Photonic quantum computing

Photonic quantum computing encodes quantum bits in single photons and processes them with linear optical elements (beam splitters, phase shifters, waveplates) together with single-photon detection. Photons interact weakly with their surroundings, so a photonic qubit keeps its coherence at room temperature; for the same reason photons barely interact with each other, so two-qubit gates must be built from interference and measurement, and they succeed only with some probability. Loss is the dominant error: if each photon reaches its detector with probability 0.9, an event that needs all 20 photons happens in only 12% of attempts.

Photonic qubits

Three encodings are common. A polarization qubit uses $|H\rangle$ and $|V\rangle$ and is manipulated with waveplates. A dual-rail or path qubit places one photon in one of two waveguides, $|1,0\rangle$ or $|0,1\rangle$; a Mach-Zehnder interferometer with a phase shifter applies any single-qubit rotation, and meshes of them implement arbitrary linear transformations on many modes. A time-bin qubit uses an early and a late pulse, which suits fiber transmission.

Linear optics plus measurement

Knill, Laflamme and Milburn (KLM, 2001) showed that linear optics, single-photon sources, detectors and feed-forward (changing later operations based on earlier detection results) suffice for universal quantum computing. Their gates are nondeterministic: an entangling operation succeeds when ancilla photons produce a particular detection pattern, and the success probability approaches 1 only as the number of ancilla photons grows. The simplest post-selected linear-optics controlled-Z gate succeeds with probability 1/9, and a Bell-state measurement with linear optics alone succeeds at most half the time. The probabilistic character follows from the linearity of the optics: two-photon interference on a beam splitter, the Hong-Ou-Mandel effect described under entangled photons, creates correlations between photons only conditionally on what the detectors record.

Measurement-based and fusion-based approaches

Rather than chaining probabilistic gates, most current architectures follow measurement-based quantum computing (Raussendorf and Briegel, 2001): prepare a large entangled cluster state, then compute by measuring photons one at a time in chosen bases. Browne and Rudolph (2005) showed that cluster states can be grown from small entangled pieces by "fusion" measurements that succeed with probability 1/2 and, on failure, leave a known, correctable defect. Fusion-based quantum computing (Bartolucci et al., 2023) generalizes this: small resource states of a few photons are generated repeatedly, and an error-correcting code is built directly into the pattern of fusion measurements, so that failed fusions and lost photons are handled as errors the code can tolerate up to a threshold.

Gaussian boson sampling

Boson sampling sends many photons through a large interferometer and records which outputs click. In Gaussian boson sampling, squeezed light replaces single photons as the input. Computing the output probabilities exactly is believed to be hard for classical computers, so large experiments have been used as demonstrations of quantum advantage, though improved classical simulation methods have challenged some of these claims.

Loss as the limiting resource

Because an $n$-photon computation usually needs every photon to survive, the success probability falls exponentially with photon number:

$$P_{\text{success}} = \eta^{\,n},$$

where $\eta$ is the total transmission per photon. With $\eta = 0.9$ (0.46 dB of loss) and $n = 20$, $P = 0.9^{20} \approx 0.12$. Raising $\eta$ to 0.99 gives 0.82. A more realistic budget multiplies source efficiency, circuit transmission and detector efficiency; with 0.9, 0.9 and 0.95 the per-photon figure is 0.77, and 20 photons all survive in only 0.53% of attempts. Fault-tolerant schemes tolerate some loss, but only below architecture-dependent thresholds, typically of order a few percent to about ten percent per photon, which is why every coupler, waveguide bend and fiber connection is budgeted in hundredths of a decibel.

Sources and detectors

Heralded sources based on spontaneous parametric down-conversion or four-wave mixing fire at random. If each of 10 sources produces a heralded photon with probability 0.05 per clock cycle, all 10 fire together with probability $0.05^{10} \approx 10^{-13}$, so many sources are multiplexed in time or space with fast switches to approach deterministic output. Quantum-dot single-photon sources emit on demand but must produce indistinguishable photons from separate emitters. Detection relies on superconducting nanowire detectors, with efficiencies above 90% in the best devices, low dark counts and timing jitter of tens of picoseconds; they operate at a few kelvin, so the cryogenic requirement comes from the detectors. Gaussian boson sampling experiments often add photon-number resolution, though threshold detectors also suffice.

Integrated platforms

Large interferometers are built as quantum photonic integrated circuits. Silicon nitride offers low propagation loss and a wide transparency window; silicon offers dense integration and pair generation by four-wave mixing; thin-film lithium niobate offers fast, low-loss electro-optic switching for multiplexing and feed-forward, plus efficient down-conversion in periodically poled waveguides. Fiber-to-chip and chip-to-chip coupling often dominate the loss budget.

Common questions

Why are photonic two-qubit gates probabilistic?

Linear optics conserves photon number and applies the same linear transformation to every photon, so photons cannot directly change each other's state. Entanglement appears only after a measurement selects the right outcome, which happens with probability below 1 unless extra ancilla photons and feed-forward are added.

Does a photonic quantum computer need cryogenics?

The photonic qubits work at room temperature. Superconducting nanowire detectors, and some quantum-dot sources, need cooling to a few kelvin.

Is boson sampling a quantum computer?

It is a restricted quantum device that samples from a distribution believed hard to simulate classically. It does not run general quantum algorithms.

References: E. Knill, R. Laflamme, G. J. Milburn, Nature 409, 46 (2001); R. Raussendorf, H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001); D. E. Browne, T. Rudolph, Phys. Rev. Lett. 95, 010501 (2005); P. Kok et al., Rev. Mod. Phys. 79, 135 (2007); C. S. Hamilton et al., Phys. Rev. Lett. 119, 170501 (2017); S. Bartolucci et al., Nat. Commun. 14, 912 (2023).