Comment on "Quantum Phase Slips and Transport in Ultrathin Superconducting Wires"

In a recent Letter (Phys. Rev. Lett.78, 1552 (1997) ), Zaikin, Golubev, van Otterlo, and Zimanyi criticized the phenomenological time-dependent Ginzburg-Laudau model which I used to study the quantum phase-slippage rate for superconducting wires. They claimed that they developed a "microscopic" model, made qualitative improvement on my overestimate of the tunnelling barrier due to electromagnetic field. In this comment, I want to point out that, i), ZGVZ's result on EM barrier is expected in my paper; ii), their work is also phenomenological; iii), their renormalization scheme is fundamentally flawed; iv), they underestimated the barrier for ultrathin wires; v), their comparison with experiments is incorrect.Comment: Substantial changes made. Zaikin et al's main result was expected from my work. They underestimated tunneling barrier for ultrathin wires by one order of magnitude in the exponen

Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap

We present a solution of the three-fermion problem in a harmonic potential across a Feshbach resonance. We compare the spectrum with that of the two-body problem and show that it is energetically unfavorable for the three fermions to occupy one lattice site rather than two. We also demonstrate the existence of an energy level crossing in the ground state with a symmetry change of its wave function, suggesting the possibility of a phase transition for the corresponding many-body case.Comment: 5 pages, 6 figures, typos corrected, references adde

Generally Covariant Conservative Energy-Momentum for Gravitational Anyons

We obtain a generally covariant conservation law of energy-momentum for gravitational anyons by the general displacement transform. The energy-momentum currents have also superpotentials and are therefore identically conserved. It is shown that for Deser's solution and Clement's solution, the energy vanishes. The reasonableness of the definition of energy-momentum may be confirmed by the solution for pure Einstein gravity which is a limit of vanishing Chern-Simons coulping of gravitational anyons.Comment: 12 pages, Latex, no figure

A dynamical approximation for stochastic partial differential equations

Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the random invariant manifold is almost surely asymptotically complete. The asymptotic dynamical behavior is thus described by a stochastic ordinary differential system on the random invariant manifold, under suitable conditions. As an application, stationary states (invariant measures) is considered for one example of stochastic partial differential equations.Comment: 28 pages, no figure

A heralded quantum gate between remote quantum memories

We demonstrate a probabilistic entangling quantum gate between two distant trapped ytterbium ions. The gate is implemented between the hyperfine "clock" state atomic qubits and mediated by the interference of two emitted photons carrying frequency encoded qubits. Heralded by the coincidence detection of these two photons, the gate has an average fidelity of 90+-2%. This entangling gate together with single qubit operations is sufficient to generate large entangled cluster states for scalable quantum computing

Efficient engineering of multi-atom entanglement through single-photon detections

We propose an efficient scheme to engineer multi-atom entanglement by detecting cavity decay through single-photon detectors. In the special case of two atoms, this scheme is much more efficient than previous probabilistic schemes, and insensitive to randomness in the atom's position. More generally, the scheme can be used to prepare arbitrary superpositions of multi-atom Dicke states without the requirements of high-efficiency detection and separate addressing of different atoms.Comment: 5 pages, 2 figure

Computation on a Noiseless Quantum Code and Symmetrization

Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant gates. Such gates - if not available from the outset - can be obtained by resorting to a symmetrization with respect to the group generated by ${\cal L}.$ Any computation can then be performed completely within the coding decoherence-free subspace.Comment: One result added, to appear in Phys. Rev. A (RC) 4 pages LaTeX, no figure

Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation

Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this stabilizer formalism. Two possible collective decoherence mechanisms arising from permutation symmetries of the system-bath coupling are examined within this framework. It is shown that in both cases universal quantum computation which always preserves the DFS (*natural fault-tolerant computation*) can be performed using only two-body interactions. This is in marked contrast to standard error correcting codes, where all known constructions using one or two-body interactions must leave the codespace during the on-time of the fault-tolerant gates. A further consequence of our universality construction is that a single exchange Hamiltonian can be used to perform universal quantum computation on an encoded space whose asymptotic coding efficiency is unity. The exchange Hamiltonian, which is naturally present in many quantum systems, is thus *asymptotically universal*.Comment: 40 pages (body: 30, appendices: 3, figures: 5, references: 2). Fixed problem with non-printing figures. New references added, minor typos correcte