Fault-tolerant hyperbolic Floquet quantum error correcting codes

Published

September 5, 2025

Author(s)

Ali Fahimniya, Hossein Dehghani, Kishor Bharti, Sheryl Mathew, Alicia Kollar, Alexey Gorshkov, Michael Gullans

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) and have a depth-3 syndrome extraction circuit. 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. 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.

Citation

Quantum

Volume

9

Pub Type

Journals

Download Paper

https://doi.org/10.22331/q-2025-09-05-1849

Local Download

Keywords

Quantum information science, quantum error correction, phase transitions

Citation

Fahimniya, A. , Dehghani, H. , Bharti, K. , Mathew, S. , Kollar, A. , Gorshkov, A. and Gullans, M. (2025), Fault-tolerant hyperbolic Floquet quantum error correcting codes, Quantum, [online], https://doi.org/10.22331/q-2025-09-05-1849, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=956707 (Accessed March 25, 2026)