A debate that has been raging for 20 years about whether a certain interaction between photons can be used in quantum computing has taken a new twist, thanks to two physicists in Canada. The researchers have shown that it should be possible to use “cross-Kerr nonlinearities” to create a cross-phase (CPHASE) quantum gate. Such a gate has two photons as its input and outputs them in an entangled state. CPHASE gates could play an important role in optical quantum computers of the future.

Photons are very good carriers of quantum bits (qubits) of information because the particles can travel long distances without the information being disrupted by interactions with the environment. But photons are far from ideal qubits when it comes to creating quantum-logic gates because photons so rarely interact with each other.

One way around this problem is to design quantum computers in which the photons do not interact with each other. Known as “linear optical quantum computing” (LOQC), it usually involves preparing photons in a specific quantum state and then sending them through a series of optical components, such as beam splitters. The result of the quantum computation is derived by measuring certain properties of the photons.

Simpler quantum computers

One big downside of LOQC is that you need lots of optical components to perform basic quantum-logic operations – and the number quickly becomes very large to make an integrated quantum computer that can perform useful calculations. In contrast, quantum computers made from logic gates in which photons interact with each other would be much simpler – at least in principle – which is why some physicists are keen on developing them.

This recent work on cross-Kerr nonlinearities has been carried out by Daniel Brod and Joshua Combes at the Perimeter Institute for Theoretical Physics and Institute for Quantum Computing in Waterloo, Ontario. Brod explains that a cross-Kerr nonlinearity is a “superidealized” interaction between two photons that can be used to create a CPHASE quantum-logic gate.

This gate takes zero, one or two photons as input. When the input is zero or one photon, the gate does nothing. But when two photons are present, the gate outputs both with a phase shift between them. One important use of such a gate is to entangle photons, which is vital for quantum computing.

The problem is that there is no known physical system – trapped atoms, for example – that behaves exactly like a cross-Kerr nonlinearity. Physicists have therefore instead looked for systems that are close enough to create a practical CPHASE. Until recently, it looked like no appropriate system would be found. But now Brod and Combes argue that physicists have been too pessimistic about cross-Kerr nonlinearities and have shown that it could be possible to create a CPHASE gate – at least in principle.

From A to B via an atom

Their model is a chain of interaction sites through which the two photons propagate in opposite directions. These sites could be pairs of atoms, in which the atoms themselves interact with each other. The idea is that one photon “A” will interact with one of the atoms in a pair, while the other photon “B” interacts with the other atom. Because the two atoms interact with each other, they will mediate an interaction between photons A and B.

Unlike some previous designs that implemented quantum error correction to protect the integrity of the quantum information, this latest design is “passive” and therefore simpler.

Brod and Combes reckon that a high-quality CPHASE gate could be made using five such atomic pairs. Brod told physicsworld.com that creating such a gate in the lab would be difficult, but if successful it could replace hundreds of components in a LOQC system.

As well as pairs of atoms, Brod says that the gate could be built from other interaction sites such as individual three-level atoms or optical cavities. He and Combes are now hoping that experimentalists will be inspired to test their ideas in the lab. Brod points out that measurements on a system with two interaction sites would be enough to show that their design is valid.

The work is described in Physical Review Letters. Brod and Combes have also teamed-up with Julio Gea-Banacloche of the University of Arkansas to write a related paper that appears in Physical Review A. This second work looks at their design in more detail.