Quantum neural network-inspired variational quantum circuit for simulating diamond 14 NV center Hamiltonian with a proximal 13 C isotope
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2025-01-03 |
| Journal | Physica Scripta |
| Authors | Chisomo Daka, Somnath Bhattacharyya |
| Citations | 1 |
Abstract
Section titled âAbstractâAbstract 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 ( <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ overflow=âscrollâ> <mml:mi>l</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> ) which anisotropically interacts with the NV centerâs electron spin, resulting in distinct hyperfine structure and coherence properties. The VQCâs 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 VQCâs cost function, enabling us to model the systemâs 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.