So what is it that I do? – Part 3: Linear Optics Quantum Computing

In my previous post I discussed quantum computing and why it has the potential to be more powerful than classical computing. Until now however I’ve only discussed quantum computing in a very abstract sense. I’ve talked about quantum gates and qubits without giving any clue as to how these things are made in practise. Clearly this is pivotal, since otherwise quantum computing would be nothing more than a cool theory without much of a future. Once again I’ll discuss the classical case as a starting point. In classical computers, as everyone is probably aware, bits are represented using electrical signals. For example, the presence of an electrical current could represent a logical ‘1’ and its absense a logical ‘0’. Using electrical signals has the advantage that we can use electronic circuits consisting of transistors to implement gates. So what about the quantum case? It turns out that in fact there are countless ways in which qubits can be represented and quantum gates constructed.

In my research I focus on one idea in particular, referred to as linear optics quantum computing, or LOQC. In LOQC we use photons, or particles of light, to represent qubits. Most of us will be familiar with the idea of polarization of light from high school experiments. For those not familar with polarization, it can simply be thought of as the orientation of light, which must always be perpendicular to the direction in which the light travels. As a crude analogy, image a plane flying along which then rolls to one side. This would be changing the plane’s polarization. Using the polarization of a photon we can very easily represent a qubit. We simply define that if a photon is polarized along say a horizontal axis that it represents a ‘0’, and a vertical axis a logical ‘1’. Naturally, the all important superpositions are possible. For example if a photon were polarized at 45 degrees to the horizontal, this would be an equal superposition of horizontal and vertical, or ‘0’ and ‘1’.

So we have our qubits. What about constructing quantum gates? In my previous post I talked about the CNOT gate, a 2-qubit quantum gate. The picture below is a schematic for an implementation of this gate using LOQC. It isn’t terribly important, or instructive, to understand exactly how it works. I really only want to draw your attention to two features. Firstly the black lines. These represent paths which the light (i.e. photons) take. Secondly, the horizontal bars. These are beamsplitters, and are nothing other than partially silvered mirrors which split a light beam into multiple weaker beams. The beamsplitters serve to interfere the photons in the circuit in a cleverly designed way such that the device implements a CNOT gate.

As this point in time, things are probably looking very bright for LOQC. Unfortunately however there are some pretty hideous problems with the gate I’ve just described. Most notably, the gate is non-determinisitc, which simply means that it has some definite probability of failing. It’s probably immediately obvious just what a problem this presents. If we only need to implement a single gate, and we have one which succeeds with say probability P, there are no worries. We simply repeat the gate over and over until it works. In practise however we’ll be wanting to make complicated circuits consisting of perhaps thousands of these gates. In this case the probability of the circuit working is P to the power the number of gates in the circuit. In other words, we could be waiting a million years for the circuit to work. Fortunately, there are some extremely clever proposals on how this problem can be circumvented. Unfortunately, they are also quite complicated and experimentally very difficult.

In conclusion, we know that in theory LOQC can work. In fact, the gate shown below has been experimentally demonstrated at the University of Queensland Quantum Technology Lab. In practise however there are many technological obstacles to overcome before any useful quantum computing algorithms can be implemented using LOQC.

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