Efficient Logic with Ultra-High-Rate Quantum Codes
Abstract
Quantum low-density parity-check (qLDPC) codes offer a promising route to reducing the qubit overhead of fault tolerance, with recent ultra-high-rate constructions achieving encoding rates above one half. In this work, we develop fast and parallel logical computation methods for ultra-high-rate codes. We first utilize the group symmetries of the codes to partition the logical qubits into orbits, and then apply parallel surgery methods to implement group-invariant collections of logical Pauli-product measurements. These measurements are highly programmable, as we may arbitrarily couple logical orbits as long as each measurement is repeated across the whole orbit(s). To reduce the space and time overheads, we develop a technique called chain-map convolution, which uses the group structure to boost both the spatial and temporal distances of our protocol in a highly efficient manner. As case studies, we construct distance-preserving parallel measurement gadgets for the [[256, 68, 12]], [[576, 148, 18]] pair-partition codes, and a [[1152, 580, 12]] rate-1/2 code, with only around 2.5× space overhead and 3-4 rounds of syndrome extraction each. The same methods also enable parallel injection of cultivated magic states into high-rate codes. Finally, we extend programmability through subgroup restrictions, revealing a tradeoff between logical control and the spacetime resources required for fault tolerance and highlighting the crucial role structured parallelism plays in reducing overhead. These results provide new methods for designing qLDPC logical operations with low spacetime overhead, opening a route toward more efficient fault-tolerant quantum architectures.
Related
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- Ultra-high-distance quantum memories from amplified qLDPC codes
- Fast and accurate neural triage decoding of ultra-high-rate quantum LDPC codes
- Injection is all you need: parallel universal logic in high-rate concatenated self-dual codes
- Quantum group codes for non-Clifford logic: enhanced decoding, addressability and parallelizability
BibTeX
@misc{maskara2026efficient,
title = {{Efficient Logic with Ultra-High-Rate Quantum Codes}},
author = {Nishad Maskara and Rohan Mehta and Zhiyang He and Varun Menon and J. Pablo Bonilla Ataides and Mikhail D. Lukin and Hengyun Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06749},
eprint = {2610.06749},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06749},
}
RIS
TY - UNPB
TI - Efficient Logic with Ultra-High-Rate Quantum Codes
AU - Nishad Maskara
AU - Rohan Mehta
AU - Zhiyang He
AU - Varun Menon
AU - J. Pablo Bonilla Ataides
AU - Mikhail D. Lukin
AU - Hengyun Zhou
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06749
UR - https://arxiv.org/abs/2610.06749
AB - Quantum low-density parity-check (qLDPC) codes offer a promising route to reducing the qubit overhead of fault tolerance, with recent ultra-high-rate constructions achieving encoding rates above one half. In this work, we develop fast and parallel logical computation methods for ultra-high-rate codes. We first utilize the group symmetries of the codes to partition the logical qubits into orbits, and then apply parallel surgery methods to implement group-invariant collections of logical Pauli-product measurements. These measurements are highly programmable, as we may arbitrarily couple logical orbits as long as each measurement is repeated across the whole orbit(s). To reduce the space and time overheads, we develop a technique called chain-map convolution, which uses the group structure to boost both the spatial and temporal distances of our protocol in a highly efficient manner. As case studies, we construct distance-preserving parallel measurement gadgets for the [[256, 68, 12]], [[576, 148, 18]] pair-partition codes, and a [[1152, 580, 12]] rate-1/2 code, with only around 2.5× space overhead and 3-4 rounds of syndrome extraction each. The same methods also enable parallel injection of cultivated magic states into high-rate codes. Finally, we extend programmability through subgroup restrictions, revealing a tradeoff between logical control and the spacetime resources required for fault tolerance and highlighting the crucial role structured parallelism plays in reducing overhead. These results provide new methods for designing qLDPC logical operations with low spacetime overhead, opening a route toward more efficient fault-tolerant quantum architectures.
ER -