Fault-tolerant error correction with the gauge color code

The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a universal set of computational operations with the minimal cost in quantum resources remains an important and ongoing challenge. One proposal of significant recent interest is the gauge color code. Notably, this code may offer a reduced resource cost over other well-studied fault-tolerant architectures using a new method, known as gauge fixing, for performing the non-Clifford logical operations that are essential for universal quantum computation. Here we examine the gauge color code when it is subject to noise. Specifically we make use of single-shot error correction to develop a simple decoding algorithm for the gauge color code, and we numerically analyse its performance. Remarkably, we find threshold error rates comparable to those of other leading proposals. Our results thus provide encouraging preliminary data of a comparative study between the gauge color code and other promising computational architectures.Comment: v1 - 5+4 pages, 11 figures, comments welcome; v2 - minor revisions, new supplemental including a discussion on correlated errors and details on threshold calculations; v3 - Author accepted manuscript. Accepted on 21/06/16. Deposited on 29/07/16. 9+5 pages, 17 figures, new version includes resource scaling analysis in below threshold regime, see eqn. (4) and methods sectio

Recent interpretations of Plato's social philosophy as fascistic

Thesis (Ph.D.)--Boston UniversityThe purpose of this dissertation, stated in the first chapter, is to examine the recent interpretations of Plato's social philosophy as fascistic and to determine the validity of these interpretations relative to the whole structure of Plato's social thought. The term "recent" refers broadly to the period extending from the close of World War I to the close of World War II. The second chapter presents an exegesis of Plato's Doctrine of Justice as the key to a general understanding of his social and political perspective. It is pointed out that what he has to say about psychology and anthropology represents a microcosmic picture of what he believes about politics and sociology. His aim to achieve harmony in the individual soul is matched by his desire to bring unity to the political community. The latter is not only patterned after the former but, as a social ideal, it is also derived from it and dependent on it. The ideal State comes into being and social justice is established when the rulers bring harmony to their souls by the rule of reason and each individual is assigned to the task for which he is best suited. Thus, the Doctrine of Justice presents political as well as psychological facets germane to the evaluation of Plato's social philosophy and the attacks made against it [TRUNCATED

Minimal resources for linear optical one-way computing

We address the question of how many maximally entangled photon pairs are needed in order to build up cluster states for quantum computing using the toolbox of linear optics. As the needed gates in dual-rail encoding are necessarily probabilistic with known optimal success probability, this question amounts to finding the optimal strategy for building up cluster states, from the perspective of classical control. We develop a notion of classical strategies, and present rigorous statements on the ultimate maximal and minimal use of resources of the globally optimal strategy. We find that this strategy - being also the most robust with respect to decoherence - gives rise to an advantage of already more than an order of magnitude in the number of maximally entangled pairs when building chains with an expected length of L=40, compared to other legitimate strategies. For two-dimensional cluster states, we present a first scheme achieving the optimal quadratic asymptotic scaling. This analysis shows that the choice of appropriate classical control leads to a very significant reduction in resource consumption.Comment: 5 pages, 2 figures, title changed, presentation improved, bounds improved, minor errors corrected, references update

Parallelizing Quantum Circuits

We present a novel automated technique for parallelizing quantum circuits via forward and backward translation to measurement-based quantum computing patterns and analyze the trade off in terms of depth and space complexity. As a result we distinguish a class of polynomial depth circuits that can be parallelized to logarithmic depth while adding only polynomial many auxiliary qubits. In particular, we provide for the first time a full characterization of patterns with flow of arbitrary depth, based on the notion of influencing paths and a simple rewriting system on the angles of the measurement. Our method leads to insightful knowledge for constructing parallel circuits and as applications, we demonstrate several constant and logarithmic depth circuits. Furthermore, we prove a logarithmic separation in terms of quantum depth between the quantum circuit model and the measurement-based model.Comment: 34 pages, 14 figures; depth complexity, measurement-based quantum computing and parallel computin

Fast decoders for qudit topological codes

Qudit toric codes are a natural higher-dimensional generalization of the well- studied qubit toric code. However, standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this paper we introduce two renormalization group decoders for qudit codes and analyse their error correction thresholds and efficiency. The first decoder is a generalization of a 'hard-decisions' decoder due to Bravyi and Haah (arXiv:1112.3252). We modify this decoder to overcome a percolation effect which limits its threshold performance for many-level quantum systems. The second decoder is a generalization of a 'soft-decisions' decoder due to Poulin and Duclos-Cianci (2010 Phys. Rev. Lett. 104 050504), with a small cell size to optimize the efficiency of implementation in the high dimensional case. In each case, we estimate thresholds for the uncorrelated bit-flip error model and provide a comparative analysis of the performance of both these approaches to error correction of qudit toric codes

Benjamin Browne Foster Correspondence

Entry is brief biographical information presumably hand written by the editor. Date range

Formaldehyde Anti-Inversion at z=0.68 in the Gravitational Lens B0218+357

We report new observations of the 110-111 (6 cm) and 211-212 (2 cm) transitions of ortho-formaldehyde (o-H2CO) in absorption at z=0.68466 toward the gravitational lens system B0218+357. Radiative transfer modeling indicates that both transitions are anti-inverted relative to the 4.6 K cosmic microwave background (CMB), regardless of the source covering factor, with excitation temperatures of ~1 K and 1.5-2 K for the 110-111 and 211-212 lines, respectively. Using these observations and a large velocity gradient radiative transfer model that assumes a gradient of 1 km s^-1 pc^-1, we obtain a molecular hydrogen number density of 2x10^3 cm^-3 < n(H2) < 1x10^4 cm^-3 and a column density of 2.5x10^13 cm^-2 < N(o-H2CO) < 8.9x10^13 cm^-2, where the allowed ranges conservatively include the range of possible source covering factors in both lines. The measurements suggest that H2CO excitation in the absorbing clouds in the B0218+357 lens is analogous to that in Galactic molecular clouds: it would show H2CO absorption against the CMB if it were not illuminated by the background quasar or if it were viewed from another direction.Comment: 10 pages, 6, figures, 6 table