Coherent and non-unitary errors in ZZ-generated gates

Kurzfassung

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, γ. 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 (\textsc{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 π (2 \%), the CZ gate fidelity depends significantly on γ.