Gate-tunable subband degeneracy in semiconductor nanowires.

Degeneracy and symmetry have a profound relation in quantum systems. Here, we report gate-tunable subband degeneracy in PbTe nanowires with a nearly symmetric cross-sectional shape. The degeneracy is revealed in electron transport by the absence of a quantized plateau. Utilizing a dual gate design, we can apply an electric field to lift the degeneracy, reflected as emergence of the plateau. This degeneracy and its tunable lifting were challenging to observe in previous nanowire experiments, possibly due to disorder. Numerical simulations can qualitatively capture our observation, shedding light on device parameters for future applications.

Majorana Zero Modes Induced by the Meissner Effect at Small Magnetic Field.

One key difficulty in realizing Majorana zero modes (MZMs) is the required high magnetic field, which causes serious issues, e.g., shrinks the superconducting gap, reduces topological region, and weakens their robustness against disorders. In this Letter, we propose that the Meissner effect can bring the topological superconducting phase to a superconductor/topological-insulator/superconductor (SC/TI/SC) hybrid system. Remarkably, the required magnetic field strength (<10 mT) to support MZMs has been reduced by several orders of magnitude compared to that (>0.5 T) in the previous schemes. Tuning the phase difference between the top and bottom superconductors can control the number and position of the MZMs. In addition, we account for the electrostatic potential in the superconductor/topological-insulator (SC/TI) interface through the self-consistent Schrödinger-Poisson calculation, which shows the experimental accessibility of our proposal. Our proposal only needs a small magnetic field of less than 10 mT and is robust against the chemical potential fluctuation, which makes the SC/TI/SC hybrid an ideal Majorana platform.

Noise-Resilient Phase Estimation with Randomized Compiling.

We develop an error mitigation method for the control-free phase estimation. We prove a theorem that under the first-order correction, the phases of a unitary operator are immune to the noise channels with only Hermitian Kraus operators, and therefore, certain benign types of noise for phase estimation are identified. By further incorporating the randomized compiling protocol, we can convert the generic noise in the phase estimation circuits into stochastic Pauli noise, which satisfies the condition of our theorem. Thus, we achieve a noise-resilient phase estimation without any quantum resource overhead. The simulated experiments show that our method can significantly reduce the estimation error of the phases by up to 2 orders of magnitude. Our method paves the way for the utilization of quantum phase estimation before the advent of fault-tolerant quantum computers.

An endometrium of type C along with an endometrial thickness of < 8 mm are risk factors for ectopic pregnancy after stimulated cycles with fresh embryo transfer.

BACKGROUND: The study investigated whether specific ultrasonographically observed endometrial features (including endometrium type and thickness) were linked to ectopic pregnancy after stimulated cycles with fresh embryo transfer. METHOD: Of 6246 pregnancy cycles after fresh embryo transfer, 6076 resulted in intrauterine pregnancy and 170 in ectopic pregnancy. The primary outcome of the study was ectopic pregnancy, with the main variables being endometrium type and endometrial thickness. Univariate and subsequent multiple-stepwise logistic regression analyses were used to identify the risk factors of ectopic pregnancy. RESULTS: 1. Compared with patients with an endometrial thickness ≥ 8 mm, the adjusted odds ratio for those with an endometrial thickness < 8 mm was 3.368 (P < 0.001). The adjusted odds ratio for women with a type-C endometrium was 1.897 (P = 0.019) compared with non-type C. 2. A larger dose of gonadotropin used during controlled ovarian hyperstimulation was a protective factor against ectopic pregnancy (P = 0.008). 3. The GnRH antagonist protocol (P = 0.007) was a risk factor for ectopic pregnancy, compared with the use of GnRH agonists. CONCLUSION: (1) An endometrial thickness < 8 mm coupled with a type C endometrium significantly increased the risk of ectopic pregnancy after fresh embryo transfer. (2) A thin endometrial thickness and a type C endometrium could be further related to an abnormal endometrial receptivity/peristaltic wave. (3) Patients at a high risk of ectopic pregnancy should therefore be given special attention, with early diagnosis during the peri-transplantation period may assist in the prevention of ectopic pregnancy.

Universal Conductance Scaling of Andreev Reflections Using a Dissipative Probe.

The Majorana search is caught up in an extensive debate about the false-positive signals from nontopological Andreev bound states. We introduce a remedy using the dissipative probe to generate electron-boson interaction. We theoretically show that the interaction-induced renormalization leads to significantly distinct universal zero-bias conductance behaviors, i.e., distinct characteristic power law in temperature, for different types of Andreev reflections, that show a sharp contrast to that of a Majorana zero mode. Various specific cases have been studied, including the cases in which two charges involved in an Andreev reflection process maintain or lose coherence, and the cases for multiple Andreev bound states with or without a Majorana. A transparent list of conductance features in each case is provided to help distinguish the observed subgap states in experiments, which also promotes the identification of Majorana zero modes.

Plateau Regions for Zero-Bias Peaks within 5% of the Quantized Conductance Value 2e

Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at 2e^{2}/h at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close to 2e^{2}/h, mostly within 5% tolerance, by sweeping gate voltages and magnetic field. We further map out the phase diagram and identify two plateau regions in the phase space. Despite the presence of disorder and quantum dots, our result constitutes a step forward toward establishing Majorana zero modes.

Suppressing Andreev Bound State Zero Bias Peaks Using a Strongly Dissipative Lead.

Hybrid semiconductor-superconductor nanowires are predicted to host Majorana zero modes that induce zero-bias peaks (ZBPs) in tunneling conductance. ZBPs alone, however, are not sufficient evidence due to the ubiquitous presence of Andreev bound states. Here, we implement a strongly resistive normal lead in InAs-Al nanowire devices and show that most of the expected Andreev bound state-induced ZBPs can be suppressed, a phenomenon known as environmental Coulomb blockade. Our result is the first experimental demonstration of this dissipative interaction effect on Andreev bound states and can serve as a possible filter to narrow down the ZBP phase diagram in future Majorana searches.

Dissipative Floquet Majorana Modes in Proximity-Induced Topological Superconductors.

We study a realistic Floquet topological superconductor, a periodically driven nanowire proximitized to an equilibrium s-wave superconductor. Because of the strong energy and density fluctuations caused by the superconducting proximity effect, the Floquet Majorana wire becomes dissipative. We show that the Floquet band structure is still preserved in this dissipative system. In particular, we find that the Floquet Majorana zero and π modes can no longer be simply described by the Floquet topological band theory. We also propose an effective model to simplify the calculation of the lifetime of these Floquet Majoranas and find that the lifetime can be engineered by the external driving field.

Quantum phase transition in a resonant level coupled to interacting leads.

A Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the 'conventional' Fermi liquids formed by interacting electrons in two and three dimensions. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms and strongly correlated bulk materials.

Proposed method for tunneling spectroscopy with ohmic dissipation using resistive electrodes: a possible Majorana filter.

We propose a scheme to distinguish zero-energy peaks due to Majorana from those due to other effects at finite temperature by simply replacing the normal metallic lead with a resistive lead (large R∼kΩ) in the tunneling spectroscopy. The dissipation effects due to the large resistance change the tunneling conductance significantly in different ways. The Majorana peak remains increase as temperature decreases G∼T(2r-1) for r=e2R/h<1/2. The zero-energy peak due to other effects splits into two peaks at finite temperature and the conductance at zero voltage bias varies with temperature by a power law. The dissipative tunneling with a Majorana mode belongs to the same universal class as the unstable critical point of the case with a non-Majorana mode.

Floquet Majorana fermions for topological qubits in superconducting devices and cold-atom systems.

We develop an approach to realizing a topological phase transition and non-Abelian braiding statistics with dynamically induced Floquet Majorana fermions (FMFs). When the periodic driving potential does not break fermion parity conservation, FMFs can encode quantum information. Quasienergy analysis shows that a stable FMF zero mode and two other satellite modes exist in a wide parameter space with large quasienergy gaps, which prevents transitions to other Floquet states under adiabatic driving. We also show that in the asymptotic limit FMFs preserve non-Abelian braiding statistics and, thus, behave like their equilibrium counterparts.

Benchmarking universal quantum gates via channel spectrum.

Noise remains the major obstacle to scalable quantum computation. Quantum benchmarking provides key information on noise properties and is an important step for developing more advanced quantum processors. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limitations, we propose channel spectrum benchmarking (CSB), a method to infer the noise properties of the target gate, including process fidelity, stochastic fidelity, and some unitary parameters, from the eigenvalues of its noisy channel. Our CSB method is insensitive to state-preparation and measurement errors, and importantly, can benchmark universal gates and is scalable to many-qubit systems. Unlike standard randomized schemes, CSB can provide direct noise information for both target native gates and circuit fragments, allowing benchmarking and calibration of global entangling gates and frequently used modules in quantum algorithms like Trotterized Hamiltonian evolution operator in quantum simulation.

Anomalous universal conductance as a hallmark of non-locality in a Majorana-hosted superconducting island.

The non-local feature of topological states of matter is the key for the topological protection of quantum information and enables robust non-local manipulation in quantum information. Here we propose to manifest the non-local feature of a Majorana-hosted superconducting island by measuring the temperature dependence of Coulomb blockade peak conductance in different regimes. In the low-temperature regime, we discover a coherent double Majorana-assisted teleportation (MT) process, where any independent tunneling process always involves two coherent non-local MTs; and we also find an anomalous universal scaling behavior, i.e., a crossover from a [Formula: see text] power-law to a [Formula: see text] power-law conductance behavior when energy scale increases - in stark contrast to the usual exponential suppression due to certain local transport. In the high-temperature regime, the conductance is instead proportional to the temperature inverse, indicating a non-monotonic temperature-dependence of the conductance. Both the anomalous power law and non-monotonic temperature-dependence of the conductance can be distinguished from the conductance peak in the traditional Coulomb block, and therefore, together serve as a hallmark for the non-local feature in the Majorana-hosted superconducting island.

Controllable Majorana vortex states in iron-based superconducting nanowires.

To reveal the non-Abelian braiding statistics of Majorana zero modes (MZMs), it is crucial to design a Majorana platform, in which MZMs can be easily manipulated in a broad topological nontrivial parameter space. This is also an essential step to confirm their existence. In this study, we propose an iron-based superconducting nanowire system with Majorana vortex states to satisfy desirable conditions. This system has a radius-induced topological phase transition, giving a lower bound for the nanowire radius. In the topological phase, the iron-based superconducting nanowires have only one pair of MZMs over a wide range of radii, chemical potential and external magnetic fields. The wave function of MZMs has a sizable distribution at the side edge of the nanowires. This property enables the control of the interaction of MZMs in neighboring vortex nanowires and paves the way for Majorana fusion and braiding.

An Endometrial Thickness < 8 mm Was Associated With a Significantly Increased Risk of EP After Freeze-Thaw Transfer: An Analysis of 5,960 Pregnancy Cycles.

Introduction: Endometrium characteristics that are most likely to induce ectopic pregnancy were investigated on the basis of the data of 5,960 pregnant freeze-thaw cycles. Methods: A total of 5,960 pregnancy cycles after freeze-thaw embryos transfer were included, with the number of intrauterine and ectopic pregnancies being 5,777 and 183, respectively. Ectopic pregnancy was the primary outcome. Endometrial thickness was the main measured variable. The risk factors of ectopic pregnancy were eventually determined based on univariate analysis and subsequent multiple-stepwise logistic regression analysis. Results: 1. After adjusting for confounders, endometrial thickness could independently predict ectopic pregnancy. The adjusted odd ratios for women with endometrial thickness in the ranges of < 8 mm, 8-9.9 mm, and 10-11.9 mm were 3.270 [95% confidence interval (CI), 1.113-9.605, P = 0.031], 2.758 (95% CI, 0.987-7.707, P = 0.053), and 1.456 (95% CI, 0.502-4.225, P = 0.489), respectively, when compared with those having an endometrial thickness of 12-13.9 mm. 2. Endometrial type and preparation protocol were however not identified as risk factors for ectopic pregnancy. Discussion: 1. After freeze-thaw embryo transfer, risks of ectopic pregnancy were significantly higher when the endometrial thickness was < 8 mm. 2. A thin endometrial thickness could be linked with abnormal endometrial peristaltic waves or abnormal endometrial receptivity. 3. Adequate attention should therefore be paid to patients with a thin endometrial thickness to prevent EP or to achieve early diagnosis during the peri-transplantation period.

[Impact of sperm source and parameters on the outcome of intracytoplasmic sperm injection].

OBJECTIVE: To evaluate the impact of sperm source and sperm parameters on the outcome of intracytoplasmic sperm injection (ICSI). METHODS: This retrospective study included 433 ICSI cycles from June 2005 to December 2008 in Reproductive Medical Center of Xiangya Hospital. The patients were divided into 2 major groups according to the source of spermatozoa used for ICSI: ejaculated (group A, n=336) and epididymal (group B, n=97). Group A was divided into 3 subgroups according to the sperm parameters: normal (Group A1, n=95), single parameter defect (Group A2, n=119), and multiple parameter defect (Group A3, n=122). RESULTS: The basic characteristics among the 4 groups had no statistic difference (P>0.05), and the difference in the fertilization rate, normal fertilization rate, cleaving embryo rate,good quality embryo rate, implanted rate, clinical pregnancy rate, and early abortion rate among the 4 groups were not significant (P>0.05). CONCLUSION: The outcome is similar no matter whether the spermatozoa is from ejaculated sperm or epididymis. ICSI can treat male infertility of various factors, and the outcome is the same with one or multiple sperm parameter abnormality. ICSI with epididymal spermatozoa through percutaneous epididymal sperm aspiration is effective for infertility due to obstructive azoospermia.

[Sperm-oocyte interaction and in vitro fertilization clinical outcomes in patients with unexplained infertility].

OBJECTIVE: To determine the sperm-zona pellucida (ZP) binding and ZP-induced acrosome reaction in patients with unexplained infertility, and to discuss the relationship between ZP-induced acrosome reaction and fertilization rate. METHODS: We compared the fertilization rate and good embryo rate in patients with unexplained infertility after fertilization in 2 ways. Based on the causes of infertility, patients were divided into an unexplained infertility group (Group A) and a pure female tubal factor group (Group B). Oocytes which were obtained by super ovulation from 25 patients with unexplained infertility were randomly divided into 2 groups with conventional in vitro fertilization (IVF) (Group A1) and intracytoplasmic sperm injection (ICSI) fertilization (Group A2). The pure female tubal factor group (Group B) had conventional IVF. We conducted sperm-ZP binding and ZP-induced acrosome reaction experiments with 2 groups of men's sperms separately. We compared the number of sperm-egg binding and ZP-induced acrosome reaction rate and discussed the relationship between the ZP-induced acrosome reaction and fertilization rate, and also the fertilization rate, good embryo rate and pregnancy rate in patients with unexplained infertility after fertilization in 2 ways. RESULTS: The average number of sperm-egg binding (78.29 ± 16.31) and the ZP-induced acrosome reaction rate (55.87 ± 27.69) % in Group A were lower than those of Group B [94.63 ± 6.72, (82.53 ± 17.99)%]. The difference between the average number of sperm-egg binding and the ZP-induced acrosome reaction was significant (P <0.01). The fertilization rate of Group A1 was significantly lower than that of Group B and Group A2 (P <0.01). But there was no significant difference in the good embryo rate among the 3 groups. There was no significant difference between Group A2 and B in fertilization rate and good embryo rate (P <0.05). There was no significant difference in pregnancy rate between Group A and B (P <0.05). Fertilization rate and the rate of acrosome reaction had marked positive correlation with statistical significance (r =0.932, P <0.01). CONCLUSION: ZP binding and ZP-induced acrosome reaction are very important experiments in sperm function test for patients with unexplained infertility. It can not only effectively avoid no embryo transferring due to complete failure of fertilization but also get a desirable outcome of pregnancy using half-ICSI fertilization in patients with unexplained infertility.

Early prediction of live birth for assisted reproductive technology patients: a convenient and practical prediction model.

Live birth is the most important concern for assisted reproductive technology (ART) patients. Therefore, in the medical reproductive centre, obstetricians often need to answer the following question: "What are the chances that I will have a healthy baby after ART treatment?" To date, our obstetricians have no reference on which to base the answer to this question. Our research aimed to solve this problem by establishing prediction models of live birth for ART patients. Between January 1, 2010, and May 1, 2017, we conducted a retrospective cohort study of women undergoing ART treatment at the Reproductive Medicine Centre, Xiangya Hospital of Central South University, Hunan, China. The birth of at least one live-born baby per initiated cycle or embryo transfer procedure was defined as a live birth, and all other pregnancy outcomes were classified as no live birth. A live birth prediction model was established by stepwise multivariate logistic regression. All eligible subjects were randomly allocated to two groups: group 1 (80% of subjects) for the establishment of the prediction models and group 2 (20% of subjects) for the validation of the established prediction models. The sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) of each prediction model at different cut-off values were calculated. The prediction model of live birth included nine variables. The area under the ROC curve was 0.743 in the validation group. The sensitivity, specificity, PPV, and NPV of the established model ranged from 97.9-24.8%, 7.2-96.3%, 44.8-83.8% and 81.7-62.5%, respectively, at different cut-off values. A stable, reliable, convenient, and satisfactory prediction model for live birth by ART patients was established and validated, and this model could be a useful tool for obstetricians to predict the live rate of ART patients. Meanwhile, it is also a reference for obstetricians to create good conditions for infertility patients in preparation for pregnancy.

Quantum phase transition and emergent symmetry in a quadruple quantum dot system.

We propose a system of four quantum dots designed to study the competition between three types of interactions: Heisenberg, Kondo, and Ising. We find a rich phase diagram containing two sharp features: a quantum phase transition (QPT) between charge-ordered and charge-liquid phases and a dramatic resonance in the charge liquid visible in the conductance. The QPT is of the Kosterlitz-Thouless type with a discontinuous jump in the conductance at the transition. We connect the resonance phenomenon with the degeneracy of three levels in the isolated quadruple dot and argue that this leads to a Kondo-like emergent symmetry from left-right Z2 to U(1).

[Effect of 7-day gonadotropin-releasing hormone agonist protocol on IGF-II and IGFBP-4 levels in the follicular fluid].

OBJECTIVE: To explore the different effect of short 7-day gonadotropin releasing hormone agonist (GnRHa) protocol and GnRHa long protocol on the insulin-like growth factor II(IGF-II) and insulin-like growth factor binding protein-4 (IGFBP-4) levels in follicular fluid. METHODS: Eighty-eight infertile patients due to tubal factors were included in this study. They were randomly divided into a short 7-day GnRHa protocol group and a GnRHa long protocol group (n = 44). Follicular fluid was obtained from dominant follicles during oocyte retrieval. Levels of IGF-II and IGFBP-4 in the follicular fluid were detected by radioimmunoassay and enzyme-linked immunosorbent assay respectively. RESULTS: Duration of controlled ovarian stimulation was significantly shorter and the injected dosages of gonadotropin were significantly lower in the short 7-day protocol group. The differences in serum levels of estradiol and estradiol per mature follicle on the day of human chorionic gonadotropin injection between the two groups were not significant. The concentrations of IGF-II and IGFBP-4 in the follicular fluid of the short 7-day protocol group were significantly lower,while the difference of the ratio of IGF-II/IGFBP-4 between the two groups was not significant. Linear correlation analysis showed that IGF-II level in the follicular fluid was positively correlated to the total dose of gonadotropin. CONCLUSION: The short 7-day and long GnRHa protocols may affect the concentrations of IGF-II and IGFBP-4 in the follicular fluid. However, changes of IGF-II and IGFBP-4 concentrations do not contribute to different clinical outcomes.