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This research presents a breakthrough in fault-tolerant quantum computing by introducing a family of constant-rate codes that support the full logical Clifford group using only transversal and fold-transversal gates. By leveraging classical codes based on Steinberg modules, this approach achieves sublogarithmic stabilizer weight growth, significantly reducing space overhead while maintaining high error-correction performance. The work directly addresses critical bottlenecks in scalable quantum architectures by enabling efficient, low-propagation-error logical operations without requiring additional physical qubits.
Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates
arXiv:2609.37699v1 Announce Type: new Abstract: Low-space-overhead fault-tolerant quantum computation requires not only high-rate quantum error-correcting codes but also space-efficient implementations of logical operations. Transversal and fold-transversal gates are promising since they limit error propagation and require no additional qubits. However, the logical operations they enable are typically restricted, and a central challenge is to construct codes that combine a complete set of logical Clifford gates with favorable code parameters. In this work, we introduce a family of quantum codes with an asymptotically constant encoding rate and sublogarithmically growing stabilizer weight, while supporting the entire logical Clifford group using only transversal and fold-transversal gates. Our construction is based on classical codes whose code spaces are absolutely irreducible Steinberg modules of their Tanner-graph automorphism groups. Taking hypergraph products of these classical codes yields quantum codes for which all logical Clifford operations can be synthesized from a fixed set of transversal and fold-transversal gates. Moreover, the slow growth of the stabilizer weight enables a high error-correcting performance in small instances. These results provide a path toward fault-tolerant quantum computation with low space overhead using transversal and fold-transversal gates.
Abstract:Low-space-overhead fault-tolerant quantum computation requires not only high-rate quantum error-correcting codes but also space-efficient implementations of logical operations. Transversal and fold-transversal gates are promising since they limit error propagation and require no additional qubits. However, the logical operations they enable are typically restricted, and a central challenge is to construct codes that combine a complete set of logical Clifford gates with favorable code parameters. In this work, we introduce a family of quantum codes with an asymptotically constant encoding rate and sublogarithmically growing stabilizer weight, while supporting the entire logical Clifford group using only transversal and fold-transversal gates. Our construction is based on classical codes whose code spaces are absolutely irreducible Steinberg modules of their Tanner-graph automorphism groups. Taking hypergraph products of these classical codes yields quantum codes for which all logical Clifford operations can be synthesized from a fixed set of transversal and fold-transversal gates. Moreover, the slow growth of the stabilizer weight enables a high error-correcting performance in small instances. These results provide a path toward fault-tolerant quantum computation with low space overhead using transversal and fold-transversal gates.
arXiv:2609.37699 [quant-ph]
(or arXiv:2609.37699v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.37699 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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