Deutsch-Jozsa algorithm as a test of quantum computation

A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a refined algorithm, which reduces the size of the register and simplifies the function evaluation, is proposed. The refined version allows a simpler analysis of the use of entanglement between the qubits in the algorithm and provides criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful test of quantum computation.Comment: 10 pages, 2 figures, RevTex, Approved for publication in Phys Rev

Quantum Faraday Effect in Double-Dot Aharonov-Bohm Ring

We investigate Faraday's law of induction manifested in the quantum state of Aharonov-Bohm loops. In particular, we propose a flux-switching experiment for a double-dot AB ring to verify the phase shift induced by Faraday's law. We show that the induced {\em Faraday phase} is geometric and nontopological. Our study demonstrates that the relation between the local phases of a ring at different fluxes is not arbitrary but is instead determined by Faraday's inductive law, which is in strong contrast to the arbitrary local phase of an Aharonov-Bohm ring for a given flux.Comment: Submitted to Phys. Rev. Let

Approximate quantum error correction can lead to better codes

We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single amplitude damping error. This code violates the usual Hamming bound calculated for a Pauli description of the error process, and does not fit into the GF(4) classification.Comment: 7 pages, 2 figures, submitted to Phys. Rev.

Full characterization of a three-photon GHZ state using quantum state tomography

We have performed the first experimental tomographic reconstruction of a three-photon polarization state. Quantum state tomography is a powerful tool for fully describing the density matrix of a quantum system. We measured 64 three-photon polarization correlations and used a "maximum-likelihood" reconstruction method to reconstruct the GHZ state. The entanglement class has been characterized using an entanglement witness operator and the maximum predicted values for the Mermin inequality was extracted.Comment: 3 pages, 3 figure

Combined Error Correction Techniques for Quantum Computing Architectures

Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we may extend the coherence times of the quantum systems and create more reliable computing devices. To this end we give a general strategy for using dynamical decoupling operations on encoded subspaces. These encodings may be of any form; of particular importance are decoherence-free subspaces and quantum error correction codes. We then give means for empirically determining an appropriate set of dynamical decoupling operations for a given experiment. Using these techniques, we then propose a comprehensive encoding solution to many of the problems of quantum computing proposals which use exchange-type interactions. This uses a decoherence-free subspace and an efficient set of dynamical decoupling operations. It also addresses the problems of controllability in solid state quantum dot devices.Comment: Contribution to Proceedings of the 2002 Physics of Quantum Electronics Conference", to be published in J. Mod. Optics. This paper provides a summary and review of quant-ph/0205156 and quant-ph/0112054, and some new result

Scheme for direct measurement of a general two-qubit Hamiltonian

The construction of two-qubit gates appropriate for universal quantum computation is of enormous importance to quantum information processing. Building such gates is dependent on accurate knowledge of the interaction dynamics between two qubit systems. This letter will present a systematic method for reconstructing the full two-qubit interaction Hamiltonian through experimental measures of concurrence. This not only gives a convenient method for constructing two qubit quantum gates, but can also be used to experimentally determine various Hamiltonian parameters in physical systems. We show explicitly how this method can be employed to determine the first and second order spin-orbit corrections to the exchange coupling in quantum dots.Comment: 4 Pages, 1 Figur

Unified model for vortex-string network evolution

We describe and numerically test the velocity-dependent one-scale (VOS) string evolution model, a simple analytic approach describing a string network with the averaged correlation length and velocity. We show that it accurately reproduces the large-scale behaviour (in particular the scaling laws) of numerical simulations of both Goto-Nambu and field theory string networks. We explicitly demonstrate the relation between the high-energy physics approach and the damped and non-relativistic limits which are relevant for condensed matter physics. We also reproduce experimental results in this context and show that the vortex-string density is significantly reduced by loop production, an effect not included in the usual `coarse-grained' approach.Comment: 5 pages; v2: cosmetic changes, version to appear in PR

Simulating quantum operations with mixed environments

We study the physical resources required to implement general quantum operations, and provide new bounds on the minimum possible size which an environment must be in order to perform certain quantum operations. We prove that contrary to a previous conjecture, not all quantum operations on a single-qubit can be implemented with a single-qubit environment, even if that environment is initially prepared in a mixed state. We show that a mixed single-qutrit environment is sufficient to implement a special class of operations, the generalized depolarizing channels.Comment: 4 pages Revtex + 1 fig, pictures at http://stout.physics.ucla.edu/~smolin/tetrahedron .Several small correction

A cryogenic surface-electrode elliptical ion trap for quantum simulation

Two-dimensional crystals of trapped ions are a promising system with which to implement quantum simulations of challenging problems such as spin frustration. Here, we present a design for a surface-electrode elliptical ion trap which produces a 2-D ion crystal and is amenable to microfabrication, which would enable higher simulated coupling rates, as well as interactions based on magnetic forces generated by on-chip currents. Working in an 11 K cryogenic environment, we experimentally verify to within 5% a numerical model of the structure of ion crystals in the trap. We also explore the possibility of implementing quantum simulation using magnetic forces, and calculate J-coupling rates on the order of 10^3 / s for an ion crystal height of 10 microns, using a current of 1 A

The Exotic Statistics of Leapfrogging Smoke Rings

The leapfrogging motion of smoke rings is a three dimensional version of the motion that in two dimensions leads to exotic exchange statistics. The statistical phase factor can be computed using the hydrodynamical Euler equation, which is a universal law for describing the properties of a large class of fluids. This suggests that three dimensional exotic exchange statistics is a common property of closed vortex loops in a variety of quantum liquids and gases, from helium superfluids to Bose-Einstein condensed alkali gases, metallic hydrogen in its liquid phases and maybe even nuclear matter in extreme conditions.Comment: 9 pages 1 figur