Enhancing Quantum Circuit Noise Robustness from a Geometric Perspective

Quantum errors in noisy environments remain a major obstacle to advancing quantum information technology. In this work, we expand a recently developed geometric framework, originally utilized for analyzing noise accumulation and creating dynamical error-correcting gates at the control pulse level, to now study noise dynamics at the quantum circuit level. Through a geometric perspective, we demonstrate how circuit noise robustness can be enhanced using twirling techniques. Additionally, we show that circuits modified by random twirling correspond to random walk trajectories in this geometric framework, and provide a fresh perspective on randomized compiling by analytically deriving the perturbative expression for the resultant Pauli noise channel. We also illustrate that combining robustness optimization strategies at both the control pulse and circuit levels can significantly boost overall circuit fidelity even further through numerical examples. This research illuminates pathways to achieving noise-resistant quantum control beyond mere optimization of control pulses.