  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,
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 delays,
each module can add thousands of physical qubits to the computational Hilbert
space. Networks of 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, each RSG can generate four logical distance-35
surface-code qubits 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 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.
