Photonic MOC

Curated map of Zoo entries in the Photonic family.

Entries

Entry	Type	Status
fusion-based-photonic-qubit	architecture	proposed
linear-optical-photonic-qubit	architecture	demonstrated
photonic-cluster-state-mbqc-qubit	architecture	demonstrated
dual-rail-photonic-qubit	qubit	demonstrated
frequency-bin-photonic-qubit	qubit	demonstrated
photonic-qubit	qubit	demonstrated
polarization-photonic-qubit	qubit	demonstrated
time-bin-photonic-qubit	qubit	demonstrated
continuous-variable-photonic-qubit	qumode	demonstrated

Composition

• architecture: 3
• qubit: 5
• qumode: 1

Curated synthesis

The highest-value organizing move in this family is to separate photonic encodings from photonic computation models. Otherwise the graph quietly conflates “what degree of freedom stores the qubit?” with “how do we actually get entangling power and fault tolerance?”

1. Encodings optimized for different physical routes

   • dual-rail-photonic-qubit is the canonical chip-scale / LOQC encoding when spatial modes and integrated interferometers are the native hardware language.
   • time-bin-photonic-qubit is the fiber-native encoding when long-distance stability and network transport matter more than on-chip rail geometry.
   • polarization-photonic-qubit is the most direct single-photon Bloch-sphere encoding, with compact wave-plate control but polarization drift in deployed links.
   • frequency-bin-photonic-qubit uses discrete spectral modes and is especially natural for electro-optic control, dense multiplexing, and frequency-comb hardware.
   • These should be read together through erasure-error-vs-pauli-error and noise-bias-and-asymmetric-error-channels: all are loss-dominated photonic qubits, but they package mode matching and phase-stability constraints very differently.

2. Continuous-variable photonics is a different information model

   • continuous-variable-photonic-qubit is correctly typed as a qumode, not a discrete qubit. Gaussian gates are deterministic and time multiplexing reaches enormous mode counts, but universality and fault tolerance require non-Gaussian resources such as GKP states.
   • Route from it to bosonic-code-hierarchy when the question becomes how a continuous oscillator is converted into a protected logical qubit.

3. Gate-based linear optics is an architecture, not an encoding

   • linear-optical-photonic-qubit is the KLM lineage: minimal interactions, heavy ancilla and feed-forward overhead.
   • It usually rides on encodings like dual-rail-photonic-qubit, but the conceptual payload is architectural: probabilistic optics plus teleportation still clear the threshold-theorem barrier in principle.

4. Resource-state / measurement-first photonics is the modern scaling branch

   • photonic-cluster-state-mbqc-qubit shifts the burden from online gates to offline cluster-state preparation plus adaptive measurement.
   • fusion-based-photonic-qubit goes one step further and treats failed entangling attempts as an architectural primitive rather than an exception.
   • Both belong in the same fault-tolerance conversation because they live or die on whether loss and fusion failures stay structured enough for erasure-aware decoding and percolation-style thresholds.

Encoding-to-architecture routing matrix

The two layers are composable rather than mutually exclusive. Use the row to choose what carries the information, then the column to choose how the machine obtains entangling power and fault tolerance.

Encoding route	Gate-based linear optics	Cluster-state MBQC	Fusion-based architecture
dual-rail-photonic-qubit	Canonical KLM-style carrier: beam splitters and phase shifters act directly on spatial rails	Natural graph-state carrier when dual-rail photons are prepared and consumed by adaptive measurements	Natural fit for discrete Bell/fusion measurements; loss is usually a detectable rail-vacancy event
polarization-photonic-qubit	Compact single-qubit control and common proof-of-principle LOQC encoding	Widely used for small photonic cluster demonstrations	Fusion-compatible, but deployed systems inherit polarization-drift and mode-matching burdens
time-bin-photonic-qubit	Possible, but active switching and interferometric delay stability replace simple on-chip rail routing	Strong fit for sequentially emitted and temporally multiplexed cluster states	Strong fit when repeated source cycles and delay networks feed fusion attempts
frequency-bin-photonic-qubit	Electro-optic mixing supplies dense mode transformations in place of spatial interferometer meshes	Useful when frequency-comb modes supply a multiplexed graph-state resource	Promising multiplexing layer for routing successful attempts, not a distinct fusion rule by itself
continuous-variable-photonic-qubit	Do not route through discrete single-photon KLM by default; Gaussian mode transformations are deterministic but not universal alone	CV cluster states are native, with non-Gaussian resources or bosonic encodings needed for fault tolerance	Keep separate from the discrete-qubit fusion branch unless a specific hybrid or GKP construction supplies the bridge

photonic-qubit does not occupy one cell: it is the carrier-level umbrella above the matrix. Likewise, linear-optical-photonic-qubit, photonic-cluster-state-mbqc-qubit, and fusion-based-photonic-qubit label columns rather than alternative encodings. This prevents a category error such as asking whether “dual rail or fusion based” is the better qubit—the former chooses a Hilbert-space encoding, while the latter chooses a resource-building architecture.

When photonic loss is actually an erasure

The slogan “photon loss is an erasure” is conditional. Leaving a one-photon codespace is useful to a decoder only when the apparatus can localize the missing photon to a known space-time mode. Otherwise the same physical loss can appear merely as an ambiguous no-click event. Keep the loss ledger separate from faults that leave the photon count apparently valid:

Failure stage	Observable syndrome	Decoder-facing model	Routing consequence
Source, switch, coupling, or propagation loss	An expected occupied mode is empty	Erasure only if heralding or the measurement pattern identifies the missing mode; otherwise it is an unlocated failure	Read discrete encodings through erasure-error-vs-pauli-error, but carry the full end-to-end efficiency budget into every architecture column
Detector inefficiency	No click, indistinguishable from upstream loss at the detector alone	Located erasure only when redundant outcomes or a protocol-level acceptance test expose it	Do not credit an encoding with erasure tolerance without specifying its detector and heralding model
Dark counts or multiphoton contamination	A false click or an apparently valid outcome with the wrong photon number	Usually an unflagged logical or measurement fault, not an erasure	Route through noise-bias-and-asymmetric-error-channels rather than folding all source and detector defects into a single loss percentage
Spectral, temporal, polarization, or spatial mismatch	Photons arrive, but interference visibility and fusion fidelity fall	Coherent or stochastic gate error unless a separate mode-quality test rejects the event	This is the shared bottleneck for KLM, cluster-state, and fusion columns even when transmission loss is low
Finite squeezing in continuous-variable-photonic-qubit	Analog quadrature displacement accumulates through the cluster	Continuous Gaussian noise until a GKP-like layer discretizes it	Use bosonic-code-hierarchy; do not import the discrete single-photon erasure story unchanged

This separation also explains why component records do not multiply into architectural maturity. Better transmission helps the first row, but cannot repair distinguishability, false outcomes, or finite-squeezing noise. Conversely, a high-visibility fusion experiment does not establish that source-to-detector loss is sufficiently localized for an erasure-aware threshold calculation. The relevant threshold claim must state which failures are flagged, where they are located, and which residual faults remain unheralded.

Where the umbrella note belongs

• photonic-qubit should be the family entry point, not a peer competitor to the more specific notes. Use it when the question is simply why photons are attractive at all: low transport decoherence, room-temperature optics, and natural network compatibility.
• Hand off from photonic-qubit to dual-rail-photonic-qubit, time-bin-photonic-qubit, polarization-photonic-qubit, or frequency-bin-photonic-qubit when the real comparison is the discrete encoding degree of freedom.
• Hand off to continuous-variable-photonic-qubit when the carrier is an oscillator quadrature rather than a two-level single-photon subspace.
• Hand off from photonic-qubit to linear-optical-photonic-qubit, photonic-cluster-state-mbqc-qubit, or fusion-based-photonic-qubit when the real comparison is the scaling architecture.
• Once the question stops being optical-hardware-specific and becomes, “what does flagged loss buy the decoder?”, cross over to cross-platform-moc through erasure-qubit instead of repeating decoder logic inside this family.