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Abstract:

If a quantum computer is stabilized by fault-tolerant quantum error correction (QEC), then most of its resources (qubits and operations) are dedicated to the extraction of error information. Analysis of this process leads to a set of central requirements for candidate computing devices, in addition to the basic ones of stable qubits and controllable gates and measurements. The logical structure of the extraction process has a natural geometry and hierarchy of communication needs; a computer whose physical architecture is designed to reflect this will be able to tolerate the most noise. The relevant networks are dominated by quantum information transport, therefore to assess a computing device it is necessary to characterize its ability to transport quantum information, in addition to assessing the performance of conditional logic on nearest neighbours and the passive stability of the memory. The transport distances involved in QEC networks are estimated, and it is found that a device relying on swap operations for information transport must have those operations an order of magnitude more precise than the controlled gates of a device which can transport information at low cost.

Abstract:

The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be understood as a combination of Pauli operators acting on the system. Each quantum error correcting code allows a subset of these errors to be corrected. In many situations the noise is such that the remaining uncorrectable errors are unlikely to arise, and hence quantum error correction has a high probability of success. In order to achieve the best noise tolerance in the presence of noise and imprecision throughout the computer, a hierarchical construction of a quantum computer is proposed.

Abstract:

We consider experimental issues relevant to quantum computing, and discuss the best way to achieve the essential requirements of reliable quantum memory and gate operations. Nuclear spins in trapped ions or atoms are a very promising candidate for the qubits. We estimate the parameters required to couple atoms using light via cavity QED in order to achieve quantum gates. We briefly comment on recent improvements to the Cirac-Zoller method for coupling trapped ions via their vibrational degree of freedom. Error processes result in a trade-off between quantum gate speed and failure probability. A useful quantum computer does appear to be feasible using a combination of ion trap and optical methods. The best understood method to stabilise a large computer relies on quantum error correction. The essential ideas of this are discussed, and recent estimates of the noise requirements in a quantum computing device are given.

Abstract:

The physical realisation of a large quantum computer, i.e. one which could perform calculations beyond the capabilities of classical computers, is discussed, It is necessary to consider both the physical mechanisms of the hardware and the noise tolerance of quantum error correction (QEC) methods, Estimates for noise tolerance which involve fewer simplifying assumptions than were previously employed are given, and the scaling of logic gate rate with logic gate precision is discussed. It is found that QEC is fast compared to methods such as adiabatic passage.