Connecting a network of small quantum computers.

We already have working prototypes of small quantum computers with a handful of qubits. This has been achieved on several different hardware platforms, including trapped ions and superconducting qubits. But so far, it has proven tricky to scale up to hundreds of qubits using the same techniques.

In the networked (also called distributed) approach to quantum technologies, one builds a network of connected nodes. The nodes themselves are built using one form of hardware and can be thought of as small quantum computers. The links between nodes could use a very different technology to the nodes. The goal could be to network small quantum computers to scale-up to a large quantum computer. Alternatively, if the nodes are separated by large distances, the technology would be used to establish a quantum communication network.

In both cases, the challenges are similar. The main one being, how we do generate high-quality entanglement over long distances. Entangled states are those that cannot be produced by classical communication and local quantum operations. Rather there has to be some form a quantum interaction between the two nodes, which is difficult over long distances.

Photons travel at the speed of light and so are the ideal quantum particle for creating entanglement. But photons have a tendency to go missing. This degrades the quality of the entanglement. Taking several copies of a weakly entangled quantum state, we can use entanglement distillation to convert this into a single high-quality entangled state. This can then form the basis of reliable quantum computation or communication.

My contribution to this field has been the development of new methods of entanglement distillation. In all my research projects, we have been using photons to generate the initial, noisy entanglement. The network could also be “all-optical” where the nodes also store quantum information using photons. Or we could have a hybrid network, where the nodes are made from matter qubits (e.g. trapped ions or NV-centers in diamond). My personal assessment is that a hybrid approach is more likely to be viable for quantum computation, but an all-optical approach might be better for quantum communication networks.

Hybrid matter-optical quantum computers

Designing architectures for hybrid matter-optical quantum computers was the topic of my PhD thesis under the supervision of Prof Simon Benjamin. Over my PhD, I came up with several different protocols for entanglement distillation in these setups, including:
IJQI 8 161 (2010)
Physical Review Letters 101 130502 (2008)
Physical Review A Rapid Communication 76 040302(R) (2007)
New Journal of Physics 9, 196 (2007)
Physical Review A 75, 042303 (2007)
With Joe Fitzsimons I also wrote an introduction to distributed quantum computing with some section based on my PhD thesis, which you can read here.

The Oxford-led NQIT quantum computing hub is the UK’s largest consortium working on quantum computing and is developing a hybrid network technology. I like to think that my PhD work helped this happen.

A highlight from these papers was our protocol for combatting photon loss. The advantage of this approach is that is can generate entanglement at a faster rate than competitor approahes (assuming loss is extreme, which it usually is). This work also deserved special mention because 9 years after publication, the protocol was experimentally realised by Ronald Hanson’s group in Delft. Read about the experiment in Science and the original proposal in Physical Review Letters 101 130502 (2008).

At the time we were mostly thinking about the measurement based model of quantum computation. Consequently, most of my papers from that period are phrased in that language, but the ideas are more generally applicable.

Renormalisation entanglement distillation

Entanglement distillation uses many copies of a noisy entangled state, but generally assumes there are no correlations between these copies (the i.i.d assumption). There are several “de Finetti” style methods for trying to discard these correlations. However, sometimes the correlations may even be useful and it is wasteful to discard them. With collaborators in Berlin, we applied the techniques of MPS (Matrix Product States) to track these correlations and showed when distillation was still possible.
Phys. Rev. Lett 116 020502 (2016)

Continous-variable entanglement distillation

There are many ways to store quantum information or entanglement in a photonic system. A photon is really an oscillating electromagnetic-field. In continuous-variable approaches, information is stored in the electric and magnetic fields. The continuous-variable approach has the advantage that your get more than a qubit (infinitely more!) from every photonic mode. However, entanglement distillation becomes tricky in the continuous-variable. Working with Jens Eisert in Berlin, we showed that continuous-variable entanglement distillation had an intriguing connection to the central-limit theorem from probability theory. We were able to use these insights to develop new distillation protocols that are less wasteful (they use less postselection that alternatives)
Phys. Rev. Lett. 108 020501 (2012)
Phys. Rev. A 87 042330 (2013)