Geometric framework for noise-resistant quantum control

Re-Bing Wu

Xiaodong Yang, Yingcheng Li, Ran Liu +4 more

Davide Pastorello

Zeng, Junkai, Yong-Ju Hai, Hao Liang +1 more

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.

Hunter T. Nelson, Evangelos Piliouras, Kyle Connelly +1 more

Noise-induced gate errors remain one of the main obstacles to realizing a broad range of quantum information technologies. Dynamical error suppression using carefully designed control schemes is critical for overcoming this challenge. Such schemes must be able to correct against multiple noise sources simultaneously afflicting a qubit to reach error-correction thresholds. Here we present a general framework for designing control fields that simultaneously suppress both noise in the fields themselves as well as transverse dephasing noise. Using the recently developed space curve quantum control formalism, in which robust quantum evolution is mapped to closed geometric curves in a multidimensional Euclidean space, we derive the minimal conditions necessary to guarantee the simultaneous cancellation of both types of noise to leading order. In particular, we find that the cancellation of control field noise requires the derivative of the space curve to have zero-area projections, which is a much more subtle property compared to the closed-curve condition needed to suppress transverse dephasing. We present several techniques for solving both these conditions simultaneously and provide explicit examples of error-resistant control fields. Our work also sheds light on the relation between holonomic evolution and the suppression of control field errors.

Michael Hush, Harrison Ball, Claire Edmunds +2 more