Biomedical subjects

Raymond Laflamme

Publications and source records attributed to Raymond Laflamme.

3 recordsLinked to original sources

PubMed2005

Unified and generalized approach to quantum error correction.

We present a unified approach to quantum error correction, called operator quantum error correction. Our scheme relies on a generalized notion of a noiseless subsystem that is investigated here. By combining the active error correction with this generalized noiseless subsystems method, we arrive at a unified approach which incorporates the known techniques--i.e., the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method--as special cases. Moreover, we demonstrate that the quantum error correction condition from the standard model is a necessary condition for all known methods of quantum error correction.

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PubMed2004

Exponential speedup with a single bit of quantum information: measuring the average fidelity decay.

We present an efficient quantum algorithm to measure the average fidelity decay of a quantum map under perturbation using a single bit of quantum information. Our algorithm scales only as the complexity of the map under investigation. Thus for those maps admitting an efficient gate decomposition, it provides an exponential speedup over known classical procedures. Fidelity decay is important in the study of complex dynamical systems, where it is conjectured to be a signature of eigenvector statistics. Our result also illustrates the role of chaos in the process of decoherence.

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PubMed2002

Interpretation of tomography and spectroscopy as dual forms of quantum computation.

It is important to be able to determine the state of a quantum system and to measure properties of its evolution. State determination can be achieved using tomography, in which the system is subjected to a series of experiments, whereas spectroscopy can be used to probe the energy spectrum associated with the system's evolution. Here we show that, for a quantum system whose state or evolution can be modelled on a quantum computer, tomography and spectroscopy can be interpreted as dual forms of quantum computation. Specifically, we find that the phase estimation algorithm (which underlies a quantum computer's ability to perform efficient simulations and to factorize large numbers) can be adapted for tomography or spectroscopy. This is analogous to the situation encountered in scattering experiments, in which it is possible to obtain information about both the state of the scatterer and its interactions. We provide an experimental demonstration of the tomographic application by performing a measurement of the Wigner function (a phase space distribution) of a quantum system. For this purpose, we use three qubits formed from spin-1/2 nuclei in a quantum computation involving liquid-state nuclear magnetic resonance.

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