Error Avoiding Quantum Codes

The existence is proved of a class of open quantum systems that admits a linear subspace ${\cal C}$ of the space of states such that the restriction of the dynamical semigroup to the states built over $\cal C$ is unitary. Such subspace allows for error-avoiding (noiseless) enconding of quantum information.Comment: 9 pages, LaTe

Decoherence suppression for oscillator-assisted geometric quantum gates via symmetrization

We propose a novel symmetrization procedure to beat decoherence for oscillator-assisted quantum gate operations. The enacted symmetry is related to the global geometric features of qubits transformation based on ancillary oscillator modes, e.g. phonons in an ion-trap system. It is shown that the devised multi-circuit symmetrized evolution endows the system with a two-fold resilience against decoherence: insensitivity to thermal fluctuations and quantum dissipation.Comment: 4 pages, 2 figure

Virtual Quantum Subsystems

The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set $\cal A$ of operationally relevant observables. The algebraic structure of $\cal A$ selects a preferred tensor product structure i.e., a partition into subsystems. The notion of compoundness for quantum system is accordingly relativized. Universal control over virtual subsystems can be achieved by using quantum noncommutative holonomiesComment: Presentation improved, to appear in PRL. 4 Pages, RevTe

Quantum phase transitions and quantum fidelity in free fermion graphs

In this paper we analyze the ground state phase diagram of a class of fermionic Hamiltonians by looking at the fidelity of ground states corresponding to slightly different Hamiltonian parameters. The Hamiltonians under investigation can be considered as the variable range generalization of the fermionic Hamiltonian obtained by the Jordan-Wigner transformation of the XY spin-chain in a transverse magnetic field. Under periodic boundary conditions, the matrices of the problem become circulant and the models are exactly solvable. Their free-ends counterparts are instead analyzed numerically. In particular, we focus on the long range model corresponding to a fully connected directed graph, providing asymptotic results in the thermodynamic limit, as well as the finite-size scaling analysis of the second order quantum phase transitions of the system. A strict relation between fidelity and single particle spectrum is demonstrated, and a peculiar gapful transition due to the long range nature of the coupling is found. A comparison between fidelity and another transition marker borrowed from quantum information i.e., single site entanglement, is also considered.Comment: 14 pages, 5 figure

Ground-State Entanglement in Interacting Bosonic Graphs

We consider a collection of bosonic modes corresponding to the vertices of a graph $\Gamma.$ Quantum tunneling can occur only along the edges of $\Gamma$ and a local self-interaction term is present. Quantum entanglement of one vertex with respect the rest of the graph is analyzed in the ground-state of the system as a function of the tunneling amplitude $\tau.$ The topology of $\Gamma$ plays a major role in determining the tunneling amplitude $\tau^*$ which leads to the maximum ground-state entanglement. Whereas in most of the cases one finds the intuitively expected result $\tau^*=\infty$ we show that it there exists a family of graphs for which the optimal value of$\tau$ is pushed down to a finite value. We also show that, for complete graphs, our bi-partite entanglement provides useful insights in the analysis of the cross-over between insulating and superfluid ground statesComment: 5 pages (LaTeX) 5 eps figures include

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

Surface ages of mid-size Saturnian satellites

The observations of the surfaces of the mid sized Saturnian satellites made by Cassini Huygens mission have shown a variety of features that allows study of the processes that took place and are taking place on those worlds. Research of the Saturnian satellite surfaces has clear implications for Saturn history and surroundings. In a recent paper, the production of craters on the mid sized Saturnian satellites by Centaur objects was calculated considering the current Solar System. We have compared our results with crater counts from Cassini images and we have noted that the number of observed small craters is less than our calculated number. In this paper we estimate the age of the surface for each observed terrain on each mid sized satellite of Saturn. We have noticed that since there are less observed small craters than calculated (except on Iapetus), this results in younger ages. This could be the result of efficient endogenous or exogenous process(es) for erasing small craters and or crater saturation at those sizes. The size limit from which the observed number of smaller craters is less than the calculated is different for each satellite, possibly indicating processes that are unique to each, but other potential common explanations would be crater saturation and or deposition of E ring particles. These processes are also suggested by the findings that the smaller craters are being preferentially removed, and the erasure process is gradual. On Enceladus, only mid and high latitude plains have remnants of old terrains; the other regions could be young; the regions near the South Polar Terrain could be as young as 50 Myr old. On the contrary for Iapetus, all the surface is old and it notably registers a primordial source of craters. As the crater size is decreased, it would be perceived to approach saturation until D less than 2 km craters, where saturation is complete.Comment: Accepted for publication in Icarus, 40 pages, 11 figure