Good approximate quantum LDPC codes from spacetime circuit Hamiltonians

We study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute. Such codes generalize stabilizer QLDPC codes, which are exact quantum error-correcting codes with sparse, low-weight stabilizer generators (i.e. each stabilizer generator acts on a few qubits, and each qubit participates in a few stabilizer generators). Our investigation is motivated by an important question in Hamiltonian complexity and quantum coding theory: do stabilizer QLDPC codes with constant rate, linear distance, and constant-weight stabilizers exist? We show that obtaining such optimal scaling of parameters (modulo polylogarithmic corrections) is possible if we go beyond stabilizer codes: we prove the existence of a family of $[[N,k,d,\varepsilon]]$ approximate QLDPC codes that encode $k = \widetilde{\Omega}(N)$ logical qubits into $N$ physical qubits with distance $d = \widetilde{\Omega}(N)$ and approximation infidelity $\varepsilon = \mathcal{O}(1/\textrm{polylog}(N))$. The code space is stabilized by a set of 10-local noncommuting projectors, with each physical qubit only participating in $\mathcal{O}(\textrm{polylog} N)$ projectors. We prove the existence of an efficient encoding map, and we show that arbitrary Pauli errors can be locally detected by circuits of polylogarithmic depth. Finally, we show that the spectral gap of the code Hamiltonian is $\widetilde{\Omega}(N^{-3.09})$ by analyzing a spacetime circuit-to-Hamiltonian construction for a bitonic sorting network architecture that is spatially local in $\textrm{polylog}(N)$ dimensions.Comment: 51 pages, 13 figure

Universal Hamiltonians for Exponentially Long Simulation

We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a consequence, we show (under plausible computational complexity assumptions) that the circuit complexity of the unitary dynamics under this Hamiltonian grows steadily with time up to an exponential value in system size. This result makes progress on a recent conjecture by Susskind, in the context of the AdS/CFT correspondence, that the time evolution of the thermofield double state of two conformal fields theories with a holographic dual has a circuit complexity increasing linearly in time, up to exponential time

DIRECTIONS OF CHANGE IN THE POLISH TWO-TIER BOARD MODEL

Purpose: This paper is devoted to the eff ectiveness of corporate boards. Its aim is to present the board models found in European companies and to propose changes that would lead to better performance of Polish corporate boards.Approach: The article presents an analysis of European corporate board models, as well as their advantages and disadvantages. Based on this analysis, the author pointed out possible directions of change in the Polish two-tier board model.Implications: The author suggests that the introduction of an optional model, whereby the shareholders can choose between the one-tier board model (board of directors) and the two-tier board model (supervisory board and management board), would enable better use of the social and intellectual capital present in the corporate boards of Polish companies

Non-invasive Monitoring of Intracranial Pressure Using Transcranial Doppler Ultrasonography: Is It Possible?

Although intracranial pressure (ICP) is essential to guide management of patients suffering from acute brain diseases, this signal is often neglected outside the neurocritical care environment. This is mainly attributed to the intrinsic risks of the available invasive techniques, which have prevented ICP monitoring in many conditions affecting the intracranial homeostasis, from mild traumatic brain injury to liver encephalopathy. In such scenario, methods for non-invasive monitoring of ICP (nICP) could improve clinical management of these conditions. A review of the literature was performed on PUBMED using the search keywords 'Transcranial Doppler non-invasive intracranial pressure.' Transcranial Doppler (TCD) is a technique primarily aimed at assessing the cerebrovascular dynamics through the cerebral blood flow velocity (FV). Its applicability for nICP assessment emerged from observation that some TCD-derived parameters change during increase of ICP, such as the shape of FV pulse waveform or pulsatility index. Methods were grouped as: based on TCD pulsatility index; aimed at non-invasive estimation of cerebral perfusion pressure and model-based methods. Published studies present with different accuracies, with prediction abilities (AUCs) for detection of ICP ≥20 mmHg ranging from 0.62 to 0.92. This discrepancy could result from inconsistent assessment measures and application in different conditions, from traumatic brain injury to hydrocephalus and stroke. Most of the reports stress a potential advantage of TCD as it provides the possibility to monitor changes of ICP in time. Overall accuracy for TCD-based methods ranges around ±12 mmHg, with a great potential of tracing dynamical changes of ICP in time, particularly those of vasogenic nature.Cambridge Commonwealth, European & International Trust Scholarship (University of Cambridge) provided financial support in the form of Scholarship funding for DC. Woolf Fisher Trust provided financial support in the form of Scholarship funding for JD. Gates Cambridge Trust provided financial support in the form of Scholarship funding for XL. CNPQ provided financial support in the form of Scholarship funding for BCTC (Research Project 203792/2014-9). NIHR Brain Injury Healthcare Technology Co-operative, Cambridge, UK provided financial support in the form of equipment funding for DC, BC and MC. The sponsors had no role in the design or conduct of this manuscript.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s12028-016-0258-

Point and Line to Plane

"Point and Line to Plane" is an 18-minute short film which depicts the psychosis that can arise when an individual attempts to extract meaning from an intense loss. Stemming from Joan Didion and Sigmund Freuds theories of "magical thinking", the film investigates the phenomenon of mental free association and irrationality endured when grieving a loved one. In 2018, I was suspended in a deep state of shock after the passing of a long-time friend and collaborator named Giacomo Grisanzio. "Point and Line to Plane" is a communion of my own journey to process, heal and document my own period of mourning and my experience of magical thinking

Regulation of the gender composition of company boards in Europe: Experience and prospects

First paragraph: The desire to increase the share of women on corporate boards in Europe has led to the incorporation of voluntary targets into corporate governance codes of best practice in some European countries and the introduction of board gender quota laws in others. Taking affirmative action by imposing a quota can create a critical mass of women on boards that is sufficient to sustain greater numerical equality once the quota is removed (Kogut et al., 2014). A quota law for company boards, set at 40% for each gender, was first proposed in Norway in 2002, to the surprise of many (Bøhren and Staubo, 2016). At the time women held only 9% of board seats (Ahern and Dittmar, 2012). Passed by the Norwegian Parliament one year later, the quota became mandatory in 2008 and sparked public debate in other countries about the possibility of using quotas to increase the representation of women on corporate boards. The European Commission, with the support of the European Parliament and a number of Member States, decided in 2012 that legislative action was necessary to improve gender balance on corporate boards and put forward the proposal for a Directive that sets a 40% target for the presence of the underrepresented gender among non-executive directors of companies listed on stock exchanges by 2020

Corporate Governance and the Growing Role of Women in the Boardroom

First paragraph: The presence of women on corporate boards and their impact on board effectiveness is now one of the most contentious issues in corporate governance. This arises from the relatively low, though increasing, number of female directors on boards around the world, despite an increasing number of well-qualified women in the labour force. Although gender discrimination is unlawful, there is a perception that many women still encounter invisible barriers to promotion, in effect facing a ‘glass ceiling’ where they can see, but not reach, high-level corporate positions. Companies that do not appoint women to their boards run the risk of suffering inferior performance as they fail to make use of the intellectual and social capital that women offer

Determinants of environmental management in the red sea hotels: Personal and organizational values and contextual variables

What motivates firms to adopt environmental management practices is one of the most significant aspects in the contemporary academic debate in which the review of the existing literature yields, with an obvious contextual bias toward developed world, contested theories and inconclusive findings. Providing a unique model that brings together the individual and organizational levels of analysis on firms' adoption of environmental management practices, this study aims to provide a new insight from the context of developing world. Data from 158 Red Sea hotels reveal two identifiable dimensions of environmental management-planning and organization, and operations-that can be explained as originating from different values. Whereas organizational altruism is a powerful predictor of both dimensions, managers' personal values and organizational competitive orientation are only relevant to environmental operations. The evidence also indicates that contextual variables such as chain affiliation, hotel star rating, and size are important to explain hotels' environmental management behaviors. © 2012 ICHRIE