  Fusion-based quantum computing (FBQC) offers a powerful approach to building
a fault-tolerant universal quantum computer using photonic components --
single-photon sources, linear-optical circuits, single-photon detectors, and
optical switching with feedforward control. Both individual optical switches
and sophisticated switch networks are needed where it is necessary to perform
operations conditionally, using feedforward of previous photon-detection
outcomes, within the lifetime of remaining photons. Most visibly, feedforward
switching is required for fault-tolerant operations at the level of logical
qubits, which are needed in turn for useful quantum algorithms. However, switch
networks are also required for multiplexing ("muxing") stages that are needed
for generating specific small entangled resource states, where it is used to
boost the probabilities for allocating quantum states to fusion gates and other
operations -- a task which dominates the footprint of photonic FBQC. Despite
their importance, limited attention has been paid to exploring possible designs
of switch networks in this setting. Here we present a wide range of new
techniques and schemes which enable major improvements in terms of muxing
efficiency and reductions in hardware requirements. Since the use of photonic
switching heavily impacts qubit losses and errors, our schemes are constructed
with low switch depth. They also exploit specific features of linear-optical
circuits which are commonly used to generate entanglement in proposed quantum
computing and quantum network schemes.
