42. Photonic Quantum Computing
42.1Photons as qubits
Encode a qubit in a mode of light: polarization, path, or time-bin. The advantage list is real: photons do not decohere in flight (there is nothing in vacuum to interact with), they propagate through telecom fiber — the best quantum network channel available — generation and detection are mature technologies, and most of the machine runs at room temperature. The disadvantage is structural: photons barely interact with each other, so there is no natural two-qubit gate. The entire field is a set of increasingly clever answers to that one sentence. And the dominant error is not decoherence at all — it is loss, which behaves differently from every noise model in Part IX.
42.2Polarization
Basis states |H⟩ and |V⟩, horizontal and vertical. Control uses waveplates — a half-wave plate is a rotation gate, a quarter-wave plate prepares circular states — and analysis uses polarizing beam splitters routing the two components to single-photon detectors. The best detectors are superconducting nanowire single-photon detectors (SNSPDs): 90–98% efficiency, picosecond timing, negligible dark counts — the platform's one cold component, needing a cryostat despite the room-temperature physics. Polarization is convenient in free space but drifts in fiber birefringence; deployed fiber systems usually prefer time-bin encoding, which moves the qubit to early-versus-late arrival slots that fiber leaves stable.
42.3Path encoding
The qubit is which of two waveguides the photon occupies. On silicon photonic chips, beamsplitters are Mach–Zehnder interferometers and phase shifters are thermo-optic or electro-optic elements — the full single-qubit gate set in lithographed hardware. Integrated photonics solves the stability problem that kills tabletop free-space optics (centimeter paths drift; millimeter on-chip paths barely move) and inherits the semiconductor fabrication ecosystem — PsiQuantum's explicit strategy is to ride commercial fabs. Photonic integrated circuits with thousands of components are routine. After spin qubits (43.1), this is the most fabrication-native quantum platform, and the only one whose manufacturing story is literally classical semiconductor engineering.
42.4Interferometry
Beam splitters and phase shifters implement arbitrary unitaries on modes: the Reck and Clements decompositions build any m×m mode unitary from O(m²) elements — a constructive theorem, and a pleasant numpy exercise. Interference of indistinguishable photons is the computational resource, which makes photon indistinguishability — spectral, temporal, and spatial purity — the hard systems requirement, and multi-photon interference fidelity the number to read first in any photonic paper. The same machinery is the entirety of boson sampling (42.7): the interferometer is the computer, and the output statistics across its ports are the result. Nothing else in the machine computes; the computation is the interference pattern.
42.5Photonic gates
No photon–photon interaction means no deterministic gate from passive optics. Three answers exist. KLM (Knill–Laflamme–Milburn, 2001): measurement-induced gates — ancilla photons plus postselection make a two-qubit gate succeed with probability below 1 but announce its success, and gate teleportation chains these heralded gates into circuits. Fusion gates: probabilistic two-qubit measurements that stitch small entangled resource states into the large cluster states fault tolerance wants (PsiQuantum's architecture). Matter-mediated gates: atoms or quantum dots in cavities providing deterministic interaction — powerful but hardware-hard. Every route ends in multiplexing: massive redundancy in sources, paths, and timing so that probabilistic operations succeed almost always. The resource arithmetic follows from 31.3-style branch probabilities.
42.6Measurement
Measurement is native and central: photonic computation is largely "prepare entangled states, measure, feed forward". Detectors are SNSPDs for photon counting (42.2) and homodyne or heterodyne detectors for continuous-variable encodings, which measure field quadratures — the route Xanadu takes with GKP qubits (42.8). Fast feed-forward electronics (microsecond scale) condition later operations on earlier outcomes, so the classical control plane is on the critical path of the quantum computation itself. Because every step is a measurement, classical post-processing throughput becomes a genuine architectural constraint, not an afterthought — the platform where the classical/quantum boundary is thinnest.
42.7Boson sampling
The platform's native benchmark: send m indistinguishable photons through a large interferometer and sample the output distribution, which relates to matrix permanents — believed hard for classical computers (Aaronson–Arkhipov, 2011). USTC's Jiuzhang experiments (2020, 2021) claimed photonic quantum advantage with tens of photons; classical-algorithm groups then compressed the claim substantially — the same dynamic as 1.8, and a case study in honest benchmarking. Boson sampling is not universal quantum computing, but it validated the photonic stack end-to-end: sources, interferometers, detectors, and analysis at unprecedented scale. Xanadu's Borealis later made a programmable, cloud-accessible version — the photonic platform's public machine.
42.8Photonic error correction
The error model is loss-dominated, so photonic QEC differs in kind from Part IX's models: use codes tolerant to erasure (you know where the photon was lost) and encode in states that fight loss directly. GKP qubits — grid states in an optical mode — were demonstrated with error correction on a photonic chip by Xanadu (2024), a below-threshold claim at small scale. Fusion-based fault tolerance (PsiQuantum) interconnects small resource states into a large code with loss tolerance built into the stitching. The resource arithmetic is unlike any other platform: millions of components, driven by the probability calculus of probabilistic gates (42.5). The bet is explicit — semiconductor fabs, not new physics, will close that gap.