Parameterized Inverse Eigenvalue Problem for Quantum Sensing

A system of tunnel-coupled quantum dots is considered in the presence of an applied electric field. Given the measurements of differences between ground state and excited state energy levels as the electric field is varied, we seek to recover the quantum Hamiltonians that describe this system. We formulate this as a parameterized inverse eigenvalue problem and develop algebraic and computational methods for solving for parameters to represent these Hamiltonians. The results demonstrate that this approach is highly precise even when there is error present within the measurements. This theory could aid in the design of high resolution tunable quantum sensors.