Strictly contractive quantum channels and physically realizable quantum computers

We study the robustness of quantum computers under the influence of errors modelled by strictly contractive channels. A channel $T$ is defined to be strictly contractive if, for any pair of density operators $\rho,\sigma$ in its domain, $\| T\rho - T\sigma \|_1 \le k \| \rho-\sigma \|_1$ for some $0 \le k < 1$ (here $\| \cdot \|_1$ denotes the trace norm). In other words, strictly contractive channels render the states of the computer less distinguishable in the sense of quantum detection theory. Starting from the premise that all experimental procedures can be carried out with finite precision, we argue that there exists a physically meaningful connection between strictly contractive channels and errors in physically realizable quantum computers. We show that, in the absence of error correction, sensitivity of quantum memories and computers to strictly contractive errors grows exponentially with storage time and computation time respectively, and depends only on the constant $k$ and the measurement precision. We prove that strict contractivity rules out the possibility of perfect error correction, and give an argument that approximate error correction, which covers previous work on fault-tolerant quantum computation as a special case, is possible.Comment: 14 pages; revtex, amsfonts, amssymb; made some changes (recommended by Phys. Rev. A), updated the reference

Safety outcomes during pediatric GH therapy: final results from the prospective GeNeSIS observational program

CONTEXT: Safety concerns regarding premature mortality, diabetes, neoplasia and cerebrovascular disease in association with growth hormone (GH) therapy have been raised. OBJECTIVE: To assess incidence of key safety outcomes. DESIGN: Prospective, multinational, observational study (1999-2015). SETTING: 22,311 GH-treated children from 827 investigative sites in 30 countries. PATIENTS: Children with growth disorders. INTERVENTIONS: GH treatment. MAIN OUTCOME MEASURES: Standardized mortality (SMR) and incidence (SIR) ratios with 95% confidence intervals (CI) for mortality, diabetes, and primary cancer, using general population registries. RESULTS: Predominant short stature diagnoses were GH deficiency (63%), idiopathic short stature (13%), and Turner syndrome (8%), with mean±SD follow-up of 4.2±3.2 years (∼92,000 person-years [PY]). Forty-two deaths occurred in patients with follow-up, with SMR (95% CI) of 0.61 (0.44-0.82); the SMR was elevated for patients with cancer-related organic GH deficiency (5.87 [3.21-9.85]). Based on 18 cases, Type 2 diabetes (T2DM) risk was elevated (SIR 3.77 [2.24-5.96]), but 72% had risk factors. In patients without cancer history, 14 primary cancers were observed (SIR 0.71 [0.39-1.20]). Second neoplasms occurred in 31/622 (5.0%) cancer survivors (10.7 [7.5-15.2] cases/1000 PY), and intracranial tumor recurrences in 67/823 (8.1%) tumor survivors (16.9 [13.3-21.5] cases/1000 PY). All 3 hemorrhagic stroke cases had risk factors. CONCLUSIONS: GeNeSIS data support the favourable safety profile of pediatric GH treatment. Overall risk for death or primary cancer was not elevated in GH-treated children, and no hemorrhagic strokes occurred in patients without risk factors. T2DM incidence was elevated compared to the general population, but most cases had diabetes risk factors

A luteinizing hormone receptor intronic variant is significantly associated with decreased risk of Alzheimer's disease in males carrying an apolipoprotein E ε4 allele

Genetic and biochemical studies support the apolipoprotein E (APOE) ε4 allele as a major risk factor for late-onset Alzheimer's disease (AD), though ~50% of AD patients do not carry the allele. APOE transports cholesterol for luteinizing hormone (LH)-regulated steroidogenesis, and both LH and neurosteroids have been implicated in the etiology of AD. Since polymorphisms of LH beta-subunit (LHB) and its receptor (LHCGR) have not been tested for their association with AD, we scored AD and age-matched control samples for APOE genotype and 14 polymorphisms of LHB and LHCGR. Thirteen gene-gene interactions between the loci of LHB, LHCGR, and APOE were associated with AD. The most strongly supported of these interactions was between an LHCGR intronic polymorphism (rs4073366; lhcgr2) and APOE in males, which was detected using all three interaction analyses: linkage disequilibrium, multi-dimensionality reduction, and logistic regression. While the APOE ε4 allele carried significant risk of AD in males [p = 0.007, odds ratio (OR) = 3.08(95%confidence interval: 1.37, 6.91)], ε4-positive males carrying 1 or 2 C-alleles at lhcgr2 exhibited significantly decreased risk of AD [OR = 0.06(0.01, 0.38); p = 0.003]. This suggests that the lhcgr2 C-allele or a closely linked locus greatly reduces the risk of AD in males carrying an APOE ε4 allele. The reversal of risk embodied in this interaction powerfully supports the importance of considering the role gene-gene interactions play in the etiology of complex biological diseases and demonstrates the importance of using multiple analytic methods to detect well-supported gene-gene interactions