A central question for fault-tolerant quantum computing is which quantum error-correcting codes are best suited to a given hardware architecture. Here we compare the Raussendorf--Harrington--Goyal (RHG) code, the Foliated Floquet Color Code (FFCC), and the reduced FFCC in a compound photon--atom architecture that directly generates measurement-based quantum computation (MBQC) resources with near-deterministic photon--atom CZ gates. RHG serves as a natural benchmark, while the FFCC variants allow us to study whether reduced graph degree improves performance under an architecture-aware circuit-level loss model with delayed heralding and correlated bond-loss propagation. We construct two generation schemes compatible with the compound hardware and evaluate circuit-level thresholds under periodic boundary conditions. RHG achieves the highest circuit-level threshold, 2.75%, and its threshold falls below that of reduced FFCC only for large excess loss on intermodule CZ connections. RHG also achieves the lowest logical error rate in most resource-matched comparisons, but some low-loss windows favor reduced FFCC. Overall, we show that when the hardware supports the native gates and connectivity required for MBQC, the benefits of lower graph degree must be weighed against each code's intrinsic IID loss tolerance, generation-scheme details, and hardware-aware resource overhead.
Comments
20 pages, 15 figures; includes Supplementary Material
A central question for fault-tolerant quantum computing is which quantum error-correcting codes are best suited to a given hardware architecture. Here we compare the Raussendorf--Harrington--Goyal (RHG) code, the Foliated Floquet Color Code (FFCC), and the reduced FFCC in a compound photon--atom architecture that directly generates measurement-based quantum computation (MBQC) resources with near-deterministic photon--atom CZ gates. RHG serves as a natural benchmark, while the FFCC variants allow us to study whether reduced graph degree improves performance under an architecture-aware circuit-level loss model with delayed heralding and correlated bond-loss propagation. We construct two generation schemes compatible with the compound hardware and evaluate circuit-level thresholds under periodic boundary conditions. RHG achieves the highest circuit-level threshold, 2.75%, and its threshold falls below that of reduced FFCC only for large excess loss on intermodule CZ connections. RHG also achieves the lowest logical error rate in most resource-matched comparisons, but some low-loss windows favor reduced FFCC. Overall, we show that when the hardware supports the native gates and connectivity required for MBQC, the benefits of lower graph degree must be weighed against each code's intrinsic IID loss tolerance, generation-scheme details, and hardware-aware resource overhead.
Fault-tolerant quantum computing requires architectures that simultaneously address scalability, connectivity, and error correction under realistic noise constraints. We present a compound photonic-atomic quantum computing platform that uses cavity QED to realize near-deterministic entangling operations between flying photonic qubits and stationary atomic qubits. Photons provide long-range connectivity and scalability via measurement-based quantum computing (MBQC), while atoms supply reusable, near-deterministic resources for photon generation and entanglement, overcoming the inefficiency of purely photonic platforms. The core primitive is a symmetrized Duan-Kimble photon-atom controlled-phase (CZ) gate, robust to experimental imperfections and high-fidelity. Using single 87Rb atoms coupled to optical cavities, we give protocols for state preparation, measurement, photon generation, and entangling gates on tens-of-nanosecond timescales, and show how large-scale cluster states with effectively unrestricted connectivity and reduced overhead can be generated through atomic reuse. We analyze fault tolerance on the Raussendorf-Harrington-Goyal (RHG) lattice with a hardware-aware noise model capturing asymmetric loss and correlated photonic-atomic errors. Logical memory simulations yield a photon-loss threshold near 2.6% per physical gate ($\sim$15\% total per trajectory). The full Clifford set -- Hadamard, phase, CNOT -- is implementable transversally or fold-transversally at thresholds matching the identity channel, and we propose two non-Clifford resource-state routes (code teleportation and magic state cultivation) within the foliated cluster-state architecture.
This review presents a detailed anatomical analysis of the blueprint for a fault-tolerant compound photon–atom quantum computing architecture proposed by Arwas et al. (2026). The architecture integrates cavity quantum electrodynamics (cavity QED) with single 87Rb atoms in high-finesse Fabry–Pérot micro-resonators to realize near-deterministic photon–atom controlled-phase (CZ) gates via a symmetrized Duan–Kimble protocol. These gates, operating on tens-of-nanoseconds timescales, enable efficient generation of large-scale cluster states for measurement-based quantum computation (MBQC) on the Raussendorf–Harrington–Goyal (RHG) lattice while supporting atomic reuse for substantial resource reduction. We dissect the physical layer (unit cell, entangling gate, state preparation and measurement (SPAM), single-photon generation, and level engineering), the architectural layer (bipartite and interleaved generation schemes), and the fault-tolerance layer (hardware-aware noise model incorporating bond-loss propagation, loss-conditioned detector error models, and minimum-weight perfect-matching decoding). Strengths include the resolution of the photon determinism versus matter connectivity tension, competitive photon-loss thresholds of approximately 2.6% per physical gate (~15% total trajectory loss), transversal or fold-transversal implementation of the full Clifford set with thresholds matching the memory channel, and two viable MBQC-native routes to magic-state preparation. Also available on Academia.edu: https://www.academia.edu/attachments/133274377/download_file?s=portfolio
Fault-tolerant measurement-based quantum computing (MBQC) provides a compelling framework for fault-tolerant quantum computation, in which quantum information is processed through single-qubit measurements on a three-dimensional entangled resource known as cluster state. To date, this resource has been predominantly studied on Euclidean lattices, most notably in the Raussendorf-Harrington-Goyal (RHG) construction, which underlies topological fault tolerance in MBQC. In this work, we introduce the hyperbolic cluster state, a generalization of the three-dimensional cluster state to negatively curved geometries, obtained via the foliation of periodic hyperbolic lattices. We present an explicit construction of hyperbolic cluster states and investigate their fault-tolerant properties under a realistic circuit-level depolarizing noise model. Using large-scale numerical simulations, we perform memory experiments to characterize their logical error rates and decoding performance. Our results demonstrate that hyperbolic cluster states exhibit a fault-tolerance threshold comparable to that of the Euclidean RHG cluster state, while simultaneously supporting a constant encoding rate in the thermodynamic limit. This represents a substantial improvement in qubit overhead relative to conventional cluster-state constructions. These findings establish hyperbolic geometry as a powerful and experimentally relevant resource for scalable, fault-tolerant MBQC and open new avenues for leveraging negative curvature in quantum information processing.
Fault-tolerant quantum computing is crucial for realizing large-scale quantum computation, and the interplay between hardware architecture and quantum error-correcting codes is a key consideration. We present a comparative study of two quantum error-correcting codes - the surface code and the honeycomb Floquet code - implemented on the spin-optical quantum computing architecture, either with controlled-Z operations or with direct parity measurements. This allows for a direct comparison of the codes using consistent noise models. Notably, we achieve a loss threshold of 6.3% with the honeycomb Floquet code implemented on our tailored architecture, almost twice as high as the loss threshold obtained with the surface code on the previous architecture, all the while requiring less physical qubits. This finding is particularly significant given that photon loss is the primary source of errors in photon-mediated quantum computing. Moreover, we benchmark the general performances of the two codes in a multi-error setting by computing the volume of the fault-tolerant region, and show that the fault-tolerant region of the honeycomb code is over twice as large as that of the surface code.
We study an architecture for fault-tolerant measurement-based quantum computation (FT-MBQC) over optically-networked trapped-ion modules. The architecture is implemented with a finite number of modules and ions per module, and leverages photonic interactions for generating remote entanglement between modules and local Coulomb interactions for intra-modular entangling gates. We focus on generating the topologically protected Raussendorf–Harrington–Goyal (RHG) lattice cluster state, which is known to be robust against lattice bond failures and qubit noise, with the modules acting as lattice sites. To ensure that the remote entanglement generation rates surpass the bond-failure tolerance threshold of the RHG lattice, we employ spatial and temporal multiplexing. For realistic system timing parameters, we estimate thecode cycle timeof the RHG lattice and the ion resources required in a bilayered implementation, where the number of modules matches the number of sites in two lattice layers, and qubits are reinitialized after measurement. For large distances between modules, we incorporate quantum repeaters between sites and analyze the benefits in terms of cumulative resource requirements. Finally, we derive and analyze a qubit noise-tolerance threshold inequality for the RHG lattice generation in the proposed architecture that accounts for noise from various sources. This includes the depolarizing noise arising from the photonically-mediated remote entanglement generation between modules due to finite optical detection efficiency, limited visibility, and presence of dark clicks, in addition to the noise from imperfect gates and measurements, and memory decoherence with time. Our work thus underscores the hardware and channel threshold requirements to realize distributed FT-MBQC in a leading qubit platform today—trapped ions.
Fault-tolerant (FT) quantum computation offers a pathway to quantum advantage, but its realization is hindered by its significant overhead. The partially FT "STAR" architecture reduces the cost of universal computation at the price of relaxing FT requirements for non-Clifford operations, increasing exposure to hardware noise. Therefore, maximizing its performance and applicability demands careful co-design with the underlying hardware. In this work we investigate the co-design of the STAR architecture with neutral-atom platforms, connecting the underlying atomic physics to logical error modeling and application-level performance. At the physical level, we identify a favorable noise bias in 171Yb Rydberg gates, and show how it can be enhanced through error-selective pulse optimization. At the logical level, we identify an intrinsic error suppression mechanism, yielding vanishing logical coherent noise in leading order. Detailed circuit-level simulations of surface code implementations show more than an order of magnitude reduction in logical error relative to previous estimates. As a concrete target application, we focus on the Fermi-Hubbard model with periodic boundaries, for which we design a simulation circuit particularly suited to early implementations. We quantify the resource tradeoff of partially and fully FT approaches to gate synthesis, with the former showing approximately an order of magnitude reduction in state-injection depth, and an even larger reduction in Clifford resources. Comparing with classical and fully FT approaches, we identify regimes where partial fault tolerance provides both lower overheads and lower error rates. In our estimates, this is accessible with moderate error rates p∼10−3 and a few thousand qubits, underlining that for these types of problems, partial FT approaches provide a compelling pathway to early quantum advantage.