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 (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 0.04π (2%), the CZ gate fidelity depends significantly on γ.

In this work, we propose a multi-scale protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged-Elastic Band (NEB) method driven by a cheap electronic structure method. Forces recalculated at the more accurate electronic structure theory for a set of points on the path are fitted with a machine-learning technique (in our case symmetric gradient domain machine learning or sGDML) to produce a semi-local reactive Potential Energy Surface (PES), embracing reactants, products and transition state (TS) regions. This approach has been successfully applied to a unimolecular (Bergman cyclization of enediyne) and a bimolecular (SN2 substitution) reaction. In particular, we demonstrate that with only 50 to 150 energy-force evaluations with the accurate reference methods (here CASSCF and CCSD) it is possible to construct a semi-local PES giving qualitative agreement for stationary-point geometries, intrinsic reaction-coordinates and barriers. Furthermore, we find a qualitative agreement in vibrational frequencies and reaction rate coefficients. The key aspect of the method's performance is its multi-scale nature, which not only saves computational effort but also allows extracting meaningful information along the reaction path, characterized by zero gradients in all but one direction. Agnostic to the nature of the TS and computationally economic, the protocol can be readily automated and routinely used for mechanistic reaction studies.