Approximating dynamical correlation functions with constant depth quantum circuits

One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically the ground state. In this work, we study approximations of these correlation functions that do not require time dynamics. We show that having access to a circuit that prepares an eigenstate of the Hamiltonian, it is possible to approximate the dynamical correlation functions up to exponential accuracy in the complex frequency domain $\omega=\Re(\omega)+i\Im(\omega)$, on a strip above the real line $\Im(\omega)=0$. We achieve this by exploiting the continued fraction representation of the dynamical correlation functions as functions of frequency $\omega$, where the level $k$ approximant can be obtained by measuring a weight $O(k)$ operator on the eigenstate of interest. In the complex $\omega$ plane, we show how this approach allows to determine approximations to correlation functions with accuracy that increases exponentially with $k$. We analyse two algorithms to generate the continuous fraction representation in scalar or matrix form, starting from either one or many initial operators. We prove that these algorithms generate an exponentially accurate approximation of the dynamical correlation functions on a region sufficiently far away from the real frequency axis. We present numerical evidence of these theoretical results through simulations of small lattice systems. We comment on the stability of these algorithms with respect to sampling noise in the context of quantum simulation using quantum computers.Comment: 29 pages, 10 figure

Approximating dynamical correlation functions with constant depth quantum circuits

One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically the ground state. In this work, we study approximations of these correlation functions that do not require time dynamics. We show that having access to a circuit that prepares an eigenstate of the Hamiltonian, it is possible to approximate the dynamical correlation functions up to exponential accuracy in the complex frequency domain $\omega=\Re(\omega)+i\Im(\omega)$, on a strip above the real line $\Im(\omega)=0$. We achieve this by exploiting the continued fraction representation of the dynamical correlation functions as functions of frequency $\omega$, where the level $k$ approximant can be obtained by measuring a weight $O(k)$ operator on the eigenstate of interest. In the complex $\omega$ plane, we show how this approach allows to determine approximations to correlation functions with accuracy that increases exponentially with $k$. We analyse two algorithms to generate the continuous fraction representation in scalar or matrix form, starting from either one or many initial operators. We prove that these algorithms generate an exponentially accurate approximation of the dynamical correlation functions on a region sufficiently far away from the real frequency axis. We present numerical evidence of these theoretical results through simulations of small lattice systems. We comment on the stability of these algorithms with respect to sampling noise in the context of quantum simulation using quantum computers

Evaluation of family histories and analysis of BRCA1 founder mutations in a population-based series of breast and ovarian cancer cases in Latvia

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BRCA1/2 mutation screening in high-risk breast/ovarian cancer families and sporadic cancer patient surveilling for hidden high-risk families

Background: The estimated ratio of hereditary breast/ovarian cancer (HBOC) based on family history is 1.5% in Latvia. This is significantly lower than the European average of 5-10%. Molecular markers like mutations and SNPs can help distinguish HBOC patients in the sporadic breast and ovarian cancer group.Methods: 50 patients diagnosed with HBOC in the Latvian Cancer Registry from January 2005 to December 2008 were screened for BRCA1 founder mutation-negatives and subjected to targeted resequencing of BRCA1 and BRCA2 genes. The newly found mutations were screened for in the breast and ovarian cancer group of 1075 patients by Real Time-PCR/HRM analysis and RFLP.Results: Four BRCA2 mutations including three novel BRCA2 frameshift mutations and one previously known BRCA2 frameshift mutation and one BRCA1 splicing mutation were identified. Two of the BRCA2 mutations were found in a group of consecutive breast cancer patients with a frequency of 0.51% and 0.38%.Conclusions: Molecular screening of sequential cancer patients is an important tool to identify HBOC families.publishersversionPeer reviewe

Germline MSH2 and MLH1 mutational spectrum in HNPCC families from Poland and the Baltic States.

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Genotype-phenotype correlations among BRCA1 4153delA and 5382insC mutation carriers from Latvia

<p>Abstract</p> <p>Background</p> <p>Mutations in the high penetrance breast and ovarian cancer susceptibility gene <it>BRCA1 </it>account for a significant percentage of hereditary breast and ovarian cancer cases. Genotype-phenotype correlations of <it>BRCA1 </it>mutations located in different parts of the <it>BRCA1 </it>gene have been described previously; however, phenotypic differences of specific <it>BRCA1 </it>mutations have not yet been fully investigated. In our study, based on the analysis of a population-based series of unselected breast and ovarian cancer cases in Latvia, we show some aspects of the genotype-phenotype correlation among the <it>BRCA1 </it>c.4034delA (4153delA) and c.5266dupC (5382insC) founder mutation carriers.</p> <p>Methods</p> <p>We investigated the prevalence of the <it>BRCA1 </it>founder mutations c.4034delA and c.5266dupC in a population-based series of unselected breast (n = 2546) and ovarian (n = 795) cancer cases. Among the <it>BRCA1 </it>mutation carriers identified in this analysis we compared the overall survival, age at diagnosis and family histories of breast and ovarian cancers.</p> <p>Results</p> <p>We have found that the prevalence of breast and ovarian cancer cases (breast: ovarian cancer ratio) differs significantly among the carriers of the c.5266dupC and c.4034delA founder mutations (OR = 2.98, 95%CI = 1.58 to 5.62, P < 0.001). We have also found a difference in the prevalence of breast and ovarian cancer cases among the 1^stand 2^nddegree relatives of the c.4034delA and c.5266dupC mutation carriers. In addition, among the breast cancer cases the c.4034delA mutation has been associated with a later age of onset and worse clinical outcomes in comparison with the c.5266dupC mutation.</p> <p>Conclusions</p> <p>Our data suggest that the carriers of the c.4034delA and c.5266dupC founder mutations have different risks of breast and ovarian cancer development, different age of onset and prognosis of breast cancer.</p

Lifestyle Factors and Breast Cancer in Females with PTEN Hamartoma Tumor Syndrome (PHTS)

Simple Summary: Females with PTEN Hamartoma Tumor Syndrome (PHTS) have very high hereditary breast cancer risks up to 76%. The aim of this European cohort study was to the describe the lifestyle in PHTS patients and to assess associations between physical activity, alcohol consumption, tobacco smoking, BMI and breast cancer in female adult PHTS patients. It was observed that of 125 patients who completed the questionnaire, 81% were >= 2 times/week physically active, 86% consumed on average = 2 times (ORtotal-adj = 0.9 (95%CI 0.3-2.6); consumed daily about 1.2-1.8 times more often >= 1 than 0-1 glasses of alcohol (ORtotal-adj = 1.2 (95%CI 0.4-4.0); ORnon-breastcancer-index-adj = 1.8 (95%CI 0.4-6.9); were about 1.04-1.3 times more often smokers than non-smokers (ORtotal-adj = 1.04 (95%CI 0.4-2.8); ORnon-breastcancer-index-adj = 1.3 (95%CI 0.4-4.2)); and overweight or obesity (72%) was about 1.02-1.3 times less common (ORtotal-adj = 0.98 (95%CI 0.4-2.6); ORnon-breastcancer-index-adj = 0.8 (95%CI 0.3-2.7)). Similar associations between lifestyle and breast cancer are suggested for PHTS and the general population. Despite not being statistically significant, results are clinically relevant and suggest that awareness of the effects of lifestyle on patients' breast cancer risk is important

High frequency of pathogenic non-founder germline mutations in BRCA1 and BRCA2 in families with breast and ovarian cancer in a founder population

Funding Information: This work was supported by State Research Program “Biomedicine for the public health (BIOMEDICINE)” project 5 “Personalised cancer diagnostics and treatment effectiveness evaluation”. Publisher Copyright: © 2018 The Author(s).Background: Pathogenic BRCA1 founder mutations (c.4035delA, c.5266dupC) contribute to 3.77% of all consecutive primary breast cancers and 9.9% of all consecutive primary ovarian cancers. Identifying germline pathogenic gene variants in patients with primary breast and ovarian cancer could significantly impact the medical management of patients. The aim of the study was to evaluate the rate of pathogenic mutations in the 26 breast and ovarian cancer susceptibility genes in patients who meet the criteria for BRCA1/2 testing and to compare the accuracy of different selection criteria for second-line testing in a founder population. Methods: Fifteen female probands and 1 male proband that met National Comprehensive Cancer Network (NCCN) criteria for BRCA1/2 testing were included in the study and underwent 26-gene panel testing. Fourteen probands had breast cancer, one proband had ovarian cancer, and one proband had both breast and ovarian cancer. In a 26-gene panel, the following breast and/or ovarian cancer susceptibility genes were included: ATM, BARD1, BLM, BRCA1, BRCA2, BRIP1, CDH1, CHEK2, EPCAM, FAM175A, MEN1, MLH1, MRE11A, MSH2, MSH6, MUTYH, NBN, PALB2, PMS2, PTEN, RAD50, RAD51C, RAD51D, STK11, TP53, and XRCC2. All patients previously tested negative for BRCA1 founder mutations. Results: In 44% (7 out of 16) of tested probands, pathogenic mutations were identified. Six probands carried pathogenic mutations in BRCA1, and one proband carried pathogenic mutations in BRCA2. In patients, a variant of uncertain significance was found in BRCA2, RAD50, MRE11A and CDH1. The Manchester scoring system showed a high accuracy (87.5%), high sensitivity (85.7%) and high specificity (88.9%) for the prediction of pathogenic non-founder BRCA1/2 mutations. Conclusion: A relatively high incidence of pathogenic non-founder BRCA1/2 mutations was observed in a founder population. The Manchester scoring system predicted the probability of non-founder pathogenic mutations with high accuracy.publishersversionPeer reviewe