Universal Robust Quantum Gates via Doubly Geometric Control

TL;DR

This paper introduces a new framework for designing universal geometric quantum gates that achieve high-order error suppression, advancing fault-tolerant quantum computation.

Contribution

It develops a hierarchical approach for embedding quantum gates to systematically suppress errors up to sixth order, overcoming previous structural limitations.

Findings

Achieves simultaneous fourth-order suppression of control errors.

Extends suppression to sixth order with higher-level constructions.

Establishes doubly geometric control as scalable for robust quantum gates.

Abstract

Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources remains a long-standing limitation, particularly in realistic large-scale circuits with complex noise environments. This limitation is largely due to the absence of a general framework that directly characterizes error accumulation and enables systematic improvement. Here we establish such a framework for universal doubly geometric gates by embedding target operations into a hierarchy of level-n identity constructions. This approach enables direct quantification of error accumulation while removing structural constraints inherent in previous schemes. We analytically show that the defining conditions lead to simultaneous fourth-order suppression of control errors, with a systematic extension to sixth-order suppression via higher-level constructions. Our results establish doubly geometric control as a general and scalable route toward high-order robust quantum gates, with potential implications for fault-tolerant quantum information processing.