Coherent and non-unitary errors in ZZ-generated gates

Abstract: Variational algorithms such as the Quantum Approximate Optimization Algorithm have attracted attention due to their potential for solving problems using near-term quantum computers. The $ZZ$ interaction typically generates the primitive two-qubit gate in such algorithms applied for a time, typically a variational parameter, $\gamma$. Different compilation techniques exist with respect to the implementation of two-qubit gates. Due to the importance of the $ZZ$-gate, we present an error analysis comparing the continuous-angle controlled phase gate (CP) against the fixed angle controlled $Z$-gate (CZ). We analyze both techniques under the influence of coherent over-rotation and depolarizing noise. We show that CP and CZ compilation techniques achieve comparable $ZZ$-gate fidelities if the incoherent error is below $0.03 \, \%$ and the coherent error is below $0.8 \, \%$. Thus, we argue that for small coherent and incoherent error a non-parameterized two-qubit gate such as CZ in combination with virtual $Z$ decomposition for single-qubit gates could lead to a significant reduction in the calibration required and, therefore, a less error-prone quantum device. We show that above a coherent error of $0.04 \pi$ ($2 \, \%$), the CZ gate fidelity depends significantly on $\gamma$.