Useful fault-tolerant quantum computers require very large numbers of physical qubits. Quantum computers are often designed as arrays of static qubits executing gates and measurements. Photonic qubits require a different approach. In photonic fusion-based quantum computing (FBQC), the main hardware components are resource-state generators (RSGs) and fusion devices connected via waveguides and switches. RSGs produce small entangled states of a few photonic qubits, whereas fusion devices perform entangling measurements between different resource states, thereby executing computations. In addition to these components, low-loss photonic delays such as optical fiber can be used as fixed-time quantum memories simultaneously storing thousands of photonic qubits. Here, we present a modular architecture for FBQC in which these components are combined to form interleaving modules consisting of one RSG with its associated fusion devices and a few fiber delays. Exploiting the multiplicative power of delay components, each interleaving module can add thousands of physical qubits to the computational Hilbert space. Networks of interleaving modules are universal fault-tolerant quantum computers, which we demonstrate using surface codes and lattice surgery as a guiding example. Our numerical analysis shows that in a network of modules containing 1-km-long fiber delays, a single RSG can generate four logical surface-code qubits with a code distance of 35 while tolerating photon loss rates above 2% in addition to the fiber-delay loss. We illustrate how the combination of interleaving with further uses of non-local fiber connections can reduce the cost of various logical operations and facilitate the implementation of unconventional geometries such as periodic boundaries or stellated surface codes. Interleaving applies beyond purely optical architectures, and can also turn many small disconnected matter-qubit devices with transduction to photons into a large-scale quantum computer.

Miniaturised frogs form a fascinating but poorly understood amphibian ecomorph and have been exceptionally prone to taxonomic underestimation. The subfamily Cophylinae (family Microhylidae), endemic to Madagascar, has a particularly large diversity of miniaturised species which have historically been attributed to the single genus Stumpffia largely based on their small size. Recent phylogenetic work has revealed that several independent lineages of cophyline microhylids evolved towards highly miniaturised body sizes, achieving adult snout–vent lengths under 16 mm. Here, we describe five new species belonging to three clades that independently miniaturised and that are all genetically highly divergent from their relatives: (i) a new genus ( Mini gen. nov.) with three new species from southern Madagascar, (ii) one species of Rhombophryne , and (iii) one species of Anodonthyla . Mini mum sp. nov. from Manombo in eastern Madagascar is one of the smallest frogs in the world, reaching an adult body size of 9.7 mm in males and 11.3 mm in females. Mini scule sp. nov. from Sainte Luce in southeastern Madagascar is slightly larger and has maxillary teeth. Mini ature sp. nov. from Andohahela in southeast Madagascar is larger than its congeners but is similar in build. Rhombophryne proportionalis sp. nov. from Tsaratanana in northern Madagascar is unique among Madagascar’s miniaturised frogs in being a proportional dwarf, exhibiting far less advanced signs of paedomorphism than other species of similar size. Anodonthyla eximia sp. nov. from Ranomafana in eastern Madagascar is distinctly smaller than any of its congeners and is secondarily terrestrial, providing evidence that miniaturisation and terrestriality may be evolutionarily linked. The evolution of body size in Madagascar’s microhylids has been more dynamic than previously understood, and future studies will hopefully shed light on the interplay between ecology and evolution of these remarkably diverse frogs.

Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum errorcorrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and resource overheads of universal logical gate sets have so far been limited. In this paper, we present a comprehensive framework for universal fault-tolerant logic motivated by the combined need for (i) platformindependent logical gate definitions, (ii) flexible and scalable tools for numerical analysis, and (iii) exploration of novel schemes for universal logic that improve resource overheads. We first introduce the theory of faulttolerant logical channels for describing logical gates holistically in space-time. Focusing on channels based on surface codes, we introduce explicit, but platform-independent representations of topological logic gates-called logical blocks-and generate new, overhead-efficient methods for universal quantum computation. As a specific example, we propose fault-tolerant schemes based on surface codes concatenated with more general low-density parity check (LDPC) codes, suggesting an alternative path toward LDPC-based quantum computation. The logical blocks framework enables a convenient software-based mapping from an abstract description of the logical gate to a precise set of physical instructions for executing both circuit-based and fusion-based quantum computation (FBQC). Using this, we numerically simulate a surface-code-based universal gate set implemented with FBQC, and verify that the threshold for fault-tolerant gates is consistent with the bulk threshold for memory. We find, however, that boundaries, defects, and twists can significantly impact the logical error rate scaling, with periodic boundary conditions potentially halving the memory resource requirements. Motivated by the favorable logical error rate suppression for boundaryless computation, we introduce a novel computational scheme based on the teleportation of twists that may offer further resource reductions.

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