Distributed quantum error correction based on hyperbolic Floquet codes

TL;DR

This work tackles the scalability challenge of fault-tolerant quantum computing by proposing distributed quantum error correction using hyperbolic Floquet codes, which combine high encoding rates with pairwise, weight-two measurements suitable for non-local checks over a quantum network. The authors design a modular architecture with fixed-size quantum processing units interconnected by photonic channels to realize non-local stabilizer checks via heralded Bell states, and they simulate distributed hyperbolic Floquet codes under a circuit-level depolarising noise model using Stim and MWPM decoding. Their results show favorable pseudo-thresholds and sub-threshold scaling (Lambda around 5) under realistic local and non-local fidelities, and they provide resource estimates for running large-scale quantum memories (MegaQuOp), indicating practical viability. This work suggests distributed QEC with hyperbolic Floquet codes as a feasible path to scalable quantum computation, leveraging long-range photonic interconnects to encode many logical qubits efficiently while tolerating non-local noise.

Abstract

Quantum computing offers significant speedups, but the large number of physical qubits required for quantum error correction introduces engineering challenges for a monolithic architecture. One solution is to distribute the logical quantum computation across multiple small quantum computers, with non-local operations enabled via distributed Bell states. Previous investigations of distributed quantum error correction have largely focused on the surface code, which offers good error suppression but poor encoding rates, with each surface code instance only able to encode a single logical qubit. In this work, we argue that hyperbolic Floquet codes are particularly well-suited to distributed quantum error correction for two reasons. Firstly, their hyperbolic structure enables a high number of logical qubits to be stored efficiently. Secondly, the fact that all measurements are between pairs of qubits means that each measurement only requires a single Bell state. Under the circuit-level noise model, we demonstrate through simulations that distributed hyperbolic Floquet codes offer good performance with achievable local and non-local fidelities of approximately $99.97\%$ and $99\%$, respectively. This shows that distributed quantum error correction is not only possible but also efficiently realisable.

Figures (5)

• Figure 1: Summary of our approach for distributed quantum error correction. (a) A segment of a hyperbolic Floquet code defined on an octagonal lattice Higgott2023constructionsFahimniya2024. Each vertex represents a physical qubit, with edges representing two-qubit measurements and faces representing stabiliser measurements formed from the surrounding edge measurements. Further details on these codes are provided in \ref{['sec:Methods']}. (b) Fine-graining approach is applied in order to produce a semi-hyperbolic code with a higher distance Higgott2023constructions. (c) The higher-distance code is distributed across multiple quantum processors of a fixed size. Non-local measurements, denoted by grey lines, are implemented using distributed Bell states, which are generated using the architecture outlined in \ref{['sec:architecture']}.
• Figure 2: An overview of the networked quantum architecture, comprising quantum processing units (QPUs), qubit-photon interfaces (QPIs), photonic switches, and photonic Bell-State Measurement stations (BSM). Each QPU is interconnected with QPIs, where spin-photon entangled states are generated. The QPI-photons feed into a photonic switch, routing any of them to any of the switch outputs. The photon paths terminate at a BSM, where successful two-photon heralds project the QPI qubits into Bell states that can be used as remote entanglement links.
• Figure 3: Applying the fine-graining procedure from Higgott2023constructions to a vertex in an $\{8, 3\}$ tiling. Fine-graining level $f=1$ corresponds to the original lattice, with higher levels corresponding to increasing the size of the hexagonal sub-lattice to increase the code distance. This requires a re-colouring of the graph to accommodate the additional faces. White dashed lines indicate the dual of the graph and show how fine-graining corresponds to tiling the face of the dual graph with a triangular sub-graph.
• Figure 4: Pseudo-threshold for H144-f3. Logical error rates are shown for a single worst-case observable in the code H144-f3 (1296 data qubits) partitioned over 32 qubit devices for 12 detector rounds (72 colour rounds). Error bars in the threshold fitting are shown as solid red lines around threshold points. The ratio of logical to physical error rate is shown as a 2D color map.
• Figure 5: Figures show (left) the logical error rate for code families with error rates fixed at $p_{\textrm{local}}=99.97\%$ and $p_{\textrm{non-local}}=99\%$. The sub-threshold error correction scaling $\Lambda$ (right) is calculated using \ref{['eq:lambda']}. The data points in the right plot are derived from the error rate fits in the left plot.