A quantum computer only needs one universe

The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum computers to ``perform many computations simultaneously'' except in a highly qualified and to some extent misleading sense. Quantum computation is therefore not well described by interpretations of quantum mechanics which invoke the concept of vast numbers of parallel universes. Rather, entanglement makes available types of computation process which, while not exponentially larger than classical ones, are unavailable to classical systems. The essence of quantum computation is that it uses entanglement to generate and manipulate a physical representation of the correlations between logical entities, without the need to completely represent the logical entities themselves.Comment: 13 pages. The paper has undergone major changes, in order to stengthen the argument and cut extraneous material. Schrodinger's Cat has been cut. The "one-way computer" model is now included, and the other remarks tightened. A positive statement on what a QC is, as opposed to what it is not, is adde

Numerical simulation of information recovery in quantum computers

Decoherence is the main problem to be solved before quantum computers can be built. To control decoherence, it is possible to use error correction methods, but these methods are themselves noisy quantum computation processes. In this work we study the ability of Steane's and Shor's fault-tolerant recovering methods, as well a modification of Steane's ancilla network, to correct errors in qubits. We test a way to measure correctly ancilla's fidelity for these methods, and state the possibility of carrying out an effective error correction through a noisy quantum channel, even using noisy error correction methods.Comment: 38 pages, Figures included. Accepted in Phys. Rev. A, 200

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.Comment: 8 pages LaTeX plus 4 figures. Submitted to Phys. Rev. Let

Local Fault-tolerant Quantum Computation

We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which estimates the scale-up in the size of the circuit due to encoding. We carry out a detailed semi-numerical threshold analysis for concatenated coding using the 7-qubit CSS code in the local and `nonlocal' setting. First, we find that the threshold in the local model for the [[7,1,3]] code has a 1/r dependence, which is in correspondence with our analytical estimate. Second, the threshold, beyond the 1/r dependence, does not depend too strongly on the noise levels for transporting qubits. Beyond these results, we find that it is important to look at more than one level of concatenation in order to estimate the threshold and that it may be beneficial in certain places, like in the transportation of qubits, to do error correction only infrequently.Comment: REVTeX, 44 pages, 19 figures, to appear in Physical Review

Quantum computer architecture for fast entropy extraction

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