Optimal Hamiltonian simulation for time-periodic systems

The implementation of time-evolution operators $U(t)$, called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of time-evolution $U(t)=e^{-iHt}$, with achieving the optimal computational resource both in time $t$ and an allowable error $\varepsilon$. In contrast, those for time-dependent systems require larger cost due to the difficulty of handling time-dependency. In this paper, we establish optimal/nearly-optimal Hamiltonian simulation for generic time-dependent systems with time-periodicity, known as Floquet systems. By using a so-called Floquet-Hilbert space equipped with auxiliary states labeling Fourier indices, we develop a way to certainly obtain the target time-evolved state without relying on either time-ordered product or Dyson-series expansion. Consequently, the query complexity, which measures the cost for implementing the time-evolution, has optimal and nearly-optimal dependency respectively in time $t$ and inverse error $\varepsilon$, and becomes sufficiently close to that of qubitization. Thus, our protocol tells us that, among generic time-dependent systems, time-periodic systems provides a class accessible as efficiently as time-independent systems despite the existence of time-dependency. As we also provide applications to simulation of nonequilibrium phenomena and adiabatic state preparation, our results will shed light on nonequilibrium phenomena in condensed matter physics and quantum chemistry, and quantum tasks yielding time-dependency in quantum computation.Comment: 55 pages, 2 figures, 1 tabl

Recursive Quantum Eigenvalue/Singular-Value Transformation: Analytic Construction of Matrix Sign Function by Newton Iteration

Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant quantum algorithms such as Hamiltonian simulation. However, finding a parameter set which realizes preferable matrix functions in these techniques is difficult for large-scale quantum systems: there is no analytical result other than trivial cases as far as we know and we often suffer also from numerical instability. We propose recursive QET or QSVT (r-QET or r-QSVT), in which we can execute complicated matrix functions by recursively organizing block-encoding by low-degree QET or QSVT. Owing to the simplicity of recursive relations, it works only with a few parameters with exactly determining the parameters, while its iteration results in complicated matrix functions. In particular, by exploiting the recursive relation of Newton iteration, we construct the matrix sign function, which can be applied for eigenstate filtering for example, in a tractable way. We show that an analytically-obtained parameter set composed of only $8$ different values is sufficient for executing QET of the matrix sign function with an arbitrarily small error $\varepsilon$. Our protocol will serve as an alternative protocol for constructing QET or QSVT for some useful matrix functions without numerical instability.Comment: 10 pages, 1figur

Surgical Treatment by Partial Petrosectomy for a Middle-Ear Carcinoid with Progressive Extension: A Case Report and Review of the Literature

We herein report a 59-year-old male patient with a recurrent carcinoid tumor of the middle ear 7 years after a tympanomastoidectomy. The CT and dynamic MRI demonstrated an extensive tumor close to the carotid artery canal and the jugular bulb, and the tumor was removed by a partial petrosectomy with a transmastoid approach. The histopathological findings revealed a solid and trabecular tumor with cells positive for cytokeratin, chromogranin A, synaptophysin, and CD56. The MIB-1 antibody for the Ki-67 antigen was positive in 6.6% of the tumor cells. The relevant literature is reviewed in regard to the present case

Disinfection of otorhinolaryngological endoscopes with electrolyzed acid water: A cross-sectional and multicenter study

Glutaraldehyde, a germicide for reprocessing endoscopes that is important for hygiene in the clinic, might be hazardous to humans. Electrolyzed acid water (EAW) has a broad anti-microbial spectrum and safety profile and might be a glutaraldehyde alternative. We sought to assess EAW disinfection of flexible endoscopes in clinical otorhinolaryngological settings and its in vitro inactivation of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and bacteria commonly isolated in otorhinolaryngology. Ninety endoscopes were tested for bacterial contamination before and after endoscope disinfection with EAW. The species and strains of bacteria were studied. The in vitro inactivation of bacteria and SARS-CoV-2 by EAW was investigated to determine the efficacy of endoscope disinfection. More than 20 colony-forming units of bacteria at one or more sampling sites were detected in 75/90 microbiological cultures of samples from clinically used endoscopes (83.3%). The most common genus detected was Staphylococcus followed by Cutibacterium and Corynebacterium at all sites including the ears, noses, and throats. In the in vitro study, more than 107 CFU/mL of all bacterial species examined were reduced to below the detection limit ( 105 PFU) was decreased to less than 5 PFU. Effective inactivation of SARS-CoV-2 was also observed with a 19:1 ratio of EAW to the virus. EAW effectively reprocessed flexible endoscopes contributing to infection control in medical institutions in the era of the coronavirus disease 2019 pandemic

Endoscopic submucosal dissection of a minute intramucosal adenocarcinoma in Barrett\u27s esophagus.

A 73-year-old man with short segmental Barrett\u27s esophagus underwent esophagoscopy, and a slightly depressed, discolored lesion was found on the anterior wall of the lower esophagus. Under a provisional diagnosis of differentiated adenocarcinoma without local lymph node metastasis, endoscopic submucosal dissection (ESD) was carried out. En bloc resection with tumor-free lateral/basal margins was accomplished without complication. The resected area was 12 x 15 mm in size, whereas the neoplastic lesion was 4 x 4 mm. Histopathological examination confirmed intramucosal well-differentiated tubular adenocarcinoma without angiolymphatic invasion adjacent to the muscularis mucosae. Repeated esophagoscopy 6 months after ESD showed neither locally recurrent nor metachronous lesions. Considering that Barrett\u27s esophagus is a precancerous condition, one may recommend eradication of both the neoplastic and non-neoplastic lesion with using ESD.Without Figure

Endoscopic Polypectomy of Esophageal Leiomyomas; Report of Two Cases

We describe esophageal leiomyomas in two young patients (aged 35 and 32 years), who complained of dysphagia and epigastralgia, which were successfully treated by endoscopic polypectomy. Upper endoscopy showed a pedunculated polyp beneath the normal mucosa located at 28 cm from the incisor in the first case and 1 cm sessile 2.1 cm semipedunculated polypoid lesion in the lower esophagus just above the esophageal-gastric junction in the second case. Both lesions were resected by snare polypectomy without any complication. Light microscopic examination and immunohistochemistry of the tumor tissue confirmed the diagnosis of leiomyoma. Endoscopic polypectomy of esophageal leiomyoma is safe and should be considered as an optional treatment modality whenever possible

A comprehensive survey on quantum computer usage: How many qubits are employed for what purposes?

Quantum computers (QCs), which work based on the law of quantum mechanics, are expected to be faster than classical computers in several computational tasks such as prime factoring and simulation of quantum many-body systems. In the last decade, research and development of QCs have rapidly advanced. Now hundreds of physical qubits are at our disposal, and one can find several remarkable experiments actually outperforming the classical computer in a specific computational task. On the other hand, it is unclear what the typical usages of the QCs are. Here we conduct an extensive survey on the papers that are posted in the quant-ph section in arXiv and claim to have used QCs in their abstracts. To understand the current situation of the research and development of the QCs, we evaluated the descriptive statistics about the papers, including the number of qubits employed, QPU vendors, application domains and so on. Our survey shows that the annual number of publications is increasing, and the typical number of qubits employed is about six to ten, growing along with the increase in the quantum volume (QV). Most of the preprints are devoted to applications such as quantum machine learning, condensed matter physics, and quantum chemistry, while quantum error correction and quantum noise mitigation use more qubits than the other topics. These imply that the increase in QV is fundamentally relevant, and more experiments for quantum error correction, and noise mitigation using shallow circuits with more qubits will take place.Comment: 14 pages, 5 figures, figures regenerate

Small Colonic Cancer with Invasion of the Subserosal Layer. Report of a Case

Small, flat-type advanced colonic adenocarcinomas are rare. We present a case of small colonic carcinoma invading the subserosal layer. A 61-year-old asymptomatic man was admitted for further examination of positive occult blood test. Barium enema and endoscopic examination revealed a small (10 mm in diameter) flat lesion with elevated margins and a central depression, in the transverse colon. Biopsy specimen taken from the tumor showed poorly differentiated adenocarcinoma. Based on radiologic and endoscopic evaluation, a provisional diagnosis was made of colonic tumor with invasion of the deep submucosal layer. Surgical resection of the transverse colon was performed. The tumor was macroscopically a type IIa + IIc lesion measuring 10 mm in diameter. Histological examination showed poorly differentiated adenocarcinoma infiltrating the subserosal layer. Awareness of this type of tumor should allow early diagnosis and treatment, resulting in improved prognosis