Quantum optimal control for bosonic quantum many-body systems

Quantum many-body systems have been extensively used in quantum computation, quantum simulation, and quantum sensing. Experimentally, bosonic systems have been realized using neutral atoms in an optical lattice, spinor BECs and photonics. Typically, these platforms offer tunable parameters in the Hamiltonian, such as the strength of coupling between two bosonic modes (e.g., tunneling between lattice sites in a system of atoms in an optical lattice), contact interaction and energy splitting between the modes (e.g., Zeeman shifts in a spinor BEC and on-site potential in an optical lattice). The goal is to develop a pulse sequence of the parameters, using the Hamiltonians of bosonic many-body systems to produce the target states or operators. The desired sequence can be obtained using quantum optimal control (QOC), i.e., optimizing a figure of merit such as the fidelity (or the Fisher information) by varying the tunable control parameters. Q-PRONTO [1, 2] is a QOC solver that can achieve quadratic convergence while most other gradient-based QOC solvers converge linearly. However, it becomes computationally challenging to implement Q-PRONTO on many-body systems since the size of systems grows rapidly. In this talk, I will describe the implement of Q-PRONTO on a novel simulation tool [3], which efficiently reduce the size of many-body systems. I will then demonstrate the numerical results for a novel application of many-body systems: a Ramsey-like interferometer for measuring gravity.