Universal Robust Quantum Gates via Doubly Geometric Control

• URL: http://arxiv.org/abs/2604.02962v1
• Date: Fri, 03 Apr 2026 10:53:26 GMT
• Title: Universal Robust Quantum Gates via Doubly Geometric Control
• Abstract summary: We introduce a framework for universal doubly geometric gates.<n>We show that the defining conditions lead to simultaneous fourth-order suppression of control errors.<n>Our results establish doubly geometric control as a general and scalable route toward high-order robust quantum gates.
• Score: 7.218693746723512
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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