Tensor Network Simulation and Optimal Control of Strongly Interacting Nitrogen-Vacancy Spins

Abstract

Nitrogen-Vacancy (NV) centers in diamond represent a promising platform for developing highly sensitive quantum sensors for magnetic fields and other physical quantities. The pursuit of sensors combining high sensitivity with high spatial resolution motivates the use of dense NV center ensembles, which inherently exhibit strong, long-range dipole-dipole interactions. Consequently, accurate simulation of these strongly interacting NVs becomes crucial. However, the exponential scaling of the Hilbert space dimension with the number of spins renders the exact simulation of their dynamics intractable for large system. Modeling the system's interaction with its environment as an open quantum system further increases the computational complexity.

This thesis addresses these challenges using tensor network methods. Specifically, the Matrix Product Density Operator (MPDO) formalism is employed to represent the many-body mixed state and simulate the dissipative dynamics of NV ensembles under strong dipole-dipole interactions. We benchmark the efficiency, numerical accuracy, and stability of different tensor network time-evolution algorithms that are capable of long-range interactions against exact numerical diagonalization, identifying a numerical instability in one algorithm when applied to MPDOs. Subsequently, we simulate the dynamics within the strong interaction regime and investigate the impact of decoherence on the accuracy of the MPDO simulations for given maximum bond dimensions.

Furthermore, we calculate the dynamics of the Quantum Fisher Information (QFI) to quantify entanglement generated by the strong interactions. This entanglement, quantified by the QFI, underlies the potential for quantum-enhanced sensitivity. Results indicate that magnetic field sensitivity can be enhanced by these strong interactions when the ensemble is driven by constant amplitude pulses. We also investigate the detrimental effects of excessively strong interactions on sensitivity.

Finally, we address the optimal control task of preparing states to maximize sensor sensitivity. The dCRAB optimization technique is implemented to find control pulses capable of achieving higher sensitivity than that attainable with constant driving fields. Successful optimized pulses for driving an ensemble of three NV centers into the target GHZ state are obtained via numerical simulation. The challenge of performing such optimizations using experimentally relevant parameters is also discussed.