The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its mathematical structure is described, with applications to understanding quantum correlations, illustrating quantum chaos and its unravelling, and developing software simulators for noisy quantum systems with efficient quantum state tomography.
Quantum information processing is now a well-evolved field of study with roots to quantum physics that has significantly evolved from pioneering works over almost more than a century. Today, we are at a stage where elementary forms of quantum computers and communication systems are being built and deployed. In this paper, we begin with a historical background into quantum information theory and coding theory for both entanglement-unassisted and assisted quantum communication systems, motivating the need for quantum error correction in such systems. We then begin with the necessary mathematical preliminaries towards understanding the theory behind quantum error correction, central to the discussions within this article, starting from the binary case towards the non-binary generalization, using the rich framework of finite fields. We will introduce the stabilizer framework, build upon the Calderbank-Shor-Steane framework for binary quantum codes and generalize this to the non-binary case, yielding generalized CSS codes that are linear and additive. We will survey important families of quantum codes derived from well-known classical counterparts. Next, we provide an overview of the theory behind entanglement-assisted quantum ECCs along with encoding and syndrome computing architectures. We present a case study on how to construct efficient quantum Reed-Solomon codes that saturate the Singleton bound for the non-degenerate case. We will also show how positive coding rates can be realized using tensor product codes from two zero-rate entanglement-assisted CSS codes, an effect termed as the coding analog of superadditivity, useful for entanglement-assisted quantum communications. We discuss how quantum coded networks can be realized using cluster states and modified graph state codes. Last, we will motivate fault-tolerant quantum computation from the perspective of coding theory. We end the article with our perspectives on interesting open directions in this exciting field.
The concept of a quantum computer and the idea of using the power of quantum mechanics to build one have been around for long; however, it was only in the 1980s that this project looked viable. Since then, many advances have made it possible to build quantum processors with hundreds of qubits. The article introduces this topic and touches upon what can be achieved with a functional quantum computer. It also outlines the intervening challenges in building one. It sets the stage for the technical discussions proffered in the subsequent articles.
Monogenic diabetes refers to a group of single gene disorders of insulin secretion impairment resulting in diabetes. We selected two of the commonest forms of monogenic diabetes namely, maturity onset of diabetes of the young (MODY) and neonatal diabetes mellitus (NDM), and looked for studies that reported these two conditions in South Asians (SA). The primary aim was to identify the number of monogenic diabetes cases reported so far in SA. We searched major databases from 1990 to 2022 to identify articles published on monogenic diabetes in SA countries and SAs. Original articles that showed the prevalence or reported cases of monogenic diabetes through genetic analysis, on children, adolescents and adults, published in the English Language were included. Following an initial screening by title and abstract by three reviewers, the full texts retrieved were independently screened by two reviewers. A total of 3176 studies on monogenic diabetes were obtained and 2525 abstracts were selected for the title and abstract screening, subsequently were excluded. The remaining 235 abstracts underwent full-text analysis. Finally, 46 studies (MODY, n = 18 and NDM, n = 28) were included in this paper. A total of 89 variants in MODY and 139 variants in NDM were recorded. Among the documented variants, 38 were causal for MODY and 116 were causal for NDM. This review provides the list of causal variants of MODY and NDM in SA. This could be helpful in the clinical setting for planning the treatment of MODY and NDM individuals in SA.
Systematic Review registration https://www.crd.york.ac.uk/prospero/#myprospero (ID: CRD42022296268).
Type 2 diabetes (T2D) is a multifactorial disorder which is predicted to rise from 537 to 643 million by 2030 according to International Diabetes Federation Atlas 2021. One of the major microvascular complications of T2D is diabetic kidney disease (DKD), earlier known as diabetic nephropathy which leads to end-stage renal disease (ESRD) and kidney failure. Kidney dialysis or transplantation is required for the ESRD patients which poses a socioeconomic burden worldwide. The prevalence of DKD in T2D is 25–40% worldwide and hence it is important to study the pathogenesis of DKD which will aid in understanding and treating the disease. It has been shown that hereditary factors (genes) play a crucial role in the pathogenesis and progression of DKD. A number of genes have been found to be associated with DKD using candidate gene approach and genome-wide association studies (GWAS). GWAS genotypes a large number of markers across cases and controls and finds out the genetic markers/polymorphisms which are significantly associated with the disease or a trait. This review focuses on the genetic understanding of DKD obtained from these GWA studies conducted between 2003 and 2022 and also covers the genes identified from the candidate gene approach.
Dairy products have been used for centuries and were generally believed to be healthy. Recently, dairy products have been implicated in the rise of non-communicable diseases especially new onset type 2 diabetes (T2D). However, the available data have been inconsistent.
To perform a systematic review and meta-analysis of all the available prospective studies on the effect of dairy products with incident (new onset) T2D.
A total of 3009 articles were retrieved from PubMed, Scopus, Medline and Science Direct from January 2000 to March 2022 from which 27 prospective cohort studies were included. We classified dairy products as ‘total dairy’ and ‘total milk’ and further stratified them based on their fat content and fermentation. A subgroup analysis was conducted in people of Asian and Western ethnicity.
Globally, total dairy products [Relative risk (RR) − 0.14; 95% Confidence Interval (CI) − 0.23; − 0.05; I2 = 30%], total fermented dairy [RR − 0.08; 95% CI − 0.16; − 0.00; I2 = 41%], and plain yogurt [RR − 0.08; 95% CI − 0.15; − 0.01; I2 = 34%] were inversely associated with incident T2D. Other dairy products including low and high fat total dairy products, low and high fat milk and cheese had a neutral effect with no significant association with T2D. Subgroup analysis by ethnicity suggested similar findings with total dairy products and milk having protective effects on T2D among the Asian population while fermented dairy products were protective against T2D in western populations. Among the fermented dairy products, plain yogurt, in particular, showed protection against T2D across both ethnicities. Further, subgroup analysis by age showed that the consumption of high fat dairy predisposed younger adults to T2D.
Total and fermented dairy products, particularly plain yogurt, are protective against new onset T2D while milk, cheese and other dairy products have a neutral effect with no effect on incident T2D.
This protocol was registered on the International Prospective Register of Systematic Reviews, PROSPERO (CRD42021249202).
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