Construction of SLH Tensor Networks to Investigate Spin Dynamics in Quantum Emitters

Spin-photon dynamics are essential to optimize the design of quantum materials for quantum control and quantum sensing. Recent advances in tensor network methods allow for the fusion of qubit states to be combined under continuous measured defect states. Here we present an extension of this methodology to continuously monitored SLH tensor network states (slhTNS) to capture underlying spin dynamics of a quantum emitter from empirical time-bin measurement including spin active defect emitter in hexagonal boron nitride. With our framework of fused-slhTNS between time-bin nodes, the slhTNS can be more cost effective in memory scaling than two-dimensional TNSs from a polynomial scaling of nodes in time to linear in time-bins. This presents a fast, but insightful way to examine the approximate spin-photon dynamics of projected continuous measured photon states. We demonstrate that this method can take advantage of fusion based-TNS to extract the quantum information of small varying magnetic fields via quantum Fisher information. Our extension of fusion-based slhTNS allows for an advancement of classical computational methods to exploit the sensitivity and precision of quantum emitters that exhibit spin-photon interactions.