Quantum Averaging for High-Fidelity Quantum Logic Gates

Analytical modeling of physical realizations of quantum logic gates is explored through a two-timescale quantum averaging theory (QAT). The theory combines the unitarity-preserving Magnus expansion with the method of averaging on Hilbert spaces to address the simultaneous presence of fast and slow timescales ubiquitous in driven quantum systems. To accurately model the system, QAT generates an effective Hamiltonian for the slowly-varying interactions while fully retaining detailed high-frequency dynamics in a dynamical phase. The efficacy of the method is demonstrated with the fast-entangling Mølmer-Sørenson gate, highlighting its potential for identifying and mitigating sources of gate error for high-precision quantum computation.