Matrix Product Representation of Locality Preserving Unitaries

The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that are unitary provides a necessary and sufficient representation of 1D unitaries that preserve locality. That is, we show that matrix product operators that are unitary are guaranteed to preserve locality by mapping local operators to local operators while at the same time all locality preserving unitaries can be represented in a matrix product way. Moreover, we show that the matrix product representation gives a straight-forward way to extract the GNVW index defined in Ref.\cite{Gross2012} for classifying 1D locality preserving unitaries. The key to our discussion is a set of `fixed point' conditions which characterize the form of the matrix product unitary operators after blocking sites. Finally, we show that if the unitary condition is relaxed and only required for certain system sizes, the matrix product operator formalism allows more possibilities than locality preserving unitaries. In particular, we give an example of a simple matrix product operator which is unitary only for odd system sizes, does not preserve locality and carries a `fractional' index as compared to their locality preserving counterparts.Comment: 14 page

Boson condensation and instability in the tensor network representation of string-net states

The tensor network representation of many-body quantum states, given by local tensors, provides a promising numerical tool for the study of strongly correlated topological phases in two dimension. However, tensor network representations may be vulnerable to instabilities caused by small perturbations of the local tensor, especially when the local tensor is not injective. For example, the topological order in tensor network representations of the toric code ground state has been shown to be unstable under certain small variations of the local tensor, if these small variations do not obey a local $Z_2$ symmetry of the tensor. In this paper, we ask the questions of whether other types of topological orders suffer from similar kinds of instability and if so, what is the underlying physical mechanism and whether we can protect the order by enforcing certain symmetries on the tensor. We answer these questions by showing that the tensor network representation of all string-net models are indeed unstable, but the matrix product operator (MPO) symmetries of the local tensor can help to protect the order. We find that, `stand-alone' variations that break the MPO symmetries lead to instability because they induce the condensation of bosonic quasi-particles and destroy the topological order in the system. Therefore, such variations must be forbidden for the encoded topological order to be reliably extracted from the local tensor. On the other hand, if a tensor network based variational algorithm is used to simulate the phase transition due to boson condensation, then such variation directions must be allowed in order to access the continuous phase transition process correctly.Comment: 44 pages, 85 figures, comments welcom

Fermionic quantum cellular automata and generalized matrix product unitaries

We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) fermionic MPUs do not necessarily feature a strict causal cone and (ii) not all fermionic Quantum Cellular Automata (QCA) can be represented as fermionic MPUs. We then introduce a natural generalization of the latter, obtained by allowing for an additional operator acting on their auxiliary space. We characterize a family of such generalized MPUs that are locality-preserving, and show that, up to appending inert ancillary fermionic degrees of freedom, any representative of this family is a fermionic QCA and viceversa. Finally, we prove an index theorem for generalized MPUs, recovering the recently derived classification of fermionic QCA in one dimension. As a technical tool for our analysis, we also introduce a graded canonical form for fermionic matrix product states, proving its uniqueness up to similarity transformations.Comment: 35 pages, no figures; v2: minor revisio

Boson condensation and instability in the tensor network representation of string-net states

The tensor network representation of many-body quantum states, given by local tensors, provides a promising numerical tool for the study of strongly correlated topological phases in two dimensions. However, the representation may be vulnerable to instabilities caused by small variations in the local tensors. For example, the topological order in the tensor network representations of the toric code ground state has been shown in Chen, Zeng, Gu, Chuang, and Wen, Phys. Rev. B 82, 165119 (2010)to be unstable if the variations break certain Z_2 symmetry of the tensor. In this work, we ask whether other types of topological orders suffer from similar kinds of instability and if so, what is the underlying physical mechanism and whether we can protect the order by enforcing certain symmetries on the tensor. We answer these questions by showing that the tensor network representations of all string-net models are indeed unstable, but the matrix product operator (MPO) symmetries of the tensors identified in Şahinoğlu, Williamson, Bultinck, Mariën, Haegeman, Schuch, and Verstraete, arXiv:1409.2150 can help to protect the order. In particular, we show that a subset of variations that break the MPO symmetries lead to instability by inducing the condensation of bosonic quasiparticles, which destroys the topological order in the wave function. Therefore such variations must be forbidden for the encoded topological order to be reliably extracted from the local tensors. On the other hand, if a tensor network based variational algorithm is used to simulate the phase transition due to boson condensation, such variation directions may prove important to access the continuous transition correctly

Artificial intelligence (AI): multidisciplinary perspectives on emerging challenges, opportunities, and agenda for research and practice

As far back as the industrial revolution, great leaps in technical innovation succeeded in transforming numerous manual tasks and processes that had been in existence for decades where humans had reached the limits of physical capacity. Artificial Intelligence (AI) offers this same transformative potential for the augmentation and potential replacement of human tasks and activities within a wide range of industrial, intellectual and social applications. The pace of change for this new AI technological age is staggering, with new breakthroughs in algorithmic machine learning and autonomous decision making engendering new opportunities for continued innovation. The impact of AI is significant, with industries ranging from: finance, retail, healthcare, manufacturing, supply chain and logistics all set to be disrupted by the onset of AI technologies. The study brings together the collective insight from a number of leading expert contributors to highlight the significant opportunities, challenges and potential research agenda posed by the rapid emergence of AI within a number of domains: technological, business and management, science and technology, government and public sector. The research offers significant and timely insight to AI technology and its impact on the future of industry and society in general

Structural and Optoelectronic Characterization of RF Sputtered ZnSnN_2

ZnSnN_2, a new earth-abundant semiconductor, is synthesized and characterized for use as a photovoltaic absorber material. Results confirm the predicted orthorhombic Pna2_1 crystal structure in RF sputtered thin films. Additionally, optical measurements reveal a direct bandgap of about 2 eV, which is larger than our calculated bandgap of 1.42 eV due to the Burstein-Moss effect

The impact of air pollution on deaths, disease burden, and life expectancy across the states of India: the Global Burden of Disease Study 2017

Summary: Background: Air pollution is a major planetary health risk, with India estimated to have some of the worst levels globally. To inform action at subnational levels in India, we estimated the exposure to air pollution and its impact on deaths, disease burden, and life expectancy in every state of India in 2017. Methods: We estimated exposure to air pollution, including ambient particulate matter pollution, defined as the annual average gridded concentration of PM2.5, and household air pollution, defined as percentage of households using solid cooking fuels and the corresponding exposure to PM2.5, across the states of India using accessible data from multiple sources as part of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017. The states were categorised into three Socio-demographic Index (SDI) levels as calculated by GBD 2017 on the basis of lag-distributed per-capita income, mean education in people aged 15 years or older, and total fertility rate in people younger than 25 years. We estimated deaths and disability-adjusted life-years (DALYs) attributable to air pollution exposure, on the basis of exposure–response relationships from the published literature, as assessed in GBD 2017; the proportion of total global air pollution DALYs in India; and what the life expectancy would have been in each state of India if air pollution levels had been less than the minimum level causing health loss. Findings: The annual population-weighted mean exposure to ambient particulate matter PM2·5 in India was 89·9 μg/m3 (95% uncertainty interval [UI] 67·0–112·0) in 2017. Most states, and 76·8% of the population of India, were exposed to annual population-weighted mean PM2·5 greater than 40 μg/m3, which is the limit recommended by the National Ambient Air Quality Standards in India. Delhi had the highest annual population-weighted mean PM2·5 in 2017, followed by Uttar Pradesh, Bihar, and Haryana in north India, all with mean values greater than 125 μg/m3. The proportion of population using solid fuels in India was 55·5% (54·8–56·2) in 2017, which exceeded 75% in the low SDI states of Bihar, Jharkhand, and Odisha. 1·24 million (1·09–1·39) deaths in India in 2017, which were 12·5% of the total deaths, were attributable to air pollution, including 0·67 million (0·55–0·79) from ambient particulate matter pollution and 0·48 million (0·39–0·58) from household air pollution. Of these deaths attributable to air pollution, 51·4% were in people younger than 70 years. India contributed 18·1% of the global population but had 26·2% of the global air pollution DALYs in 2017. The ambient particulate matter pollution DALY rate was highest in the north Indian states of Uttar Pradesh, Haryana, Delhi, Punjab, and Rajasthan, spread across the three SDI state groups, and the household air pollution DALY rate was highest in the low SDI states of Chhattisgarh, Rajasthan, Madhya Pradesh, and Assam in north and northeast India. We estimated that if the air pollution level in India were less than the minimum causing health loss, the average life expectancy in 2017 would have been higher by 1·7 years (1·6–1·9), with this increase exceeding 2 years in the north Indian states of Rajasthan, Uttar Pradesh, and Haryana. Interpretation: India has disproportionately high mortality and disease burden due to air pollution. This burden is generally highest in the low SDI states of north India. Reducing the substantial avoidable deaths and disease burden from this major environmental risk is dependent on rapid deployment of effective multisectoral policies throughout India that are commensurate with the magnitude of air pollution in each state. Funding: Bill & Melinda Gates Foundation; and Indian Council of Medical Research, Department of Health Research, Ministry of Health and Family Welfare, Government of India

SARS-CoV-2 seroprevalence among the general population and healthcare workers in India, December 2020–January 2021

Background: Earlier serosurveys in India revealed seroprevalence of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) of 0.73% in May–June 2020 and 7.1% in August–September 2020. A third serosurvey was conducted between December 2020 and January 2021 to estimate the seroprevalence of SARS-CoV-2 infection among the general population and healthcare workers (HCWs) in India. Methods: The third serosurvey was conducted in the same 70 districts as the first and second serosurveys. For each district, at least 400 individuals aged ≥10 years from the general population and 100 HCWs from subdistrict-level health facilities were enrolled. Serum samples from the general population were tested for the presence of immunoglobulin G (IgG) antibodies against the nucleocapsid (N) and spike (S1-RBD) proteins of SARS-CoV-2, whereas serum samples from HCWs were tested for anti-S1-RBD. Weighted seroprevalence adjusted for assay characteristics was estimated. Results: Of the 28,598 serum samples from the general population, 4585 (16%) had IgG antibodies against the N protein, 6647 (23.2%) had IgG antibodies against the S1-RBD protein, and 7436 (26%) had IgG antibodies against either the N protein or the S1-RBD protein. Weighted and assay-characteristic-adjusted seroprevalence against either of the antibodies was 24.1% [95% confidence interval (CI) 23.0–25.3%]. Among 7385 HCWs, the seroprevalence of anti-S1-RBD IgG antibodies was 25.6% (95% CI 23.5–27.8%). Conclusions: Nearly one in four individuals aged ≥10 years from the general population as well as HCWs in India had been exposed to SARS-CoV-2 by December 2020