2 ) which anisotropically interacts with the NV center’s electron spin, resulting in distinct hyperfine structure and coherence properties. The VQC’s ansatz unitary was implemented stepwise (through optimization Trotter steps) to mimic a multi-layered QNN configuration. The dynamical evolution of the 14 NV- 13 C Hamiltonian was simulated while maintaining flexibility for optimization on noisy intermediate-scale quantum (NISQ) platforms. Qiskit SDK was used to design and execute the circuit on 127-qubit IBM quantum hardware. Ansatz parameters were optimized using six classical optimization algorithms initialized with pseudo-random parameter vectors. We successfully determined optimal ansatz parameters for estimating the minimum energy eigenvalues of the 14 NV- 13 C observable using the VQC’s cost function, enabling us to model the system’s ground state dynamics. Our findings show that gradient-free optimizers are efficient for the designed Hardware Efficient SU(2) 2-local circuit (ESU2) ansatz, characterized by a barren plateau landscape. We further established that a maximally entangled VQC initialization (i.e., GHZ 3 ) retains its entanglement scheme irrespective of the optimization pathway. Hence, this approach highlights the effectiveness of QNN-inspired VQC circuits for accurately simulating NV centers coupled with strongly interacting nearest-neighbor nuclear spins. Our work lays down a foundational step for realizing precise control on near-term quantum hardware that utilizes NV centers, leading to high fidelities.

DOI
10.1088/1402-4896/ada58d

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Abstract We present a variational quantum circuit (VQC) that utilizes the architecture of a quantum neural network (QNN) to simulate hyperfine interactions in diamond nitrogen vacancy (NV) centers, which is typically a challenging task for traditional computation methods. Isotopes of 13 C, though naturally rare, possess a nuclear spin ( l = 1 2 ) which anisotropically interacts with the NV center’s electron spin, resulting in distinct hyperfine structure and coherence properties. The VQC’s ansatz unitary was implemented stepwise (through optimization Trotter steps) to mimic a multi-layered QNN configuration. The dynamical evolution of the 14 NV- 13 C Hamiltonian was simulated while maintaining flexibility for optimization on noisy intermediate-scale quantum (NISQ) platforms. Qiskit SDK was used to design and execute the circuit on 127-qubit IBM quantum hardware. Ansatz parameters were optimized using six classical optimization algorithms initialized with pseudo-random parameter vectors. We successfully determined optimal ansatz parameters for estimating the minimum energy eigenvalues of the 14 NV- 13 C observable using the VQC’s cost function, enabling us to model the system’s ground state dynamics. Our findings show that gradient-free optimizers are efficient for the designed Hardware Efficient SU(2) 2-local circuit (ESU2) ansatz, characterized by a barren plateau landscape. We further established that a maximally entangled VQC initialization (i.e., GHZ 3 ) retains its entanglement scheme irrespective of the optimization pathway. Hence, this approach highlights the effectiveness of QNN-inspired VQC circuits for accurately simulating NV centers coupled with strongly interacting nearest-neighbor nuclear spins. Our work lays down a foundational step for realizing precise control on near-term quantum hardware that utilizes NV centers, leading to high fidelities.
Quantum computers have the potential to speed up certain problems that are hard for classical computers. Hybrid systems, such as the nitrogen-vacancy (NV) center in diamond, are among the most promising systems to implement quantum computing, provided the control of the different types of qubits can be efficiently implemented. In the case of the NV center, the anisotropic hyperfine interaction allows one to control the nuclear spins indirectly, through gate operations targeting the electron spin, combined with free precession. Here, we demonstrate that this approach allows one to implement a full quantum algorithm, using the example of Grover's quantum search in a single NV center, whose electron is coupled to a carbon nuclear spin.
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.
Precise characterization of the local spin environment of single diamond nitrogen-vacancy (NV) centers is crucial for advancing quantum sensing, quantum networking, and the optimization of quantum materials. However, single NV center fluorescence measurements requires long averaging times to obtain clean data that is suitable for conventional model fitting, and that constitutes a key experimental bottleneck for high-throughput characterization. To address this, we introduce \textsc{NVRNet}, a physics-informed simulation-to-reality machine learning pipeline that maps minimal-sweep, noisy Ramsey data to a denoised waveform while directly estimating the hyperfine coupling to proximal 13C{}^{13}\mathrm{C}13C nuclear spins. The pipeline's denoiser utilizes a two-stage time-frequency U-Net and an attention-augmented time-domain U-Net, pretrained on Hamiltonian-based spin-dynamics simulations with experimentally calibrated noise. To effectively bridge the simulation-to-reality gap, parameter-efficient adapters are attached to the backbone and fine-tuned on targeted experimental data. Across three distinct NV centers, this experimentally fine-tuned model reduces the median reconstruction error on held-out, few-sweep traces to 0.44-0.67×0.44\text{-}0.67\times0.44-0.67× of the raw experimental noise level. Subsequently, a transformer-based estimator extracts the underlying hyperfine parameters. Forward reconstructions derived from these inferred parameters faithfully reproduce the dominant experimental time- and frequency-domain features, yielding representative normalized fast Fourier transform (FFT) reconstruction errors of 0.10-0.190.10\text{-}0.190.10-0.19. By reducing both the required data volume and acquisition time, \textsc{NVRNet} enables up to ∼40×\sim 40\times∼40× acceleration of the measurement process, establishing a fast, hardware-compatible pathway for robust hyperfine inference and autonomous qubit characterization.
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
Individual nuclear spins in diamond can be optically detected through hyperfine couplings with the electron spin of a single nitrogen-vacancy (NV) center; such nuclear spins have outstandingly long coherence times. Among the hyperfine couplings in the NV center, the nearest neighbor 13C nuclear spins have the largest coupling strength. Nearest neighbor 13C nuclear spins have the potential to perform fastest gate operations, providing highest fidelity in quantum computing. Herein, we report on the control of coherences in the NV center where all three nearest neighbor carbons are of the 13C isotope. Coherence among the three and four qubits are generated and analyzed at room temperature.
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{{{{{{{\mathcal{O}}}}}}}}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.