The KLM Linear-Optics Scheme

The Knill-Laflamme-Milburn scheme shows that scalable quantum computing is possible with single photons, linear optics, and measurement, despite the lack of photon-photon interaction.

The Central Obstacle

Photons make ideal carriers of quantum information but they do not interact with one another in ordinary linear optical elements such as beam splitters and phase shifters. A deterministic two-qubit gate seems impossible without a nonlinearity. In 2001 Knill, Laflamme, and Milburn proved otherwise: measurement itself can supply an effective nonlinearity, and this is enough, in principle, for universal quantum computation.

Measurement-Induced Nonlinearity

The key insight is that when photons pass through an interferometer and some output modes are measured, the act of detecting a specific photon-number pattern projects the remaining photons into an entangled state that could not be produced by linear optics alone. Ancilla photons and photon-counting detectors thus enable gates such as the controlled-sign gate. These gates succeed only for certain measurement outcomes, so they are nondeterministic.

• Beam splitters, phase shifters, and detectors are the only components.
• Ancilla photons plus number-resolving detection create the effective nonlinearity.
• Gates are heralded: a specific detection pattern signals success.

From Probabilistic to Near-Deterministic

A gate that works only sometimes is not directly useful, so KLM introduced quantum teleportation of gates. By preparing entangled ancilla resources offline and teleporting the gate onto the data qubits, a probabilistic gate can be made to succeed with high probability, and failures become detectable and correctable. Adding more ancillas pushes the success probability arbitrarily close to one, at a large resource cost.

Legacy

The original KLM protocol is resource-hungry, but it changed the field by proving linear optics is a viable route to quantum computing. Modern photonic architectures descend from it, often combining its gate-teleportation ideas with the measurement-based cluster-state model to reduce overhead. The overhead in ancillas and multiplexing remains the practical challenge, but the possibility question was settled by KLM.