Symmetrizing Evolutions

We introduce quantum procedures for making $\cal G$-invariant the dynamics of an arbitrary quantum system S, where $\cal G$ is a finite group acting on the space state of S. Several applications of this idea are discussed. In particular when S is a N-qubit quantum computer interacting with its environment and $\cal G$ the symmetric group of qubit permutations, the resulting effective dynamics admits noiseless subspaces. Moreover it is shown that the recently introduced iterated-pulses schemes for reducing decoherence in quantum computers fit in this general framework. The noise-inducing component of the Hamiltonian is filtered out by the symmetrization procedure just due to its transformation properties.Comment: Presentation improved, to appear in Phys. Lett. A. 5 pages LaTeX, no figure

Calculating the Thermal Rate Constant with Exponential Speed-Up on a Quantum Computer

It is shown how to formulate the ubiquitous quantum chemistry problem of calculating the thermal rate constant on a quantum computer. The resulting exact algorithm scales exponentially faster with the dimensionality of the system than all known ``classical'' algorithms for this problem.Comment: 10 pages, no figure

Entangling capacities of noisy two-qubit Hamiltonians

We show that intrinsic fluctuations in system control parameters impose limits on the ability of two-qubit (exchange) Hamiltonians to generate entanglement starting from mixed initial states. We find three classes for Gaussian and Laplacian fluctuations. For the Ising and XYZ models there are qualitatively distinct sharp entanglement-generation transitions, while the class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement for any finite noise level. Our findings imply that exchange Hamiltonians are surprisingly robust in their ability to generate entanglement in the presence of noise, thus potentially reducing the need for quantum error correction.Comment: 5 pages, incl. 2 figures. replaced with published versio