Relation between two-phase quantum walks and the topological invariant

We study a position-dependent discrete-time quantum walk (QW) in one dimension, whose time-evolution operator is built up from two coin operators which are distinguished by phase factors from $x\geq0$ and $x\leq-1$. We call the QW the ${\it complete\;two}$-${\it phase\;QW}$ to discern from the two-phase QW with one defect[13,14]. Because of its localization properties, the two-phase QWs can be considered as an ideal mathematical model of topological insulators which are novel quantum states of matter characterized by topological invariants. Employing the complete two-phase QW, we present the stationary measure, and two kinds of limit theorems concerning ${\it localization}$ and the ${\it ballistic\;spreading}$, which are the characteristic behaviors in the long-time limit of discrete-time QWs in one dimension. As a consequence, we obtain the mathematical expression of the whole picture of the asymptotic behavior of the walker in the long-time limit. We also clarify relevant symmetries, which are essential for topological insulators, of the complete two-phase QW, and then derive the topological invariant. Having established both mathematical rigorous results and the topological invariant of the complete two-phase QW, we provide solid arguments to understand localization of QWs in term of topological invariant. Furthermore, by applying a concept of ${\it\;topological\;protections}$, we clarify that localization of the two-phase QW with one defect, studied in the previous work[13], can be related to localization of the complete two-phase QW under symmetry preserving perturbations.Comment: 50 pages, 13 figure

Measurement optimization of variational quantum simulation by classical shadow and derandomization

Simulating large quantum systems is the ultimate goal of quantum computing. Variational quantum simulation (VQS) gives us a tool to achieve the goal in near-term devices by distributing the computation load to both classical and quantum computers. However, as the size of the quantum system becomes large, the execution of VQS becomes more and more challenging. One of the most severe challenges is the drastic increase in the number of measurements; for example, the number of measurements tends to increase by the fourth power of the number of qubits in a quantum simulation with a chemical Hamiltonian. This work aims to dramatically decrease the number of measurements in VQS by recently proposed shadow-based strategies such as classical shadow and derandomization. Even though previous literature shows that shadow-based strategies successfully optimize measurements in the variational quantum optimization (VQO), how to apply them to VQS was unclear due to the gap between VQO and VQS in measuring observables. In this paper, we bridge the gap by changing the way of measuring observables in VQS and propose an algorithm to optimize measurements in VQS by shadow-based strategies. Our theoretical analysis not only reveals the advantage of using our algorithm in VQS but theoretically supports using shadow-based strategies in VQO, whose advantage has only been given numerically. Additionally, our numerical experiment shows the validity of using our algorithm with a quantum chemical system

Study on Application of Static Magnetic Field for Adjuvant Arthritis Rats

In order to examine the effectiveness of the application of static magnetic field (SMF) on pain relief, we performed a study on rats with adjuvant arthritis (AA). Sixty female Sprague–Dawley (SD) rats (age: 6 weeks, body weight: approximately 160 g) were divided into three groups [SMF-treated AA rats (Group I), non-SMF-treated AA rats (Group II) and control rats (Group III)]. The SD rats were injected in the left hind leg with 0.6 mg/0.05 ml Mycobacterium butyrium to induce AA. The rats were bred for 6 months as chronic pain model. Thereafter, the AA rats were or were not exposed to SMF for 12 weeks. We assessed the changes in the tail surface temperature, locomotor activity, serum inflammatory marker and bone mineral density (BMD) using thermography, a metabolism measuring system and the dual-energy X-ray absorptiometry (DEXA) method, respectively. The tail surface temperature, locomotor activity and femoral BMD of the SMF-exposed AA rats were significantly higher than those of the non-SMF-exposed AA rats, and the serum inflammatory marker was significantly lower. These findings suggest that the pain relief effects are primarily due to the increased blood circulation caused by the rise in the tail surface temperature. Moreover, the pain relief effects increased with activity and BMD of the AA rats

Error-mitigated quantum metrology via virtual purification

Quantum metrology with entangled resources aims to achieve sensitivity beyond the standard quantum limit by harnessing quantum effects even in the presence of environmental noise. So far, sensitivity has been mainly discussed from the viewpoint of reducing statistical errors under the assumption of perfect knowledge of a noise model. However, we cannot always obtain complete information about a noise model due to coherence time fluctuations, which are frequently observed in experiments. Such unknown fluctuating noise leads to systematic errors and nullifies the quantum advantages. Here, we propose an error-mitigated quantum metrology that can filter out unknown fluctuating noise with the aid of purification-based quantum error mitigation. We demonstrate that our protocol mitigates systematic errors and recovers superclassical scaling in a practical situation with time-inhomogeneous bias-inducing noise. Our results reveal the usefulness of purification-based error mitigation for unknown fluctuating noise, thus paving the way not only for practical quantum metrology but also for quantum computation affected by such noise.Comment: 6+11 pages, 3+4 figure

Bullous Variant of Sweet's Syndrome after Herpes Zoster Virus Infection

Aim: Cutaneous manifestations of Sweet’s syndrome (SS) are typically painful plaque-forming erythematous papules, while bullae are quite uncommon. We present a case of bullous variant of SS in acute myeloid leukaemia. In this case, herpes infection of the left mandible had preceded the development of SS. Case Report: A 75-year-old male with myelodysplastic syndrome first presented with herpes zoster virus infection-like bullae and erosive plaques on the left side of the face and neck. Treatment with valacyclovir and antibiotics was effective only for the initial lesions, whereas the other bullae kept developing predominantly on the left side. Histopathological study revealed epidermal bulla formation, pandermal neutrophilic infiltration, erythrocyte extravasation and subepidermal oedema, but no vasculitis. The findings suggested the diagnosis of bullous variant of SS. Discussion: Our case was unique in that bullous SS symptoms developed predominantly on one side of the cheek and neck where the herpes zoster infection occurred prior to SS. The tendency may explain the possible association between viral infection and development of SS

DEVELOPMENT OF LABEL-FREE BIOSENSOR FOR DETECTING STEROID HORMONE CONCENTRATION IN FISH

A novel label-free immunosensor for detecting steroid hormone was developed. The principle of the sensor system is based on differences in the electrochemical activity induced by an immunoreaction that depends on the levels of steroid hormone in the sample. A gold electrode functionalized with 3-mercaptopropionic acid (MPA) self- assembled monolayer was used to fabricate electrochemical immunosensor. In addition, single-wall carbon nanotube (SWCNT) was selected to expandthe dynamic range of the sensor. The sensor was immersed into a sample solution and measurements were determined by cyclic voltammetry. Each electrochemical measurement including sample immerse only took about 15min. In this study, we introduced an application of our sensor in detecting 17, 20β- dihydroxy-4-pregnen- 3-one (DHP). The immunosensor showed a specific response to DHP, and the oxidation peak current linearly decreased in the range of 7.8-500.0pg ml-1 (without SWCNT) and 15.6-50000.0pg ml-1 (with SWCNT). The sensor system was then applied to monitor DHP of goldfish (Carassiusauratus) and was compared with the levels of the same samples determined using ELISA as the convention method. Blood plasma of fish was collected every 3h after administering a DHP inducer. A good relationship (coefficient: 0.934) was observed between DHP levels determined by both methods. Keyword: Biosensor, Steroid hormone, Immunoassay, Fish, Single-walled carbon nanotube

Generalized quantum subspace expansion

One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop practical hardware-friendly quantum error mitigation (QEM) techniques to suppress unwanted errors. Here, we propose a novel generalized quantum subspace expansion method which can handle stochastic, coherent, and algorithmic errors in quantum computers. By fully exploiting the substantially extended subspace, we can efficiently mitigate the noise present in the spectra of a given Hamiltonian, without relying on any information of noise. The performance of our method is discussed under two highly practical setups: the quantum subspaces are mainly spanned by powers of the noisy state $\rho^m$ and a set of error-boosted states, respectively. We numerically demonstrate in both situations that we can suppress errors by orders of magnitude, and show that out protocol inherits the advantages of previous error-agnostic QEM techniques as well as overcoming their drawbacks.Comment: 6+8 pages, 3+5 figure