## Towards Quantum Information Technology

Prepared for the PdJ Production & ARTE by Simon Benjamin and Artur Ekert.

## Shrinking Computer

Civilisation has advanced as people discovered new ways of exploiting various physical resources such as materials, forces and energies. In the twentieth century information was added to the list when the invention of computers allowed complex information processing to be performed outside human brains. The history of computer technology has involved a sequence of changes from one type of physical realisation to another --- from gears to relays to valves to transistors to integrated circuits and so on. Today’s advanced lithographic techniques can create chips with features only a fraction of micron wide (a micron is a micrometre, i.e. a millionth of a metre).

Figure 1: From the beginning to the present: on the left an early computing machine built from mechanical gears, on the right a state-of-the art IBM chip with 0.25 micron features. The production version will contain 200 million transistors.

## Nanocomputers

Over the last few decades computer power has grown at an amazing rate, doubling every couple of years. This increase is essentially due to the continual miniaturization of the computer's most elementary component, the transistor. As transistors became smaller more could be integrated into a single microchip, and so the computational power increased. However this miniaturization process is now reaching a limit, a quantum threshold below which transistors will cease to function. Present ‘state-of-the-art’ components possess features only a few hundreds of nanometres across (a nanometre is a thousandth of a micron, or a billionth of a metre). If these chips were to be miniaturized further to the scale of tens of nanometres then their operation would be disrupted by the emergence of quantum phenomena , such as electrons tunneling through the barriers between wires. In order for the science of computation to progress further an alternative to transistor technology must be found, one whose components will function through quantum effects rather than in despite of them.

Figure 2: The transition from microtechnology to nanotechnology. The structure on the right is a single-electron transistor (SET) which was carved by the tip of a scanning tunneling microscope (STM). According to classical physics, there is no way that electrons can get from the 'source' to the 'drain', because of the two barrier walls either side of the 'island'. But the structure is so small that quantum effects occur, and electrons can, under certain circumstances, *tunnel* through the barriers (but only one electron at a time can do this!). Thus the SET wouldn't work without quantum mechanics.

As shown by the figure above, there are ways to redesign transistors to work using quantum effects. But it might be better to give up the idea of transistors all together, and use a completely new architecture that is more suitable for the nanometre scale. One such idea is shown below.

Figure 3: As an alternative to using new kinds of transistor, nanocomputers might have an entirely new type of architecture made up of many simple units called 'cells'. The figure shows how a particular circuit called a 'half-adder' can be made from a pattern composed of two kinds of cell. This type of architecture is very suitable for the nanometre-scale, where simple units form naturally. One way to make the cells would be using structures called quantum-dots, which are also know as 'artificial atoms'.

The first generation of nanocomputers will have components that behave according to quantum mechanics, but the *algorithms* that they run will probably not involve quantum mechanics. We might call such computers 'nanometre-scale *classical* computers' (here the word 'classical' means 'not quantum'). But scientists have recently realized that there is another, more exciting possibility - quantum mechanics might be used in an entirely new kind of algorithm that would be fundamentally more powerful than any classical scheme. A computer that could run such an algorithm would be a true 'quantum computer'.

Figure 4: From an SET (on the left) to the ultimate computer element: a molecule! Although both these structures use quantum mechanics, only the one on the right could be employed in a true 'quantum computer'. The 1H and 13C nuclei in isotopically labeled chloroform behave like small magnets, and interact with an external magnetic field. Nuclear spins can store and process information in the so called quantum superpositions (see below).

## Quantum Computers

To explain what makes quantum computers so different from their classical counterparts we begin by having a closer look at a basic chunk of information namely one bit. From a physical point of view a bit is a physical system which can be prepared in one of the two different states representing two logical values --- no or yes, false or true, or simply 0 or 1. For example, in today's digital computers, the voltage between the plates in a capacitor represents a bit of information: a charged capacitor denotes bit value 1 and an uncharged capacitor bit value 0. One bit of information can be also encoded using two different polarisations of light or two different electronic states of an atom. However, if we choose an atom as a physical bit then quantum mechanics tells us that apart from the two distinct electronic states the atom can be also prepared in a *coherent superposition* of the two states. This means that the atom is *both *in state 0 *and* state 1. There is no equivalent of this superposition in the classical world, it is a purely quantum mechanical phenomenon. Since we are used to seeing classical physics at work in the every day world, such quantum phenomena often seem counter-intuitive.

Now we push the idea of superposition of numbers a bit further. Consider a register composed of three physical bits. Any classical register of that type can store in a given moment of time only one out of eight different numbers i.e. the register can be in only one out of eight possible configurations such as 000, 001, 010, ... 111. A quantum register composed of three qubits can store in a given moment of time all eight numbers in a quantum superposition .

This is quite remarkable that all eight numbers are physically present in the register but it should be no more surprising than a qubit being both in state 0 and 1 at the same time. If we keep adding qubits to the register we increase its storage capacity exponentially i.e. three qubits can store 8 different numbers at once, four qubits can store 16 different numbers at once, and so on; in general L qubits can store 2^{L} numbers at once (here 2^{L} means 2 to the power of L). Once the register is prepared in a superposition of different numbers we can perform operations on all of them. For example, if qubits are atoms then suitably tuned laser pulses affect atomic electronic states and evolve initial superpositions of encoded numbers into different superpositions. During such evolution each number in the superposition is affected and as the result we generate a massive parallel computation albeit in one piece of quantum hardware. This means that a quantum computer can in only one computational step perform the same mathematical operation on 2^{L} different input numbers encoded in coherent superpositions of L qubits. In order to accomplish the same task any classical computer has to repeat the same computation 2^{L} times or one has to use 2^{L} different processors working in parallel. In other words a quantum computer offers an enormous gain in the use of computational resources such as time and memory.

Future registers in quantum computers may look like this ion trap.

All ions in the trap have the same charge and repel each other. Any motion of one of the ions is transferred by this electrostatic repulsion to other ions in the trap, inducing various collective motions known as phonons. A single ion can be set in motion by directing a laser pulse at that particular ion --- each ion can be addressed separately because the inter-ion separation is much larger then the wavelength that induces the excitation. Combination of laser light and phonons can induce non-trivial logic and can be used in quantum computation. This kind of quantum logic gates are currently being implemented by experimental groups both in Europe and in the U.S.A.