Homological Product Codes

Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum LDPC codes known to this date suffer from a poor distance scaling limited by the square-root of the code length. This is in a sharp contrast with the classical case where good families of LDPC codes are known that combine constant encoding rate and linear distance. Here we propose the first family of good quantum codes with low-weight stabilizers. The new codes have a constant encoding rate, linear distance, and stabilizers acting on at most $\sqrt{n}$ qubits, where $n$ is the code length. For comparison, all previously known families of good quantum codes have stabilizers of linear weight. Our proof combines two techniques: randomized constructions of good quantum codes and the homological product operation from algebraic topology. We conjecture that similar methods can produce good stabilizer codes with stabilizer weight $n^a$ for any $a>0$. Finally, we apply the homological product to construct new small codes with low-weight stabilizers.Comment: 49 page

The Critical Project in Schelling, Tillich and Goodchild

2 Altizer and Tillich repeat a Cartesian trope that lies at the kernel of modernity: beginnings must be destructive; they ... The Critical Project in Schelling, Tillich, and Goodchild Daniel Whistler Radical Apologetics: Paul Tillich and Radical ..

Description of a quantum convolutional code

We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances in classical communication. The particular example shown here uses the stabilizer formalism, which provides an explicit encoding circuit. An associated error estimation algorithm is given explicitly and shown to provide the most likely error over any memoryless quantum channel, while its complexity grows only linearly with the number of encoded qubits.Comment: 4 pages, uses revtex4. Minor correction in the encoding and decoding circuit

Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance $n^\epsilon$. Their rate is evaluated via Euler characteristic arguments and their distance using $\mathbb{Z}_2$-systolic geometry. This construction answers a queston of Z\'emor, who asked whether homological codes with such parameters could exist at all.Comment: 21 page

Lived religion: Rethinking human nature in a neoliberal age

This article considers the relationship between philosophy of religion and an approach to the study of religion, which prioritises the experience of lived religion. Considering how individuals and communities live out their faith challenges some of the assumptions of analytic philosophers of religion regarding the position the philosopher should adopt when approaching the investigation of religion. If philosophy is understood principally as a means for analysing belief, it will have little space for an engagement with what it feels like to live out one’s faith

“Trapped in an Empty Waiting Room”—The Existential Human Core of Loneliness in Old Age: A Meta-Synthesis

Loneliness in old age has a negative influence on quality of life, health and survival. To understand the phenomenon of loneliness in old age, the voices of lonely older adults should be heard. Therefore, the purpose of this meta-synthesis was to synthesize scientific studies of older adults’ experiences of loneliness. Eleven qualitative articles that met the inclusion criteria were analyzed and synthesized according to Noblit and Hare’s meta-ethnographic approach. The analysis revealed the overriding meaning of the existential human core of loneliness in old age expressed through the metaphor "trapped in an empty waiting room". Four interwoven themes were found: 1) the negative emotions of loneliness, 2) the loss of meaningful interpersonal relationships, 3) the influence of loneliness on self-perception and 4) the older adults’ endeavors to deal with loneliness. The joint contribution of family members, health care providers, and volunteers is necessary to break the vicious circle of loneliness

Smoothing Codes and Lattices: Systematic Study and New Bounds

In this article we revisit smoothing bounds in parallel between lattices and codes. Initially introduced by Micciancio and Regev, these bounds were instantiated with Gaussian distributions and were crucial for arguing the security of many lattice-based cryptosystems. Unencumbered by direct application concerns, we provide a systematic study of how these bounds are obtained for both lattices and codes, transferring techniques between both areas. We also consider multiple choices of spherically symmetric noise distribution. We found that the best strategy for a worst-case bound combines Parseval's Identity, the Cauchy-Schwarz inequality, and the second linear programming bound, and this holds for both codes and lattices and all noise distributions at hand. For an average-case analysis, the linear programming bound can be replaced by a tight average count. This alone gives optimal results for spherically uniform noise over random codes and random lattices. This also improves previous Gaussian smoothing bound for worst-case lattices, but surprisingly this provides even better results with uniform ball noise than for Gaussian (or Bernouilli noise for codes). This counter-intuitive situation can be resolved by adequate decomposition and truncation of Gaussian and Bernouilli distributions into a superposition of uniform noise, giving further improvement for those cases, and putting them on par with the uniform cases

Whose Science and whose Religion? Reflections on the Relations between Scientific and Religious Worldviews

Arguments about the relationship between science and religion often proceed by identifying a set of essential characteristics of scientific and religious worldviews and arguing on the basis of these characteristics for claims about a relationship of conflict or compatibility between them. Such a strategy is doomed to failure because science, to some extent, and religion, to a much larger extent, are cultural phenomena that are too diverse in their expressions to be characterized in terms of a unified worldview. In this paper I follow a different strategy. Having offered a loose characterization of the nature of science, I pose five questions about specific areas where religious and scientific worldviews may conflict - questions about the nature of faith, the belief in a God or Gods, the authority of sacred texts, the relationship between scientific and religious conceptions of the mind/soul, and the relationship between scientific and religious understandings of moral behavior. My review of these questions will show that they cannot be answered unequivocally because there is no agreement amongst religious believers as to the meaning of important religious concepts. Thus, whether scientific and religious worldviews conflict depends essentially upon whose science and whose religion one is considering. In closing, I consider the implications of this conundrum for science education