# Photonic qubits

**Photonic qubits** encode quantum information in the degrees of freedom of single photons, most commonly polarization, path, or time-bin, and use linear optical elements like beamsplitters and phase shifters to implement gates. Unlike matter-based qubits, photons barely interact with their environment, which makes them nearly immune to decoherence during flight and a natural choice for quantum communication. It also makes them hard to compute with, since two-qubit gates normally need photons to interact with each other, and photons don't interact directly.

The standard workaround is the KLM scheme (Knill-Laflamme-Milburn), which achieves effective two-photon interactions using only linear optics, single-photon sources and detectors, and measurement-induced nonlinearity: an entangling gate is implemented probabilistically, and a heralding measurement tells you whether it succeeded. An alternative approach, continuous-variable photonics, encodes information in the quadratures of the electromagnetic field rather than in discrete photon number, using squeezed light and homodyne detection instead of single-photon counting.

For a single optical mode, the free evolution is generated by the harmonic oscillator Hamiltonian of the field itself:

$$H = \hbar\omega\left(a^\dagger a + \frac{1}{2}\right)$$

where $a^\dagger$ and $a$ are the photon creation and annihilation operators for a mode of frequency $\omega$. Linear optical elements act as passive transformations on these mode operators (beamsplitters mix pairs of modes, phase shifters rotate a single mode), and it is the combination of these passive transformations with photon-number-resolving measurement that produces the effective nonlinear, entangling gates a photonic quantum computer needs.

## Where photonics fits

Photonic qubits are the natural medium for quantum networking and distributing entanglement between distant quantum processors, since photons are the only qubit type that travels well through fiber or free space. Companies building photonic quantum computers (e.g. PsiQuantum, Xanadu) generally pair single-photon or squeezed-light sources with large-scale integrated silicon photonic chips and measurement-based computation rather than the gate-by-gate circuit model used on matter qubits.