Quantum Physics and Computers

Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit quantum features could factor large composite integers. This task is believed to be out of reach of classical computers as soon as the number of digits in the number to factor exceeds a certain limit. The additional power of quantum computers comes from the possibility of employing a superposition of states, of following many distinct computation paths and of producing a final output that depends on the interference of all of them. This “quantum parallelism” outstrips by far any parallelism that can be thought of in classical computation and is responsible for the “exponential” speed-up of computation. Experimentally, however, it will be extremely difficult to “decouple” a quantum computer from its environment. Noise fluctuations due to the outside world, no matter how little, are sufficient to drastically reduce the performance of these new computing devices. To control the nefarious effects of this environmental noise, one needs to implement efficient error–correcting techniques. 1 Computation and Physics We are not used to think of computation in physical terms. We look on it as made up of theoretical, mathematical operations; but under close scrutiny, effecting a computation is essentially a physical process. Take a simple example, say “2+3”; how is this trivial computation handled by a computer? The inputs 2 and 3 are two abstract quantities, and before carrying out any computation, they are encoded in a physical system. This can take several radically different forms depending on the computing device: voltage potentials at the gates of a transistor on a silicon microchip, beads on the rods of an abacus, nerve impulses on the synapse of a neuron, etc. The computation itself consists of a set of instructions (referred to as an algorithm) carried out by means of a physical process. Completion of the algorithm yields a result that can be reinterpreted in abstract terms: we observe the physical system (for instance, by looking at the display of a calculator) and conclude that the result is 5. The crucial point here is that, although 2+3 may be defined abstractly, the process that enables us to conclude that 2 + 3 equals 5 is purely physical. The theory of computation has been long considered a completely theoretical field, detached from physics. Nevertheless, pioneers such as Turing, Church, Post