Surface code implementation of block code state distillation

State distillation is the process of taking a number of imperfect copies of a particular quantum state and producing fewer better copies. Until recently, the lowest overhead method of distilling states |A>=(|0>+e^{i\pi/4}|1>)/\sqrt{2} produced a single improved |A> state given 15 input copies. New block code state distillation methods can produce k improved |A> states given 3k+8 input copies, potentially significantly reducing the overhead associated with state distillation. We construct an explicit surface code implementation of block code state distillation and quantitatively compare the overhead of this approach to the old. We find that, using the best available techniques, for parameters of practical interest, block code state distillation does not always lead to lower overhead, and, when it does, the overhead reduction is typically less than a factor of three.Comment: 26 pages, 28 figure

A brief introduction to equi-chordal and equi-isoclinic tight fusion frames

Equi-chordal and equi-isoclinic tight fusion frames (ECTFFs and EITFFs) are both types of optimal packings of subspaces in Euclidean spaces. In the special case where these subspaces are one-dimensional, ECTFFs and EITFFs both correspond to types of optimal packings of lines known as equiangular tight frames. In this brief note, we review some of the fundamental ideas and results concerning ECTFFs and EITFFs

Access to Nature in New Hampshire: Equity and Quality of Life

This is a recording of Cody Crytzer’s thesis defense “Access to Nature in New Hampshire: Equity and Quality of Life” in partial fulfillment of his MS in Natural Resources from UNH, presented on April 17, 2023. A file with the slides is linked below. This research aims to understand how people working in New Hampshire’s nature economy identify natural assets, access to nature, and barriers and opportunities for access to nature, with a focus on access and equity for underserved communities. Qualitative data were collected through 19 statewide interviews, including a mini-case of Rochester, New Hampshire

Extensive microscale N isotopic heterogeneity in chondritic organic matter

Introduction: H and N isotopic anomalies (mainly excesses of D and 15N) in organic matter from primitive meteorites and IDPs suggest preservation of presolar molecular cloud material [1-3]. However, there have been very few spatially correlated H and N studies for either chondrites or IDPs [4, 5]. We report C and N isotopic imaging data for organic matter from four meteorites and three IDPs. D/H imaging data for many of the same samples are presented in [6, 7] and bulk organic isotope data in [8]

A Search for Pulsation in Very Low-mass Stars and Brown Dwarfs

Brown dwarfs and very low-mass stars constitute a crucial link between the intertwined processes of star formation and planet formation. To date, however, observational methods to uncover their formation mechanism or determine important properties such as mass and age have been lacking. Pulsation powered by deuterium burning in brown dwarfs and very low-mass stars is a newly suggested phenomenon that offers unprecedented opportunities to probe the interiors and evolution of these objects. We report on a photometric campaign to search for low-amplitude pulsations among young star-cluster members using a number of telescopes

On Representations of Semigroups Having Hypercube-like Cayley Graphs

The $n-dimensional hypercube, or n-cube, is the Cayley graph of the Abelian group Z2n. A number of combinatorially-interesting groups and semigroups arise from modified hypercubes. The inherent combinatorial properties of these groups and semigroups make them useful in a number of contexts, including coding theory, graph theory, stochastic processes, and even quantum mechanics. In this paper, particular groups and semigroups whose Cayley graphs are generalizations of hypercubes are described, and their irreducible representations are characterized. Constructions of faithful representations are also presented for each semigroup. The associated semigroup algebras are realized within the context of Clifford algebras

Transport Properties of a spinon Fermi surface coupled to a U(1) gauge field

With the organic compound $\kappa$-(BEDT-TTF)$_2$-Cu$_2$(CN)$_3$ in mind, we consider a spin liquid system where a spinon Fermi surface is coupled to a U(1) gauge field. Using the non-equilibrium Green's function formalism, we derive the Quantum Boltzmann Equation (QBE) for this system. In this system, however, one cannot a priori assume the existence of Landau quasiparticles. We show that even without this assumption one can still derive a linearized equation for a generalized distribution function. We show that the divergence of the effective mass and of the finite temperature self-energy do not enter these transport coefficients and thus they are well-defined. Moreover, using a variational method, we calculate the temperature dependence of the spin resistivity and thermal conductivity of this system.Comment: 12 page