Noise-induced barren plateaus in variational quantum algorithms.

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

Uterine Fundus Remodeling after Hysteroscopic Metroplasty: A Prospective Pilot Study.

The septate uterus is the most common congenital uterine malformation and is treated by hysteroscopic metroplasty. There are few studies on the fundal uterine changes that occur after surgery. We designed a pilot prospective observational study to evaluate by three-dimensional transvaginal ultrasound (3D-TVS) the changes not only of the internal fundal uterine profile, but also of the external one, after hysteroscopic metroplasty. Sixty women who underwent hysteroscopic metroplasty for partial or complete uterine septum (U2a and U2b subclasses of ESHRE/ESGE classification) were enrolled. We performed 3D-TVS after surgery confirming optimal removal of the septum. However, at ultrasound follow-up after three months, we observed a significant increase (p < 0.001) in the residual septum (Zr) (3.7 mm (95% CI: 3.1-4.4)), the myometrial wall thickness (Y) (2.5 mm (95% CI: 2.0-3.0)) and the total fundal wall thickness (Y + Zr) (6.2 mm (95% CI: 5.5-6.9)). Forty-three patients (72%) required a second step of hysteroscopic metroplasty. Moreover, the shape of uterine fundus changed in 58% of cases. We actually observed a remodeling of the uterine fundus with modifications of its external and internal profiles. Therefore, we propose to always perform a second ultrasound look at least three months after the metroplasty to identify cases that require a second- step metroplasty.

Uterine PEComa initially misdiagnosed as a leiomyoma: Sonographic findings and review of the literature.

Perivascular epithelioid cell neoplasms (PEComas) are rare mesenchymal tumors with malignant potential that arise from gynecological organs in up to 25% of cases. The lack of data regarding the preoperative US features of uterine PEComas is reflected by the frequent misdiagnosis with leiomyomas. We describe the sonographic appearance of a richly vascularized cervical PEComa mimicking a myoma and report the analysis of six additional cases in the literature with a description of their ultrasound features. Most cases involved a single lesion arising from the uterine cervix with a rapid growth pattern, regular margins, heterogeneous echogenicity, absence of shadowing, and moderate-to-rich vascularity.

Fertility Sparing Treatment of Endometrial Cancer with and without Initial Infiltration of Myometrium: A Single Center Experience.

Endometrial cancer (EC) is the fourth largest female cancer in Europe and North America. In 5% of cases, the diagnosis is made in women who wish to become pregnant. In our retrospective study, we reported our experience about fertility sparing treatment of G1 endometrioid endometrial cancer (G1 EEC) or atypical endometrial hyperplasia/endometrial intraepithelial neoplasm (AEH/EIN) in young women desiring pregnancy treated in our Center. Conservative treatment was based on operative hysteroscopy and hormone therapy with megestrol acetate (160 mg/die for 9 months). For the first time we included women with G1 EEC with minimal myometrial infiltration. The minimum follow-up period was two years and consisted of serial outpatient hysteroscopies with endometrial biopsies. Among the 36 women with G1 EEC we observed one case of disease persistence and four recurrences and four recurrences among the 46 women diagnosed with AEH/EIN. To date, 35 live births were obtained in both groups. Our results advance the hypothesis that conservative treatment can represent a safe and feasible alternative to propose to young women with desire for pregnancy. Further randomized and multicentric studies are needed to arrive at unambiguous and standardized guidelines on the surgical and medical treatment of young women with EEC or AEH/EIN.