Basis-Adaptive Quantum Simulation Applied to Matter-Wave Scattering

We develop an iterative approach to quantum Hamiltonian simulation in which the basis used to represent the quantum state dynamics is modified throughout the Hamiltonian simulation, informed by measurements at intermediate simulation times. These measurements provide information about the instantaneous quantum state and guide a time-step-dependent recompilation of the simulation algorithm. This approach aims to achieve compact representations of the time-dependent quantum state, reducing discretization errors and qubit number requirements. We demonstrate the method by simulating matter-wave scattering in real space, considering future applications in neutron scattering and quantum information. We then benchmark how the adaptive basis method impacts overall depth of the quantum circuits and simulation accuracy. Finally the role of measurement noise and uncertainty on algorithm performance is assessed and we explore how the adaptive technique relates to other methods such as Hamiltonian simulation in the interaction picture.