Quantum Locally Testable Code with Exotic Parameters

In this paper, we present a few simple constructions of quantum locally testable codes that achieve interesting parameters which were previously unknown. We introduce an operation which we give the name check product, and show how this operation gives rise to quantum locally testable codes of constant soundness and linear rate, with varying distance and locality

Single-shot decoding of good quantum LDPC codes

Quantum Tanner codes constitute a family of quantum low-density parity-check (LDPC) codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Z\'emor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.Comment: 35 pages, 3 figure

A multicenter study of fetal chromosomal abnormalities in Chinese women of advanced maternal age

AbstractObjectiveThis study aimed to determine the rates of different fetal chromosomal abnormalities among women of advanced maternal age in China and to discuss the possible misdiagnosis risks of newer molecular techniques, for selection of appropriate prenatal screening and diagnostic technologies.Materials and MethodsSecond trimester amniocentesis and fetal karyotype results of 46,258 women were retrospectively reviewed. All women were ≥ 35 years old with singleton pregnancies. The rates of clinically significant chromosomal abnormalities (CSCAs), incidence of chromosomal abnormalities, and correlations with age were determined.ResultsFrom 2001 to 2010, the proportion of women of advanced maternal age undergoing prenatal diagnosis increased from 20% to 46%. The mean age was 37.4 years (range, 35–46 years). A total of 708 cases of CSCAs, with a rate of 1.53% were found. Trisomy 21 was the most common single chromosome abnormality and accounted for 55.9% of all CSCAs with an incidence of 0.86%. Trisomy 13, trisomy 18, and trisomy 21, the most common chromosome autosomal aneuploidies, accounted for 73.6% of all CSCAs, with a rate of 1.13%. As a group, the most common chromosomal aneuploidies (13/18/21/X/Y) accounted for 93.9% of all abnormalities, with a rate of 1.44%. The incidence of trisomy 21, trisomy 13/18/21 as a group, and 13/18/21/X/Y as a group was significantly greater in women aged 39 years and older (p < 0.001), but was not different between women aged 35 years, 36 years, 37 years, and 38 years.ConclusionThese findings may assist in genetic counseling of advanced maternal age pregnant women, and provide a basis for the selection of prenatal screening and diagnostic technologies

Precise Measurements of Branching Fractions for Ds+D_s^+ Meson Decays to Two Pseudoscalar Mesons

We measure the branching fractions for seven $D_{s}^{+}$ two-body decays to pseudo-scalar mesons, by analyzing data collected at $\sqrt{s}=4.178\sim4.226$ GeV with the BESIII detector at the BEPCII collider. The branching fractions are determined to be $\mathcal{B}(D_s^+\to K^+\eta^{\prime})=(2.68\pm0.17\pm0.17\pm0.08)\times10^{-3}$, $\mathcal{B}(D_s^+\to\eta^{\prime}\pi^+)=(37.8\pm0.4\pm2.1\pm1.2)\times10^{-3}$, $\mathcal{B}(D_s^+\to K^+\eta)=(1.62\pm0.10\pm0.03\pm0.05)\times10^{-3}$, $\mathcal{B}(D_s^+\to\eta\pi^+)=(17.41\pm0.18\pm0.27\pm0.54)\times10^{-3}$, $\mathcal{B}(D_s^+\to K^+K_S^0)=(15.02\pm0.10\pm0.27\pm0.47)\times10^{-3}$, $\mathcal{B}(D_s^+\to K_S^0\pi^+)=(1.109\pm0.034\pm0.023\pm0.035)\times10^{-3}$, $\mathcal{B}(D_s^+\to K^+\pi^0)=(0.748\pm0.049\pm0.018\pm0.023)\times10^{-3}$, where the first uncertainties are statistical, the second are systematic, and the third are from external input branching fraction of the normalization mode $D_s^+\to K^+K^-\pi^+$. Precision of our measurements is significantly improved compared with that of the current world average values