ZN\mathbb{Z}_N symmetry breaking in Projected Entangled Pair State models

We consider Projected Entangled Pair State (PEPS) models with a global $\mathbb Z_N$ symmetry, which are constructed from $\mathbb Z_N$-symmetric tensors and are thus $\mathbb Z_N$-invariant wavefunctions, and study the occurence of long-range order and symmetry breaking in these systems. First, we show that long-range order in those models is accompanied by a degeneracy in the so-called transfer operator of the system. We subsequently use this degeneracy to determine the nature of the symmetry broken states, i.e., those stable under arbitrary perturbations, and provide a succinct characterization in terms of the fixed points of the transfer operator (i.e.\ the different boundary conditions) in the individual symmetry sectors. We verify our findings numerically through the study of a $\mathbb Z_3$-symmetric model, and show that the entanglement Hamiltonian derived from the symmetry broken states is quasi-local (unlike the one derived from the symmetric state), reinforcing the locality of the entanglement Hamiltonian for gapped phases.Comment: 11 page

Ethics as a Way of Life: A Case Study at Yezreel Valley College

The dynamic landscape of ethics in higher education is pivotal as organizations and individuals navigate diverse stakeholder needs. Ethical responsibility becomes an integral facet of all professionals, highlighting the crucial role of ethical education in preparing students for post-graduation success. The acquisition of ethical competence, rooted in knowledge of ethical principles, equips students with the tools to make ethical decisions, shaping their ethical behavior and responses. Yezreel Valley College exemplifies this commitment, with a well-defined Code of Academic Ethics reflecting universal values and principles, overseen by the College Ethics Committee. In summary, this case study offers insights into Yezreel Valley College's ethical education practices, emphasizing the significance of ethics in higher education and the dynamic interplay between ethics and professionalism. The college's proactive approach positions it as a leader in addressing ethical challenges and adapting to changing environments while fostering ethical competence in its students

Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory

Based on numerically-optimized real-device gates and parameters we study the performance of the phase-flip (repetition) code on a linear array of Gallium Arsenide (GaAs) quantum dots hosting singlet-triplet qubits. We first examine the expected performance of the code using simple error models of circuit-level and phenomenological noise, reporting, for example, a circuit-level depolarizing noise threshold of approximately 3%. We then perform density-matrix simulations using a maximum-likelihood and minimum-weight matching decoder to study the effect of real-device dephasing, read-out error, quasi-static as well as fast gate noise. Considering the trade-off between qubit read-out error and dephasing time (T2) over measurement time, we identify a sub-threshold region for the phase-flip code which lies within experimental reach.Comment: 22 page

Fundamental thresholds of realistic quantum error correction circuits from classical spin models

Mapping the decoding of quantum error correcting (QEC) codes to classical disordered statistical mechanics models allows one to determine critical error thresholds of QEC codes under phenomenological noise models. Here, we extend this mapping to admit realistic, multi-parameter noise models of faulty QEC circuits, derive the associated strongly correlated classical spin models, and illustrate this approach for a quantum repetition code with faulty stabilizer readout circuits. We use Monte-Carlo simulations to study the resulting phase diagram and benchmark our results against a minimum-weight perfect matching decoder. The presented method provides an avenue to assess fundamental thresholds of QEC circuits, independent of specific decoding strategies, and can thereby help guiding the development of near-term QEC hardware

Dynamical subset sampling of quantum error correcting protocols

Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous operation of logical qubits in realistic quantum computing architectures. Typical quantum error correction techniques contain intermediate measurements and classical feedback that determine the actual noisy circuit sequence in an instance of performing the protocol. Dynamical subset sampling enables efficient simulation of such non-deterministic quantum error correcting protocols for any type of quantum circuit and incoherent noise of low strength. As an importance sampling technique, dynamical subset sampling allows one to effectively make use of computational resources to only sample the most relevant sequences of quantum circuits in order to estimate a protocol's logical failure rate with well-defined error bars. We demonstrate the capabilities of dynamical subset sampling with examples from fault-tolerant (FT) QEC. We show that, in a typical stabilizer simulation with incoherent Pauli noise of strength $p = 10^{-3}$, our method can reach a required sampling accuracy on the logical failure rate with two orders of magnitude fewer samples than direct Monte Carlo simulation. Furthermore, dynamical subset sampling naturally allows for efficient simulation of realistic multi-parameter noise models describing faulty quantum processors. It can be applied not only for QEC in the circuit model but any noisy quantum computing framework with incoherent fault operators including measurement-based quantum computation and quantum networks.Comment: 33 pages, 26 figure

Computational Capabilities and Compiler Development for Neutral Atom Quantum Processors: Connecting Tool Developers and Hardware Experts

Neutral Atom Quantum Computing (NAQC) emerges as a promising hardware platform primarily due to its long coherence times and scalability. Additionally, NAQC offers computational advantages encompassing potential long-range connectivity, native multi-qubit gate support, and the ability to physically rearrange qubits with high fidelity. However, for the successful operation of a NAQC processor, one additionally requires new software tools to translate high-level algorithmic descriptions into a hardware executable representation, taking maximal advantage of the hardware capabilities. Realizing new software tools requires a close connection between tool developers and hardware experts to ensure that the corresponding software tools obey the corresponding physical constraints. This work aims to provide a basis to establish this connection by investigating the broad spectrum of capabilities intrinsic to the NAQC platform and its implications on the compilation process. To this end, we first review the physical background of NAQC and derive how it affects the overall compilation process by formulating suitable constraints and figures of merit. We then provide a summary of the compilation process and discuss currently available software tools in this overview. Finally, we present selected case studies and employ the discussed figures of merit to evaluate the different capabilities of NAQC and compare them between two hardware setups.Comment: 32 pages, 13 figures, 2 table

Predictors of Indoor Air Concentrations in Smoking and Non-Smoking Residences

Indoor concentrations of air pollutants (benzene, toluene, formaldehyde, acetaldehyde, acrolein, nitrogen dioxide, particulate matter, elemental carbon and ozone) were measured in residences in Regina, Saskatchewan, Canada. Data were collected in 106 homes in winter and 111 homes in summer of 2007, with 71 homes participating in both seasons. In addition, data for relative humidity, temperature, air exchange rates, housing characteristics and occupants’ activities during sampling were collected. Multiple linear regression analysis was used to construct season-specific models for the air pollutants. Where smoking was a major contributor to indoor concentrations, separate models were constructed for all homes and for those homes with no cigarette smoke exposure. The housing characteristics and occupants’ activities investigated in this study explained between 11% and 53% of the variability in indoor air pollutant concentrations, with ventilation, age of home and attached garage being important predictors for many pollutants

The role of multi-slice computed tomography in stable angina management: a current perspective

Contrast-enhanced CT coronary angiography (CTCA) has evolved as a reliable alternative imaging modality technique and may be the preferred initial diagnostic test in patients with stable angina with intermediate pre-test probability of CAD. However, because CTCA is moderately predictive for indicating the functional significance of a lesion, the combination of anatomic and functional imaging will become increasingly important. The technology will continue to improve with better spatial and temporal resolution at low radiation exposure, and CTCA may eventually replace invasive coronary angiography. The establishment of the precise role of CTCA in the diagnosis and management of patients with stable angina requires high-quality randomised study designs with clinical outcomes as a primary outcome

Towards a greater dialogue on disability between Muslims and Christians

Attitudes to disability and disabled people by Muslims – focusing on attitudes in the Middle East and North Africa - and Christians – focusing on the West (here taken to mean Europe, North America and Australasia) - were examined through a grounded theory literature search, with the study being divided into three phases of reading and analysis. The aims of study were to develop a dialogue on disability between the two cultures, to inform an understanding of the attitudes to disability in the two cultures, and to inform cultural practice in promoting support and equality in both cultures. The study finds that Islam and Christianity have much in common and are a force for good in promoting and developing disability equality in both Muslim and Christian cultures