Type-II Quantum Algorithms

We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type-II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical lattice-Boltzmann scheme. We derive a sufficient and necessary constraint on the unitary operator representing the quantum mechanical part of the computation which ensures that the model reproduces the Boltzmann approximation of a lattice-gas model satisfying semi-detailed balance. Models which do not satisfy this constraint represent new lattice-Boltzmann schemes which cannot be formulated as the average over some underlying lattice gas. We close the paper with some discussion of the strengths, weaknesses and possible future direction of Type-II quantum computing.Comment: To appear in Physica

Quantum logic as superbraids of entangled qubit world lines

Presented is a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a superbraid. The crossing of world lines is purely quantum in nature, most conveniently expressed analytically with ladder-operator-based quantum gates. At a crossing, independent world lines can become entangled. Complicated superbraids are systematically reduced by recursively applying novel quantum skein relations. If the superbraid is closed (e.g. representing quantum circuits with closed-loop feedback, quantum lattice gas algorithms, loop or vacuum diagrams in quantum field theory), then one can decompose the resulting superlink into an entangled superposition of classical links. In turn, for each member link, one can compute a link invariant, e.g. the Jones polynomial. Thus, a superlink possesses a unique link invariant expressed as an entangled superposition of classical link invariants.Comment: 4 page

Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades

A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a BEC described by the Gross-Pitaevskii equation on grids up to 5760^3. For the first time, an accurate power law scaling for the quantum Kelvin wave cascade is determined: k^{-3}. The incompressible kinetic energy spectrum exhibits very distinct power law spectra in 3 ranges of k-space: a classical Kolmogorov k^{-5/3} spectrum at scales much greater than the individual quantum vortex cores, and a quantum Kelvin wave cascade spectrum k^{-3} on scales of order the vortex cores. In the semiclassical regime between these two spectra there is a pronounced steeper spectral decay, with non-universal exponent. The Kelvin k^{-3} spectrum is very robust, even on small grids, while the Kolmogorov k^{-5/3} spectrum becomes more and more apparent as the grids increase from 2048^3 grids to 5760^3.Comment: 4 pages, 2 figure

Local Unitary Quantum Cellular Automata

In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. It is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth of applications.Comment: To appear in Physical Review

One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum

We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.Comment: 10 pages, 1 figur

Ophthalmic Manifestations of Congenital Zika Syndrome in Colombia and Venezuela

IMPORTANCE The ocular manifestations and sequelae of Zika virus infection are not well known. Recently, the World Health Organization changed the declaration of Zika as a public health emergency and designated the viral outbreak and related microcephaly clusters as a long-term program of work. This change indicates the urgent need to evaluate and document ophthalmic manifestations in patients for timely management of this disease. In addition, confirmation whether the public health problem in Brazil extends to other regions in South America is needed. OBJECTIVE To report the ocular manifestations of congenital Zika syndrome with microcephaly in Colombia and Venezuela. DESIGN, SETTING, AND PARTICIPANTS This prospective case series included 43 patients from 2 ophthalmic centers in Colombia and Venezuela who underwent evaluation from October 1, 2015, through June 30, 2016, and were clinically diagnosed with congenital Zika syndrome. Twenty patients were Hispanic; 13, African; 8, white; and 2, Native American. INTERVENTIONS Ophthalmic and systemic evaluations and serologic testing were performed on all infants. Patients underwent external ocular examination and dilated ophthalmoscopy. Serologic testing ruled out toxoplasmosis, rubella, cytomegalovirus, syphilis, and human immunodeficiency virus. MAIN OUTCOMES AND MEASURES Ophthalmic manifestations of congenital Zika syndrome. RESULTS Of the 43 patients included in this series (28 female and 15 male), the mean (SD) age at examination was 2.1 (1.5) months. The mothers of all the children had no ophthalmic findings and did not report ocular symptoms during pregnancy. All patients had bilateral ophthalmic manifestations. Optic nerve findings included hypoplasia with the double-ring sign, pallor, and increased cup-disc ratio in 5 patients (11.6%). Macular abnormalities included mild to severe pigment mottling in 27 patients (63%) and lacunar maculopathy in 3 (6.9%). Chorioretinal scarring was present in 3 patients (7%). Eleven patients (26%) had a combination of lesions in the posterior pole. Five patients (12%) were diagnosed with congenital glaucoma, characterized by the clinical triad of epiphora, photophobia, and blepharospasm; increased intraocular pressure; corneal clouding at birth; and buphthalmos. These data reveal that 12%(95%CI, 5%-24%) of cases of congenital Zika with microcephaly had anterior segment abnormalities and 88%(95%CI, 76%-94%) had important macular and optic nerve abnormalities. The visual sequelae of these ophthalmic manifestations remain unknown. CONCLUSIONS AND RELEVANCE Congenital Zika syndrome in the current study had severe ocular abnormalities, and all patients had bilateral involvement. Ocular findings were focal macular pigment mottling, chorioretinal atrophy with a predilection for the macular area, congenital glaucoma and optical nerve hypoplasia, and optic disc abnormalities. Ophthalmic examination is recommended in patients with congenital Zika syndrome

One dimensional Coulomb-like problem in deformed space with minimal length

Spectrum and eigenfunctions in the momentum representation for 1D Coulomb potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that correction due to the deformation is proportional to square root of the deformation parameter. We obtain the same spectrum using Bohr-Sommerfeld quantization condition.Comment: 11 pages, typos corrected, references adde