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

• Published in: Physica scripta 2025-02, Vol.100 (2), p.25111
• Main Authors: Daka, Chisomo, Bhattacharyya, Somnath
• Format: Article
• Language: English
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ada58d

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.