OpenAlex ·
Achieving the limits of automorphism gates
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.19250
- Original
- Read it at the publisher
- Topics
Abstract
Universal fault-tolerant quantum computing combines versatile but expensive operations with specialized but cheap ones. Its efficiency depends on how much computation can be pushed onto the cheap operations and on the size of the code needed to do so. Automorphism gates provide such cheap operations using only physical single-qubit Clifford gates and qubit permutations. Yet no general theory characterizes their maximum logical power or the minimum code size needed to attain it. We develop such a theory. For stabilizer codes encoding $k\geq3$ logical qubits, we show that the largest logical group attainable by automorphisms is generated by all addressable $S$ and $\mathrm{CX}$ gates, and we construct codes attaining it. While this group contains exponentially fewer gates than the full Clifford group, adding one suitable non-Clifford gate yields universality. We further classify the largest logical groups attainable using qubit permutations, physical single-qubit Cliffords, or both across general stabilizer and CSS codes, and derive refined bounds for self-dual CSS subclasses. Achieving the maximum-size logical group through automorphisms requires $n=Θ(2^k)$ physical qubits. By contrast, all addressable diagonal Clifford gates, generated by $S$ and $\mathrm{CZ}$, require only $n=Θ(k^2)$ physical qubits when implemented using physical single-qubit Cliffords alone. Both bounds are tight. This polynomial qubit cost extends beyond Cliffords to all addressable diagonal gates at any fixed level of the Clifford hierarchy, using physical single-qubit diagonal gates. Thus, for full addressability, the sharpest physical-qubit cost divide lies between diagonal and $\mathrm{CX}$-type gates, not between Clifford and non-Clifford gates.
The authors’ abstract, as arXiv lists it. arXiv’s listings, abstracts included, are free for anyone to reuse.
Read it on ReadSearch
Each opens after you create an account, and brings you back to this paper.
More in Artificial Intelligence
EDCT-Bench: Uncovering Faithfulness Gaps in VLMs via Explanation-Driven Counterfactual Testing
CoreSense: Traceable Failure Recall and Conflict-Aware Belief Gating for Auditable Robot Decisions
Measuring AI Leadership: Development and Validation of a Multidimensional Measure for AI-Native Organizations
QVAC Genesis III: A Large-Scale, High-Quality Open Synthetic STEM Corpus for Efficient Language Model Pre-Training
Memory Has Geometry: Non-Uniform Geometric Memory for Long-Horizon Personalized AI
Get the few papers worth your time in Artificial Intelligence every morning.
ReadSearch reads the new papers in your field each day and brings you the few worth reading, each with its key finding in a sentence.