Asymptotically Good Quantum Codes with Addressable Transversal T Gates
quant-ph
Submitted: 2026-09-28
Updated: 2026-09-28
Comments: 27 pages, no figures. Comments are welcome
License: http://creativecommons.org/licenses/by/4.0/
The gist: Designing quantum codes with both transversal non-Clifford gates and good error-correcting parameters is an important goal in fault-tolerant quantum computation.
Terminology
Abstract
Designing quantum codes with both transversal non-Clifford gates and good error-correcting parameters is an important goal in fault-tolerant quantum computation. Here, we construct an explicit family of binary CSS codes with constant rate and linear distance that admit fully addressable transversal T gates. Specifically, any prescribed tensor product of logical powers of T is implemented by a tensor product of physical powers of T, without any subsequent correction. Our construction combines algebraic-geometry codes with suitable binary embedding to obtain generalized divisibility of binary codes. This divisibility then enables fully addressable transversal T gates. Furthermore, we formulate the minimum binary embedding length problem as a minimum-weight problem over an affine space and numerically improve the constants in the asymptotic rate and relative-distance bounds.
Sources
- On Constructing and Decoding Quantum Triorthogonal Codes
- Quantum Lego Power-up: Designing Transversal Gates with Tensor Networks
- Transversal gates for quantum CSS codes
- Quantum Codes with Arbitrary Z-Rotation logical Gates and Applications to Fault-Tolerant Code Switching
- Purely-logarithmic-time- and constant-space-overhead fault-tolerant quantum computation
- Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates
- Quantum Codes with Addressable and Transversal Non-Clifford Gates
- Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes
- Asymptotically good CSS codes that realize the logical transversal Clifford group fault-tolerantly
- Realizing Logical Diagonal Gates via Transversal Physical Z-Rotations in CSS Codes
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