Fault-tolerant hyperbolic Floquet quantum error correcting codes
1Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
2Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
3Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, # 16-16 Connexis, Singapore 138632, Republic of Singapore
| Published: | 2025-09-05, volume 9, page 1849 |
| Editor: | Joschka Roffe |
| Eprint: | arXiv:2309.10033v4 |
| Doi: | https://doi.org/10.22331/q-2025-09-05-1849 |
| Citation: | Quantum 9, 1849 (2025). |
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Abstract
A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes.'' These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for $n$ qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate $(1/8+2/n)$ while still requiring only two-body measurements. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in $n$. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1% in a phenomenological noise model and 0.25% in an entangling measurements noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a $[[400,52,8]]$ code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.
Featured image: Hyperbolic Floquet codes in this work are based on periodic three-colored octagonal lattices.
Popular summary
These codes achieve a finite encoding rate—roughly one logical qubit for every eight physical qubits—while maintaining good error protection. For example, a [[400, 52, 8]] code encodes 52 logical qubits in 400 physical ones, far more efficient than existing honeycomb Floquet codes, which would need around five times more qubits for comparable performance.
Using a matching-based decoder, the authors show that these codes can tolerate realistic noise levels (up to about 0.25%) and that logical error rates fall exponentially with code distance. The trade-off is that the codes are not geometrically local, making hardware layouts more challenging.
Overall, hyperbolic Floquet codes offer a promising route toward scalable, fault-tolerant quantum computing with significantly lower resource costs.
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The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 20:10:18) and SAO/NASA ADS (last updated successfully 2026-08-09 20:10:28). The list may be incomplete as not all publishers provide suitable and complete citation data.
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