Error-divisible two-qubit quantum gates

We present theoretical results for a set of criteria and waveforms in performing error-divisible two-qubit gates, where the error for a fractional gate decreases proportionally to the quantum rotation desired. This is achieved by instantaneously cancelling unwanted terms over the entire duration of the quantum gate, instead of only as a net result at the end of the gate. This would provide a significant advantage for implementing noisy intermediate-scale quantum (NISQ) algorithms, where an algorithm such as VQE or QAOA implemented with error-divisible gates could see error rates up to an order of magnitude lower than one using a standard gate set (e.g. CZ + single qubit rotations). The techniques presented in this work using an error-divisible implementation of a two-qubit gate achieve an eight-fold reduction in final gate error for a CPHASE(π/4) operation compared to a stock gate set implementation using CZ gates.