Diamond-shaped quantum circuit for real-time quantum dynamics in one dimension

In recent years, quantum computing has evolved as an exciting frontier, with the development of numerous algorithms dedicated to constructing quantum circuits that adeptly represent quantum many-body states. However, this domain remains in its early stages and requires further refinement to understand better the effective construction of highly-entangled quantum states within quantum circuits. Here, we demonstrate that quantum many-body states can be universally represented using a quantum circuit comprising multi-qubit gates. Furthermore, we evaluate the efficiency of a quantum circuit constructed with two-qubit gates in quench dynamics for the transverse-field Ising model. In this specific model, despite the initial state being classical without entanglement, it undergoes long-time evolution, eventually leading to a highly-entangled quantum state. Our results reveal that a diamond-shaped quantum circuit, designed to approximate the multi-qubit gate-based quantum circuit, remarkably excels in accurately representing the long-time dynamics of the system. Moreover, the diamond-shaped circuit follows the volume law behavior in entanglement entropy, offering a significant advantage over alternative quantum circuit constructions employing two-qubit gates.Comment: 15 pages, 13 figure

Fast ignitor research at the Institute of Laser Engineering, Osaka University

Copyright 2001 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Plasmas, 8(5), 2268-2274, 2001 and may be found at http://dx.doi.org/10.1063/1.135259

Recurrent dislocation of the patella accompanying hypotrochlea of the femur and malalignment of the patella

This case report describes a rare case of recurrent dislocation of the patella which was accompanied with trochlear dysplasia and malalignment of the patella in a 15-year-old girl. She complained of hemoarthrosis and recurrent patellar dislocation in the early knee flexion phase. Plain radiography and computed tomography (CT) showed patellar malalignment (quadriceps angle 20°) and severe dysplasia of the trochlea of the femur (sulcus angle 170°). Surgery was performed, consisting of trochleoplasty in addition to proximal and distal realignment. Trochleoplasty was undertaken using a modified Dejour technique. After surgery, the patient complained of joint contracture. Arthroscopic release of fibrous tissue relieved symptoms and obtained normal range of motion without patellar dislocation. Postoperative radiography and CT demonstrated improvement of the quadriceps angle (10°) and sulcus angle (140°)

Direction of the formation of anterior lumbar vertebral osteophytes

<p>Abstract</p> <p>Background</p> <p>X-ray images of lumbar degenerative diseases often show not only claw osteophytes, but also pairs of osteophytes that form in a direction away from the adjacent disc. We have investigated the direction of the formation of anterior lumbar vertebral osteophytes across the lumbar vertebrae using a sufficient number of lumbar radiographs, because osteophytes images can provide essential information that will contribute to the understanding of the pathology and progress of lumbar spine degeneration.</p> <p>Methods</p> <p>The direction of the formation of 14,250 pairs of anterior lumbar vertebral osteophytes across the adjacent intervertebral discs in 2,850 patients who were all over 60 years old was investigated. Anterior lumbar vertebral osteophytes were distributed into six groups based on the direction of extension of each pair of osteophytes across the intervertebral disc space.</p> <p>Results</p> <p>In L1–L2 and L2–L3, the number of patients classified into groups B (the pair of osteophytes extended in the direction of the adjacent disc) and C (almost complete bone bridge formation by a pair of osteophytes across the intervertebral disc space) was larger than that classified into group D (the pair of osteophytes extended in a direction away from the adjacent disc). In L3–L4, L4–L5 and L5-S1, the number of patients in group D was greater than that of patients belonging to groups B and C.</p> <p>Conclusion</p> <p>Our study showed that pairs of osteophytes frequently formed in the direction of the adjacent disc in the upper lumbar vertebrae (L1–L2 and L2–L3) and in the direction away from the adjacent disc in middle or lower lumbar vertebrae (L3–L4, L4–L5, and L5-S1).</p