Characterizing barren plateaus in quantum ansätze with the adjoint representation.

Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups. It has been postulated that many properties of variational quantum algorithms can be understood by studying their corresponding groups, chief among them the presence of vanishing gradients or barren plateaus, but a theoretical derivation has been lacking. Using tools from the representation theory of compact Lie groups, we formulate a theory of barren plateaus for parameterized quantum circuits whose observables lie in their dynamical Lie algebra, covering a large variety of commonly used ansätze such as the Hamiltonian Variational Ansatz, Quantum Alternating Operator Ansatz, and many equivariant quantum neural networks.

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.

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.

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.

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.