Active stabilisation, quantum computation and quantum state synthesis

Active stabilisation of a quantum system is the active suppression of noise (such as decoherence) in the system, without disrupting its unitary evolution. Quantum error correction suggests the possibility of achieving this, but only if the recovery network can suppress more noise than it introduces. A general method of constructing such networks is proposed, which gives a substantial improvement over previous fault tolerant designs. The construction permits quantum error correction to be understood as essentially quantum state synthesis. An approximate analysis implies that algorithms involving very many computational steps on a quantum computer can thus be made possible. All physical systems are subject to noise, arising from an unavoidable coupling to an environment which can not be completely analysed or controlled. Typically, noise is a problem we wish to minimise, and for this purpose passive and active stabilisation can be applied. By passive stabilisation we mean the careful construction and isolation of a system so as to reduce the noise level to a minimum. By active stabilisation we mean the use of detection and feedback to suppress the tendency of a system to depart from some desired state. An early example is the governor in a steam engine, and a common modern example is the electronic servo based on a stable voltage reference, a high-performance amplifier and a low-noise resistor (see inset to Fig. 2). Passive stabilisation is insufficient to stabilise any but the most simple devices, whereas active stabilisation is a very powerful method and is used throughout the natural world, whether in man-made devices or in living organisms. The above examples of active stabilisation are classical, not quantum systems, however. Is it possible to apply active stabilisation in quantum physics? That is, can the complete unitary evolution of the state throughout its Hilbert space be actively stabilised against the effects of random noise? It has been widely supposed that the answer to this question is ‘no’. The reason is because active stabilisation is based on amplification and dissipation. However, a general