Analytically Realizing Hybrid Boson-Qubit Operations via Hamiltonian Simulation Techniques

Circuit QED enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson operations are realizable only through optimal control theory (OCT). OCT is oftentimes intractable and uninterpretable, yielding only a pulse which performs the desired operation. This pulse provides no physical intuition and is computationally intensive to produce. In this talk, we introduce an analytic approach for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie-Trotter and Baker-Campbell-Hausdorff product formulas. We show how this technique can be used to realize a number of operations of interest, including polynomials of annihilation and creation operators, i.e., a^p a^†q for integer p, q. This work demonstrates how techniques from Hamiltonian simulation can be applied to better control hybrid boson-qubit devices.