Quantum simulation of nonlinear three-wave interactions with engineered cubic couplings

Quantum three-wave gates are building blocks for simulating lattice gauge theory, nonlinear optics, weak turbulence, and laser plasma interactions. Although the underlying cubic couplings are usually absent in the quantum hardware, we show that effective three-wave vertices can be generated using control pulse engineering. In particular, for a three-wave Hamiltonian whose conserved actions are positive, we show that its Hilbert space can be decomposed into a direct sum of D-dimensional subspaces. Within each subspace, the quantum states are readily mapped onto the memory of quantum computers, and the Hamiltonian matrix becomes tridiagonal. Such a Hamiltonian is realized on the LLNL Quantum Design and Integration Testbed (QuDIT), utilizing three levels of a qudit. The qudit is controlled by digitally synthesized microwave pulses, whose wave forms are optimized numerically. Less accurate but cheaper control pulses may also be generated by interpolation, when parameters of the Hamiltonian vary. The resultant three-wave gates are applied to simulate the temporal three-wave problem, and physically meaningful results are obtained despite noise in the quantum computer.