Engineering Strong Beamsplitter Interaction between Bosonic Modes
via Quantum Optimal Control Theory
Abstract
In continuous-variable quantum computing with qubits encoded in the infinite-dimensional Hilbert
space of bosonic modes, it is a difficult task to realize strong and on-demand interactions between the
qubits. One option is to engineer a beamsplitter interaction for photons in two superconducting
cavities by driving an intermediate superconducting circuit with two continuous-wave drives, as
demonstrated in a recent experiment. Here, we show how quantum optimal control theory (OCT) can
be used in a systematic way to improve the beamsplitter interaction between the two cavities. We find
that replacing the two-tone protocol by a three-tone protocol accelerates the effective beamsplitter rate
between the two cavities. The third tone's amplitude and frequency are determined by gradient-free
optimization and make use of cavity-transmon sideband couplings. We show how to further improve
the three-tone protocol via gradient-based optimization while keeping the optimized drives
experimentally feasible. Our work exemplifies how to use OCT to systematically improve practical
protocols in quantum information applications.