In short

A photon can carry a qubit in four standard encodings: polarisation (|H\rangle vs |V\rangle), path or dual-rail (|L\rangle vs |R\rangle — which arm of an interferometer), time-bin (photon arrived early vs late), and frequency mode (different colours). All four encodings are interchangeable by linear optical elements. Sources: parametric down-conversion (a pump photon splits into signal + idler, probabilistic, ~1% efficient); quantum dots (on-demand single-photon emitters, >70% efficiency on the best 2024 devices); single-atom emission (deterministic but slow). Single-qubit gates: beam splitters and phase shifters implement arbitrary SU(2) rotations on a dual-rail photon — exactly and trivially. Two-qubit gates: photons don't interact with each other, so you can't build a CNOT from linear optics alone. The 2001 Knill-Laflamme-Milburn (KLM) protocol solves this with ancilla photons + measurement: probabilistic gates that succeed with fixed probability and can be teleported into determinism using resource states. Measurement: superconducting nanowire single-photon detectors (SNSPDs) reach >95% efficiency; photon-number-resolving detectors count how many photons arrived. 2024 state of the art: USTC Jiuzhang 3.0 boson-sampling machine (255 squeezed modes, supremacy-scale sampling). PsiQuantum targeting a million-qubit silicon-photonics fault-tolerant machine by the late 2020s. Xanadu Borealis: first fully programmable photonic quantum computer, 216 squeezed modes. Photonic QC's advantages: room-temperature operation (no fridge), natural networking over fibre, no in-flight decoherence. Disadvantages: photon loss, probabilistic gates, resource-intensive KLM overhead.

Every other hardware platform in the QC book has one thing in common: the qubit lives in a massive particle. A superconducting transmon is an electron pair in a circuit. A trapped ion is a single charged atom. A neutral atom is a neutral charged atom. A spin qubit is a nuclear or electronic spin in a solid. All of them have rest mass, all of them sit somewhere in space, all of them have to be cooled.

Photonic quantum computing makes a different choice: the qubit is a photon. A single quantum of light, travelling at c, massless, bosonic, and — importantly — barely interacting with anything as it flies. Your qubit doesn't sit in a vacuum chamber; it zips through an optical fibre or a silicon waveguide on the way to its next gate.

This sounds magical until you remember what gates are for. A CNOT requires the target qubit's behaviour to depend on the control qubit's state. In the massive-particle platforms, this is done by letting the two qubits interact — Coulomb repulsion between ions, capacitive coupling between transmons, Rydberg blockade between atoms. Photons, sadly, barely interact with each other at all. A laser beam can pass through another laser beam with essentially zero cross-talk; two photons in a fibre ignore each other. That is wonderful for transmission — it is why photons are the basis of the internet — but terrible for building a CNOT.

The Knill-Laflamme-Milburn (KLM) paper of 2001 solved this in a way nobody had expected. You can build a universal quantum computer from photons alone, using nothing but beam splitters, phase shifters, and single-photon detectors — if you allow your gates to be probabilistic and repair them with measurement and ancilla photons. A modern photonic quantum computer is built on this trick, dressed up in clever resource-state protocols that amplify probabilistic gates into near-deterministic ones. PsiQuantum is betting that silicon photonics — the same fabrication base as modern CMOS chips — can scale this to a million qubits.

This chapter is the photonic playbook. How to encode a qubit in a photon. How to generate one. How to gate one. Why KLM is the break-through. Where the technology stands in 2026.

Encoding a qubit in a photon

A qubit is two orthogonal states with a controllable superposition. A photon has several degrees of freedom that come in pairs, and any one of them can host a qubit. Four standard choices.

Polarisation

A photon's electric field oscillates in a plane perpendicular to its direction of travel. Pick two orthogonal directions in that plane — horizontal and vertical — and call them |H\rangle and |V\rangle. A general polarisation state is

|\psi\rangle = \alpha |H\rangle + \beta |V\rangle, \quad |\alpha|^2 + |\beta|^2 = 1.

This is the canonical textbook qubit. Polariser plates, half-wave plates, and quarter-wave plates implement single-qubit gates directly and exactly. Polarisation is what every BB84 QKD demo uses.

Path (dual-rail)

Send a photon into an interferometer with two arms — left and right. The photon is a superposition of being in the left arm and the right arm:

|\psi\rangle = \alpha |L\rangle + \beta |R\rangle.

"Dual-rail" means the qubit is encoded in which of two modes the photon occupies, with exactly one photon total. Beam splitters mix the two modes; phase shifters on one arm change the relative phase. This is the encoding most often used in integrated-photonics quantum processors (PsiQuantum's silicon-photonics chips).

Time-bin

Chop the photon arrival time into two windows: an "early" slot at t_0 and a "late" slot at t_1 = t_0 + \Delta t. Encode

|\psi\rangle = \alpha |\text{early}\rangle + \beta |\text{late}\rangle.

Time-bin qubits are robust over long fibre links (they don't depolarise the way polarisation can), and are used in most real-world QKD deployments. They need an unbalanced Mach-Zehnder interferometer to create the superposition and a matching one at the receiver to measure it.

Frequency mode

The photon's colour. Pick two frequencies \omega_0 and \omega_1 and encode |\psi\rangle = \alpha |\omega_0\rangle + \beta |\omega_1\rangle. Frequency qubits are the newest encoding — practical mainly since high-quality electro-optic modulators that can coherently mix frequencies became available.

Four photonic qubit encodingsA diagram showing four ways to encode a qubit in a photon, arranged in a two by two grid: polarisation with horizontal and vertical arrows, path with two waveguides, time bin with two pulse envelopes at different times, and frequency with two coloured peaks at different frequencies.Four photonic qubit encodingsPolarisation|H⟩|V⟩Path (dual-rail)|L⟩upper modelower modeTime bintearly (t₀)late (t₁)Frequencyωω₀ω₁
The four standard encodings. Polarisation uses the transverse field direction. Path (dual-rail) uses which of two waveguides or beams holds the photon. Time-bin uses which of two arrival windows. Frequency uses which of two colours. They are physically different but mathematically equivalent: beam splitters, polarising beam splitters, unbalanced Mach-Zehnders, and electro-optic modulators can convert any encoding into any other.

Second-quantisation view

Formally, all four encodings are modes of the electromagnetic field. A single photon in mode a is the Fock state |1\rangle_a \otimes |0\rangle_b; a single photon in mode b is |0\rangle_a \otimes |1\rangle_b. Call these |10\rangle and |01\rangle — or |L\rangle and |R\rangle, |H\rangle and |V\rangle, etc. A dual-rail qubit is the pair of modes with exactly one photon shared between them. This is called a dual-rail encoding precisely because two modes "rail" the photon's identity. Why: dual-rail is the natural language of linear optics. Beam splitters act on pairs of modes; a linear optical network is a unitary on the mode-space, which maps dual-rail qubits to dual-rail qubits in a straightforward way.

Generating single photons

To do quantum computing with photons, you need a source that emits exactly one photon at a time, on demand, with high rate and high indistinguishability. This is harder than it sounds. Three approaches.

Parametric down-conversion

A high-frequency pump laser illuminates a nonlinear crystal (BBO, PPKTP, lithium niobate). Occasionally — with small probability per pulse, typically \sim 1\% — one pump photon splits into two lower-frequency photons, conventionally called signal and idler. Energy conservation (\omega_p = \omega_s + \omega_i) and phase matching fix their frequencies. Momentum conservation fixes their emission directions.

Detecting the idler heralds the signal: if you see the idler photon, you know the signal was emitted too, and you can use it as your single-photon input. Parametric down-conversion (PDC) is probabilistic — you can't demand a photon; you can only wait for one. It is also intrinsically photon-pair-generating, which is useful for entanglement but wasteful for deterministic single-photon logic.

Typical rates: 10^6 pair detections per second from a few mW of pump power.

Quantum dots

Semiconductor nanostructures (InGaAs quantum dots grown in a GaAs matrix, typically ~10 nm in size) act as artificial atoms. They have a single ground state and a single bright exciton excited state; optical excitation followed by spontaneous emission yields exactly one photon per excitation pulse. With modern cavity engineering (micropillar cavities, photonic-crystal waveguides), the emission is deterministic, bright (>70% of pulses produce a usable photon in 2024 devices), and highly indistinguishable.

Quantum dots are the leading deterministic single-photon source for photonic QC. The Bristol, Würzburg, and Copenhagen groups have demonstrated quantum-dot sources feeding multi-photon experiments at rates that PDC cannot match.

Trapped atom / ion emission

A single trapped atom or ion emits exactly one photon per excitation cycle. The emission is deterministic and can be tailored (via Purcell enhancement in a cavity) to be indistinguishable. The downside: slow (μs per emission cycle) and the overall throughput is limited by the atomic repetition rate. This is the approach used for quantum-network experiments (atom-to-atom entanglement via shared photons).

Parametric down-conversion sourceA schematic showing a pump laser beam entering a nonlinear crystal and splitting into two output beams, labelled signal and idler, diverging at equal angles. A detector on the idler beam heralds the signal photon.Heralded single-photon generation via parametric down-conversionpump (405 nm)χ⁽²⁾nonlinearcrystalsignal (810 nm)idler (810 nm)Dheralding click→ signal output
A high-frequency pump photon (blue, 405 nm) enters a nonlinear crystal. A small fraction of the pump splits into a signal-idler pair of lower-frequency photons (both 810 nm in a degenerate configuration). Detecting the idler heralds the signal — you know a single photon is in the signal arm ready for use. Rate is set by pump power and crystal efficiency: ~10$^6$ heralded photons per second is routine.

Linear optics — single-qubit gates

Given a dual-rail photon (one photon shared between two modes), the full set of single-qubit gates is implemented by beam splitters and phase shifters.

Beam splitter

A beam splitter is a semi-transparent mirror that takes two input modes and produces two output modes. In the second-quantisation picture, a lossless beam splitter with reflectivity r and transmittivity t = \sqrt{1-r^2} acts as

\begin{pmatrix} a'_\text{out} \\ b'_\text{out} \end{pmatrix} = \begin{pmatrix} t & r \\ -r & t \end{pmatrix} \begin{pmatrix} a_\text{in} \\ b_\text{in} \end{pmatrix}.

For a 50:50 beam splitter (r = t = 1/\sqrt 2), this is the Hadamard gate on a dual-rail qubit — it sends |10\rangle \to (|10\rangle - |01\rangle)/\sqrt 2 and |01\rangle \to (|10\rangle + |01\rangle)/\sqrt 2.

Phase shifter

A phase shifter on one mode multiplies the amplitude of a photon in that mode by e^{i\phi}. On a dual-rail qubit with \phi applied to the second mode, this is the R_z(\phi) gate — a rotation about the z axis of the Bloch sphere.

Arbitrary single-qubit gates

Any SU(2) rotation can be decomposed into three phase shifters and two beam splitters (a Mach-Zehnder interferometer bracketed by phase shifters). Every single-qubit gate on a dual-rail photon is implementable exactly with linear optics. No approximation, no probability, no overhead.

This is a remarkable property. Compare to ions (where single-qubit gates are laser pulses with calibration overhead) or transmons (where they are microwave pulses with timing constraints): photonic single-qubit gates are passive optical elements. Once built, they run forever with zero control overhead.

Example 1: Polarisation qubit and a 50:50 beam-splitter rotation

Let a polarisation qubit |\psi\rangle = \alpha |H\rangle + \beta |V\rangle enter a polarising beam splitter (PBS) followed by a half-wave plate (HWP). Show that this can implement a Hadamard gate.

Step 1. Write the PBS action. A PBS transmits |H\rangle and reflects |V\rangle, separating them into two spatial modes. After the PBS, we can relabel: |H\rangle \to |L\rangle (left arm), |V\rangle \to |R\rangle (right arm). So the polarisation qubit has been converted into a dual-rail (path) qubit. Why: PBS is the standard tool for converting between polarisation and path encodings. It's a clean unitary in both directions.

Step 2. Apply a 50:50 beam splitter that combines the two paths. The BS matrix is

B = \frac{1}{\sqrt 2} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}.

This is exactly the Hadamard matrix. Why: a 50:50 beam splitter with the right phase convention implements H on the path qubit. This is not a coincidence — the algebraic structure of linear optics on two modes is SU(2), same as single-qubit gates.

Step 3. Apply to our state. Starting from |\psi\rangle = \alpha |L\rangle + \beta |R\rangle (after the PBS):

B|\psi\rangle = \frac{1}{\sqrt 2} \big[(\alpha + \beta) |L\rangle + (\alpha - \beta)|R\rangle\big].

For input |L\rangle (i.e. \alpha = 1, \beta = 0), output is (|L\rangle + |R\rangle)/\sqrt 2 — a |+\rangle state. For input |R\rangle, output is (|L\rangle - |R\rangle)/\sqrt 2 — a |-\rangle state. Why: H|0\rangle = |+\rangle and H|1\rangle = |-\rangle — the Hadamard turns computational-basis states into X-basis states. The beam splitter does exactly this on a path-encoded qubit.

Step 4. Convert back to polarisation. Another PBS combines the two paths into a common beam with polarisation encoding the superposition. After this conversion, |L\rangle \to |H\rangle and |R\rangle \to |V\rangle, so the output is \alpha' |H\rangle + \beta' |V\rangle with \alpha' = (\alpha + \beta)/\sqrt 2, \beta' = (\alpha - \beta)/\sqrt 2. Why: the combined transformation PBS-BS-PBS on polarisation is the same Hadamard unitary. You can equivalently implement the Hadamard on polarisation directly using a half-wave plate oriented at 22.5° — either works.

Step 5. Check with a half-wave plate alternative. An HWP oriented at angle \theta implements a rotation by 2\theta in polarisation space. For \theta = 22.5°, the rotation is 45° and the unitary on \{|H\rangle, |V\rangle\} is exactly H. Why: the half-wave plate is the simplest single-element Hadamard gate for polarisation. No beam splitters, no interferometry, no alignment. Just one plate.

Result. A Hadamard on a photonic qubit is trivial — a beam splitter, or a half-wave plate, or a sequence of path-polarisation converters. All are exact, lossless in principle, with no control overhead.

Beam splitter Hadamard on a dual-rail photonA schematic of a 50:50 beam splitter with two input modes and two output modes. A photon entering the upper mode produces an equal superposition on the two output modes.50:50 beam splitter = Hadamard on a path qubit|L⟩ in|R⟩ inBS(|L⟩+|R⟩)/√2(|L⟩−|R⟩)/√2photon
A 50:50 beam splitter on two input modes implements the Hadamard gate on a dual-rail qubit. Entering $|L\rangle$ gives an equal superposition of the two output modes with a + relative phase; entering $|R\rangle$ gives the superposition with a $-$ relative phase. This is exactly $H$ acting on $|0\rangle$ and $|1\rangle$.

What this shows. Photonic single-qubit gates are just linear optics. No calibration, no laser pulses, no timing. A static optical element realises the gate, exactly, every time. This is why photonic chips can run at GHz-equivalent clock rates once the sources and detectors keep up.

The problem: photons don't interact

Single-qubit gates are easy. Two-qubit gates are the roadblock.

A two-qubit gate like CNOT has to correlate the states of two photons: the second photon must evolve differently depending on the state of the first. For this to happen through a standard optical element, the two photons would have to interact — their electromagnetic fields would have to feel each other.

Photon-photon interaction in vacuum is absurdly weak (a fourth-order process in QED, cross-section \sim 10^{-65} m^2 for visible light). In a nonlinear medium (like a \chi^{(3)} Kerr crystal), it can be enhanced but remains tiny at the single-photon level — typical single-photon Kerr phase shifts are \sim 10^{-12}, whereas a CNOT needs \pi. There is no direct photon-photon gate you can simply build.

This was the conventional wisdom until 2001, when Knill, Laflamme, and Milburn proved something astonishing: linear optics + single-photon detectors + extra (ancilla) photons = universal quantum computation.

The KLM protocol

The KLM 2001 paper [arXiv:quant-ph/0006088] showed how to build a universal quantum computer from three ingredients, none of which involves nonlinear photon-photon interaction:

  1. Linear optical elements — beam splitters, phase shifters.
  2. Single-photon sources and ancilla photons — extra photons in known initial states.
  3. Single-photon detectors — and feedforward conditional on their outcomes.

The KLM idea is that measurement effectively introduces nonlinearity. A measurement collapses a joint superposition — that is a nonlinear operation on the quantum state, even though the optical elements doing the mixing are perfectly linear.

The probabilistic CZ gate

Here is the canonical KLM CZ (controlled-Z) gate. You have two dual-rail qubits (4 modes, 2 photons) and you add two ancilla photons (2 more modes, 2 more photons, initially in fixed states).

Pass all 6 modes through a specific linear-optical network (a specific beam-splitter-and-phase-shifter arrangement). Measure the two ancilla modes with photon detectors. If you see one specific measurement outcome (say, both detectors click once), you know that a CZ gate was successfully applied to the two input qubits. If you see a different outcome, the gate failed — the two qubits are no longer in a valid dual-rail encoding and must be discarded.

The probability of success for the canonical KLM CZ is p = 1/16.

KLM controlled-Z with ancilla photonsA schematic of a KLM style CZ gate. Two input photons enter on the left across four modes; two ancilla photons enter on two additional modes. All six modes pass through a linear optical network represented as a box labelled U. The two ancilla modes feed into detectors on the right; the four qubit modes exit on the right and proceed conditional on the detector pattern.KLM controlled-Z — linear optics + ancillas + measurementq₁ upperq₁ lowerq₂ upperq₂ loweranc₁anc₂Ulinear-opticalnetworkDDmeasureancillasclick pattern (1,1) → success (p = 1/16); other patterns → failure
The KLM CZ gate. Two qubits (4 modes, 2 photons) plus two ancillas (2 modes, 2 photons) enter a linear-optical network $U$. The ancilla modes are measured by single-photon detectors. If both detectors click exactly once — the "(1,1) outcome" — the qubits leaving have had a CZ gate applied to them. Any other click pattern means the gate failed. Success probability is $1/16$.

From probabilistic to deterministic

A 1/16 success probability is useless by itself — a 100-gate circuit would succeed with probability 1/16^{100}, which is zero. The KLM innovation is gate teleportation, a trick from measurement-based quantum computation that turns probabilistic gates into near-deterministic ones.

The idea: prepare the CZ gate ahead of time on a small ancilla resource state (a Bell pair or similar). If the off-line preparation succeeds (which you verify by measurement), you hold onto the resource state; if it fails, you discard and retry. Since the resource-state preparation is off-line — not blocking the main circuit — you can retry until it succeeds.

Once you have the successful resource state, you teleport the input qubits through it using standard Bell measurements. The teleportation step succeeds deterministically (up to simple Pauli corrections). The effective CZ gate is then deterministic at the cost of enormous resource-state overhead.

KLM originally showed this requires O(n^2) ancilla photons per gate at success probability 1 - 1/n, which is enormous but finite. Subsequent refinements (Nielsen 2004, Browne-Rudolph 2005) brought the overhead down to near-constant factors using cluster states as the universal resource. This is the foundation of modern photonic quantum computing, including PsiQuantum's architecture.

Example 2: KLM-style sign flip with ancilla photons

Design a specific linear-optical network that implements a sign flip (CZ) on two dual-rail qubits, conditioned on a measurement outcome.

Step 1. Set up the modes. Let the two qubits be encoded in modes \{a_1, a_2\} (qubit 1's lower, upper rails) and \{b_1, b_2\} (qubit 2's). Add ancilla modes c_1, c_2, each initially populated by a single photon. Total: 6 modes, 4 photons. Why: KLM-style gates always involve more photons in than qubits present, with the extras serving as ancillas whose measurement conditions the gate.

Step 2. Write the desired unitary. The CZ gate on qubits 1 and 2 has matrix \text{diag}(1, 1, 1, -1) on the computational basis \{|00\rangle, |01\rangle, |10\rangle, |11\rangle\}. In the dual-rail Fock representation, |00\rangle = |a_2 b_2\rangle (photon in lower rails), |11\rangle = |a_1 b_1\rangle (photon in upper rails), etc. The gate flips the sign of the |a_1 b_1\rangle amplitude only. Why: the |11\rangle sign flip is what distinguishes CZ from identity, and it is the only nontrivial element.

Step 3. Construct the linear-optical network. KLM show that a specific 6-mode unitary U, built from ten beam splitters and phase shifters, produces the following property: after applying U to the joint state and measuring ancilla modes c_1, c_2, the outcome "both detectors see exactly one photon" occurs with probability 1/16, and conditional on that outcome, the qubit modes have undergone CZ. Why: by design. The KLM paper constructs U such that the ancilla-click pattern encodes which branch of the joint state the system collapsed into, and one specific branch carries the desired CZ.

Step 4. Measure the ancillas. Two superconducting-nanowire detectors (SNSPDs) on c_1, c_2 register photon counts.

  • Outcome (1,1): success, CZ applied. Probability 1/16. Continue the computation.
  • Outcome (0,0), (2,0), (0,2), (1,0), (0,1): failure. Probability 15/16. Discard.

Why: detection is the nonlinear step. A heralding detector click collapses the joint state onto one branch; the probability is set by the amplitude structure that U was designed to produce.

Step 5. Boost to determinism. Use the KLM gate-teleportation trick: pre-prepare the CZ gate off-line on a Bell-pair resource state (retry until success), then teleport the qubits through it using a deterministic Bell measurement. The resulting gate is deterministic at the cost of O(n^2) ancilla photons per effective CZ — reduced to near-constant overhead using cluster-state encoding (Browne-Rudolph). Why: the off-line preparation decouples the probabilistic step from the main circuit. Failure is cheap (discard resource, try again); success is reused (apply to many circuits).

Result. A single KLM CZ succeeds 1/16 of the time; with teleportation boosting, the overhead can be made constant in circuit depth but is large (in practice, each logical CZ might use hundreds of ancilla photons after boosting and error correction).

KLM gate teleportation schematicA flowchart diagram with an off-line resource preparation block on the left, showing repeated probabilistic attempts until success, feeding a stored resource state into a Bell measurement with an input qubit on the right, producing a deterministic output.Probabilistic gate → deterministic via teleportation boostingOff-line resource preprun KLM gate on ancillasretry until successstore successful stateBell measurementinput qubit + resource→ teleportation outcomedeterministicPauli correction→ effective CZ
The boosting protocol. The probabilistic KLM gate runs off-line on ancilla photons, retrying until success. Once a good resource state is ready, the input qubit is teleported through it via a Bell measurement; a classical correction completes the effective CZ. The expensive retries happen out of line with the main computation, so the main circuit runs deterministically.

What this shows. The measurement-boosting trick is the heart of KLM and, by extension, of all modern photonic architectures. Nothing in a photonic quantum computer is deterministic at the physical level — every gate is a post-selected event. What makes computing work is that resource-state preparation and teleportation decouple the probabilistic events from the circuit execution path.

Measurement — single-photon detectors

Photon counting, once a niche precision-physics technique, is now a mature, high-efficiency technology.

Superconducting nanowire single-photon detectors (SNSPDs)

A superconducting nanowire, cooled to ~2 K, is biased just below its critical current. A single absorbed photon heats a local region above the critical temperature, producing a voltage pulse. SNSPDs reach >95% detection efficiency, <100 ps timing jitter, and <10 Hz dark counts — the best single-photon detectors ever built. Quantinuum, PsiQuantum, and every serious photonic-QC effort uses SNSPDs.

Photon-number-resolving detectors

A more demanding capability: not just "did a photon arrive?" but "how many photons arrived?" Required for some photonic protocols (boson sampling, photon-counting error correction). Realised via arrays of SNSPDs (each bin resolves 0 vs 1; the array counts total) or by transition-edge sensors (TES), which directly count photons via calorimetric heating. Efficiency up to 98% at the best.

Single-photon avalanche diodes (SPADs)

The consumer-grade option: silicon or InGaAs SPADs at room temperature or modest cooling. Efficiency 50-70%, timing jitter ~50 ps. Good enough for QKD over metro-distance fibre.

PsiQuantum — the million-qubit bet

PsiQuantum (founded 2016, headquartered in Palo Alto, with major operations at GlobalFoundries' New York fab) is the most ambitious photonic-QC company. Their thesis: silicon photonics + fault-tolerant architecture + KLM-style protocols = the first million-physical-qubit quantum computer.

The technology stack

The bet

PsiQuantum's argument is that photonic QC's "scale problem" — enormous ancilla-photon overhead per effective gate — is solvable by standard chip fabrication. A silicon-photonic chip with 10^6 components is not in principle different from a silicon CMOS chip with 10^{10} components. If the company can build chips with uniform, low-loss waveguides, efficient sources, and efficient detectors at wafer scale, the KLM overhead becomes a matter of chip area, not fundamental physics.

As of 2026

PsiQuantum has demonstrated: integrated silicon-photonic sources and detectors at wafer scale; single-chip experiments showing high-fidelity single-qubit gates; multi-chip experiments showing fibre interconnects. The company targets a fault-tolerant machine — not a NISQ demo — and has published a roadmap targeting 1 million physical qubits by the late 2020s. Execution is uncertain; the technology risks are real (losses in silicon waveguides, source efficiencies, classical control complexity); but no other photonic-QC effort has the same scale of industrial backing.

Boson sampling — a separate photonic milestone

Not every photonic experiment is aimed at universal computation. Boson sampling (Aaronson-Arkhipov 2011, covered in chapter 102) is a non-universal quantum-advantage demonstration that uses photons passing through a large linear-optical network. The output photon-number distribution is classically hard to sample but trivial to measure on the quantum side.

USTC's Jiuzhang 3.0 (2023) and Xanadu's Borealis (2022) are the leading boson-sampling demonstrators, both claiming quantum computational supremacy on specific sampling tasks. These machines are not universal — you can't run Shor on them — but they are important proofs that photonic quantum processors at scale are achievable and can outperform classical simulation in their target domain.

Advantages and disadvantages of photonic QC

Advantages

Disadvantages

Indian context

Raman Research Institute, Bangalore has run photonic quantum-optics experiments for decades. Urbasi Sinha's group at RRI conducts entanglement experiments with photon pairs from PDC, and has done foundational Bell-inequality tests — a direct continuation of C.V. Raman's legacy in India's optics tradition.

IIT Madras (Prof. Anil Prabhakar and colleagues) runs a photonic quantum-information programme focused on integrated photonics and quantum key distribution. The institute has demonstrated free-space BB84 over kilometre-scale links.

ISRO is running a satellite-QKD programme: the 2022–2024 experiments sent entangled photon pairs between a ground station in Bangalore and a satellite in low Earth orbit — a demonstration of truly long-distance photonic entanglement. India's satellite-QKD work places it as one of four countries with active efforts (alongside China, Austria, and the UK).

National Quantum Mission funding (2023, ₹6000 crore) earmarks significant support for photonic quantum technologies under both the computing and communication pillars.

Common confusions

Going deeper

If you understand that a photon can carry a qubit in polarisation, path, time-bin, or frequency, that single-qubit gates are implemented exactly by linear optical elements (beam splitters, phase shifters, wave plates), that photons don't interact with each other so two-qubit gates require the 2001 KLM trick of measurement-induced nonlinearity with ancilla photons (probabilistic gates boosted to near-deterministic via teleportation), that modern single-photon sources (quantum dots, PDC) and detectors (SNSPDs at >95% efficiency) make all of this practical, and that PsiQuantum is betting silicon photonics can scale this to a million qubits while Jiuzhang and Borealis demonstrate boson-sampling supremacy — you have chapter 168. What follows is the linear-optics formalism in detail, the KLM CZ construction, cluster-state-based computation, PsiQuantum's FBQC architecture, and single-photon source engineering.

Linear optics formalism

A linear optical network on N modes is described by an N \times N unitary matrix U acting on the mode operators:

a'_i = \sum_j U_{ij}\, a_j.

The network is physically decomposable into beam splitters (acting on pairs of modes) and phase shifters (acting on single modes). The Reck-Zeilinger decomposition (1994) shows that any N \times N unitary can be implemented by a triangular array of N(N-1)/2 Mach-Zehnder interferometers — the network is universal over linear optics.

At the single-photon level, a state with n photons distributed across N modes transforms as

a_{i_1}^\dagger \cdots a_{i_n}^\dagger |0\rangle \;\to\; \sum_{j_1, \ldots, j_n} U_{i_1 j_1} \cdots U_{i_n j_n}\, a_{j_1}^\dagger \cdots a_{j_n}^\dagger |0\rangle.

This is the basis of boson sampling: computing the output probability of a specific photon pattern requires evaluating a permanent of the n \times n submatrix of U, which is \#P-hard classically.

KLM CZ construction

The original KLM CZ gate uses a 6-mode network of 10 beam splitters and phase shifters. The key fact (proved algebraically in the 2001 paper): there exists a specific 6-mode unitary U_{\text{KLM}} such that

\text{Pr}(n_{c_1} = 1, n_{c_2} = 1 \mid \text{input} = |q_1 q_2\rangle \otimes |1_{c_1} 1_{c_2}\rangle) = \frac{1}{16}

independent of |q_1 q_2\rangle, and conditional on that outcome the reduced state of the qubits is \text{CZ}|q_1 q_2\rangle. The beam-splitter reflectivities were originally 1/3 and (1+\sqrt 2)^{-1}, but subsequent work (Ralph-Pryde 2010) showed the same gate can be built with 50:50 beam splitters at slightly different success probabilities.

Cluster states and measurement-based photonic QC

The cluster state (Raussendorf-Briegel 2001) is a specific multi-qubit entangled resource state with the property that single-qubit measurements on a cluster can implement any unitary. For photonic QC, the cluster state is prepared off-line using probabilistic KLM-style gates, then the computation proceeds by single-photon measurements along a path through the cluster. Success probability of the cluster preparation is low but can be boosted; once prepared, the actual computation is deterministic.

Browne-Rudolph (2005) showed that cluster states can be built up linearly with constant overhead per photon — a huge improvement over the original KLM O(n^2) overhead. This result is the foundation of modern photonic MBQC and of PsiQuantum's architecture.

PsiQuantum's fusion-based architecture (FBQC)

PsiQuantum uses fusion-based quantum computation (Bartolucci et al. 2021), a refinement of cluster-state MBQC designed for silicon-photonic implementation. The architecture:

The upshot: a photonic quantum computer is a machine that continuously produces small entangled states, attempts fusions, and routes successful fusions into a growing computation. The architecture is fundamentally probabilistic and loss-tolerant — unlike gate-based architectures, where a single lost photon ruins the whole computation.

Single-photon source engineering

The holy grail is a deterministic, indistinguishable, bright single-photon source. State-of-the-art quantum-dot sources (2024):

For PsiQuantum-scale experiments, 10^6 or more photons per gate means source arrays with \geq 10^9 emitters/s per chip — feasible with on-chip integration but demanding on uniformity.

Where this leads next

References

  1. Emanuel Knill, Raymond Laflamme, and Gerard J. Milburn, A scheme for efficient quantum computation with linear optics (2001), Nature — arXiv:quant-ph/0006088.
  2. Pieter Kok et al., Linear optical quantum computing with photonic qubits (2007), Reviews of Modern Physics — arXiv:quant-ph/0512071.
  3. Sara Bartolucci et al., Fusion-based quantum computation (2021) — arXiv:2101.09310.
  4. Wikipedia, Linear optical quantum computing.
  5. PsiQuantum, Technology overview — psiquantum.com.
  6. John Preskill, Lecture Notes on Quantum Computation, Chapter 7 — theory.caltech.edu/~preskill/ph229.