Analytical Formulation of the Second-Order Derivative of Energy for the Orbital-Optimized Variational Quantum Eigensolver: Application to Polarizability.

We develop a quantum-classical hybrid algorithm to calculate the analytical second-order derivative of the energy for the orbital-optimized variational quantum eigensolver (OO-VQE), which is a method to calculate eigenenergies of a given molecular Hamiltonian by utilizing near-term quantum computers and classical computers. We show that all quantities required in the algorithm to calculate the derivative can be evaluated on quantum computers as standard quantum expectation values without using any ancillary qubits. We validate our formula by numerical simulations of quantum circuits for computing the polarizability of the water molecule, which is the second-order derivative of the energy, with respect to the electric field. Moreover, the polarizabilities and refractive indices of thiophene and furan molecules are calculated as a test bed for possible industrial applications. We finally analyze the error scaling of the estimated polarizabilities obtained by the proposed analytical derivative versus the numerical derivative obtained by the finite difference. Numerical calculations suggest that our analytical derivative requires fewer measurements (runs) on quantum computers than the numerical derivative to achieve the same fixed accuracy.

Molecular Structure Optimization Based on Electrons-Nuclei Quantum Dynamics Computation.

A new concept of the molecular structure optimization method based on quantum dynamics computations is presented. Nuclei are treated as quantum mechanical particles, as are electrons, and the many-body wave function of the system is optimized by the imaginary time evolution method. The numerical demonstrations with a two-dimensional H2 + system and a H-C-N system exemplify two possible advantages of our proposed method: (1) the optimized nuclear positions can be specified with a small number of observations (quantum measurements) and (2) the global minimum structure of nuclei can be obtained without starting from any sophisticated initial structure and getting stuck in the local minima. This method is considered to be suitable for quantum computers, the development of which will realize its application as a powerful method.

Analytical Energy Gradient for State-Averaged Orbital-Optimized Variational Quantum Eigensolvers and Its Application to a Photochemical Reaction.

Elucidating photochemical reactions is vital to understanding various biochemical phenomena and developing functional materials such as artificial photosynthesis and organic solar cells, albeit with notorious difficulty in both experiments and theories. The best theoretical way so far to analyze photochemical reactions at the level of ab initio electronic structure is the state-averaged multiconfigurational self-consistent field (SA-MCSCF) method. However, the exponential computational cost of classical computers with the increasing number of molecular orbitals hinders applications of SA-MCSCF for large systems we are interested in. Utilizing quantum computers was recently proposed as a promising approach to overcome such computational cost, dubbed as state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE). Here, we extend a theory of SA-OO-VQE so that analytical gradients of energy can be evaluated by standard techniques that are feasible with near-term quantum computers. The analytical gradients, known only for the state-specific OO-VQE in previous studies, allow us to determine various characteristics of photochemical reactions such as the conical intersection (CI) points. We perform a proof-of-principle calculation of our methods by applying it to the photochemical cis-trans isomerization of 1,3,3,3-tetrafluoropropene. Numerical simulations of quantum circuits and measurements can correctly capture the photochemical reaction pathway of this model system, including the CI points. Our results illustrate the possibility of leveraging quantum computers for studying photochemical reactions.

Iodide-Mediated [3 + 2]-Cycloaddition Reaction with N-Tosylaziridines and α,ß-Unsaturated Ketones.

The [3 + 2]-cycloaddition reaction between N-tosylaziridines and α,ß-unsaturated ketones was promoted with lithium iodide. The reaction proceeded under mild conditions to provide N-tosylpyrrolidines. Quaternary carbon-possessing 3,3-disubstituted pyrrolidines including spiro compounds were afforded in high yields. A simple procedure with easy to handle reagents makes this reaction concise. The intramolecular version of this reaction was applied to synthesize tropane skeletons.

Universality in volume-law entanglement of scrambled pure quantum states.

A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. The thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and mandate a correction to this simple volume law. The elucidation of the size dependence of the entanglement entropy is thus essentially important in linking quantum physics with thermodynamics. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing equilibrium. We numerically find that our formula applies universally to any sufficiently scrambled pure state representing thermal equilibrium, i.e., energy eigenstates of non-integrable models and states after quantum quenches. Our formula is exploited as diagnostics for chaotic systems; it can distinguish integrable models from non-integrable models and many-body localization phases from chaotic phases.

Efficacy of biolimus A9-eluting stent for treatment of right coronary ostial lesion with intravascular ultrasound guidance: a multi-center registry.

The aim of this study was to assess the efficacy of a biolimus A9-eluting stent in patients with a right coronary artery (RCA) ostial lesion. Ostial lesions of the RCA have been a limitation of percutaneous coronary intervention even in the drug-eluting stent (DES) era. However, clinical outcomes after the deployment of a second generation DES to an RCA ostial lesion with intravascular ultrasound (IVUS) guidance have not been fully elucidated. From September 2011 to March 2013, 74 patients were enrolled in 17 centers from Japan. RCA ostial lesion was defined as de novo significant stenotic lesion located within 15 mm from ostium. IVUS was used for all cases to confirm the location of ostium and evaluate stent coverage of ostium. Patients with hemodialysis were excluded. The primary endpoint is a major adverse cardiac event (MACE) at 1 year. Forty two percent of patients had multi-vessel disease. Angiographically severe calcification was observed in 26% of the lesions. The mean stent diameter was 3.3 ± 0.3 mm (3.5 mm, 72%, 3.0 mm, 25%, and 2.75 and 2.5 mm, 3%), stent length was 17.5 ± 5.8 mm, and dilatation pressure of stenting was 15.6 ± 4.1 atm. RCA ostium was covered by stent in all lesions in IVUS findings. Post dilatation was performed for 64% of lesions (balloon size 3.7 ± 0.6 mm). MACE rate at 1 year was 5.4% (target lesion revascularization 5.4%, myocardial infarction 1.2%, and no cardiac death). The biolimus A9-eluting stent for RCA ostial lesions with IVUS guidance showed favorable results at 1-year follow-up.

Evaluation for the efficacy and safety of the crosser catheter as a CTO crossing device and a flossing device.

The Crosser catheter is a unique device that facilitates antegrade intraluminal recanalization by high-frequency vibration energy and cavitation. We used this device not only as a chronic total occlusion (CTO) crossing device, but also as a flossing device in stenotic lesions and we also evaluated the efficacy of this device when used with both the "Crosser preceding" and the "Guidewire preceding" in CTOs. Complications related to this device were investigated, too. We retrospectively analyzed a total of 90 consecutive patients with peripheral artery disease in the femoropopliteal artery and below-the-knee artery (BTA). Primary technical success was defined as the successful delivery of this device into the distal true lumen. Secondary technical success was defined as successful revascularization. The safety endpoints were events of angiographic complications, including the occurrence of detachment of the metal tip from the shaft, slow flow, dissections, and perforations. Overall primary technical success rate was 93.3% and the secondary technical success rate was 96.7%. Detachment and slow flow occurred 14.4 and 4.4%, respectively, with no occurrences of either dissection or perforation. A predictor of detachment was Proposed Peripheral Arterial Calcium Scoring System (PACSS) grade 4 (OR 14.6; CI 1.26-168.5; P = 0.032). The Crosser catheter is useful not only as a CTO crossing device used with both the "Crosser preceding" and the "Guidewire preceding", but also as a flossing device in stenotic lesions. But we have to pay attention to complications related to the Crosser.

Two-year clinical outcome in patients with small coronary artery disease treated with everolimus- versus paclitaxel-eluting stenting.

BACKGROUND: Percutaneous coronary interventions involving small coronary vessels represent a true challenge because of the increased risk of restenosis and adverse outcomes. We evaluated the 2-year clinical outcomes between single everolimus-eluting stents (EES) and paclitaxel-eluting stents (PES) in small coronary artery disease. METHODS: From the data of SACRA (SmAll CoronaRy Artery treated by TAXUS Liberté) and PLUM (PROMUS/Xience V Everolimus-ELUting Coronary Stent for sMall coronary artery disease) registries, 245 patients with 258 lesions and 264 patients with 279 lesions, respectively, were enrolled in this study. RESULTS: The 2-year clinical driven target lesion revascularization (4.5% vs. 10.6%, p=0.01) and target vessel revascularization (8.0% vs. 13.9%, p=0.03) rates were significantly lower in the EES group compared with the PES group. Major adverse cardiac events in the EES group tended to be lower than those in the PES group (8.7% vs. 14.3%, p=0.05). On the other hand, all new lesions for remote target vessel revascularization were observed at the proximal site of target lesions in both groups and those rates were not different between the two groups (3.4% vs. 3.3%, p>0.99). CONCLUSION: EES showed better clinical results at 2-year follow-up compared with PES in small coronary artery diseases, however, new lesions at the proximal remote site of the target lesion remain problematic.

Sheath rendezvous method: a novel distal protection technique during endovascular treatment of subclavian artery occlusions.

To describe an innovative distal protection technique, "sheath rendezvous method", during endovascular treatment for subclavian arterial occlusions. 4.5F and 6F guiding sheath were inserted from left brachial and common femoral artery, respectively. 0.014″ guidewire retrogradely passed through occlusion and into antegrade sheath to establish a pull-through system. 3.0 mm balloon was used to expand occlusion and anchor to deliver retrograde sheath into antegrade one. Both sheaths locked by balloon dilatation crossed occlusion until antegrade sheath passed over lesion. Balloon expandable stent was delivered within antegrade sheath. Sheath was removed, and stent was implanted. We obtained an excellent outcome without complications.

Practical enantioselective arylation and heteroarylation of aldehydes with in situ prepared organotitanium reagents catalyzed by 3-aryl-H8-BINOL-derived titanium complexes.

A highly efficient and practical method for the catalytic enantioselective arylation and heteroarylation of aldehydes with organotitanium reagents, prepared in situ by the reaction of aryl- and heteroaryllithium reagents with ClTi(OiPr)3, is described. Titanium complexes derived from DPP-H8 -BINOL (3d; DPP=3,5-diphenylphenyl) and DTBP-H8 -BINOL (3e; DTBP=3,5-di-tert-butylphenyl) exhibit excellent catalytic activity in terms of enantioselectivity and turnover efficiency for the transformation, providing diaryl-, aryl heteroaryl-, and diheteroarylmethanol derivatives in high enantioselectivity at low catalyst loading (0.2-2 mol%). The reaction begins with a variety of aryl and heteroaryl bromides through their conversion into organolithium intermediates by Br/Li exchange with nBuLi, thus providing straightforward access to a range of enantioenriched alcohols from commercially available starting materials. Various 2-thienylmethanols can be synthesized enantioselectively by using commercially available 2-thienyllithium in THF. The reaction can be carried out on a 10 mmol scale at 0.5 mol% catalyst loading, demonstrating its preparative utility.

Fabrication of nano-hydroxyapatite on electrospun silk fibroin nanofiber and their effects in osteoblastic behavior.

In this study, a novel tissue engineering scaffold material of electrospun silk fibroin/nano-hydroxyapatite (nHA) biocomposite was prepared by means of an effective calcium and phosphate (Ca-P) alternate soaking method. nHA was successfully produced on regenerated silk fibroin nanofiber as a substrate within several minutes without any pretreatments. The morphologies of both nonmineralized and mineralized nanofibers were analyzed using a field-emission scanning electron microscopy (FESEM). The crystallographic phases of the nHA were analyzed using X-ray diffraction (XRD). Fourier transform infrared (FTIR) spectrophotometer and thermogravimetry analyses (TGA) were employed to determine the type of functional groups and the amount of nHA presenting in the silk/nHA biocomposite nanofibers, respectively. The osteoblastic activities of this novel nanofibrous biocomposite scaffold were also investigated by employing osteoblastic-like MC3T3-E1 cell line. The cell functionality such as alkaline phosphatase (ALP) activity was ameliorated on mineralized nanofibers. All these results indicated that this silk/nHA biocomposite scaffold material may be a promising biomaterial for bone tissue engineering.

Intravascular ultrasound, angioscopic and histopathological characterisation of heterogeneous patterns of restenosis after sirolimus-eluting stent implantation: insights into potential "thromborestenosis" phenomenon.

AIMS: Histopathology of DES restenosis remains unclear. The purpose is to examine restenotic tissue characteristics after sirolimus-eluting stent (SES) and comparing with that after bare-metal stent (BMS). METHODS AND RESULTS: Intravascular ultrasound (IVUS), coronary angioscopy (CAS), and directional coronary atherectomy were performed simultaneously in 21 patients who presented restenosis after SES (n=13) and BMS (n=8). Mean time of restenosis was 10.8 months in the SES versus 7.5 months in the BMS. Typical "black hole'', echolucent appearance by IVUS was observed in one SES case, and corresponded to a fibrin rich tissue by histology which appeared translucent tissue by CAS. CAS did not reveal red thrombus, but showed white thrombus in six SES versus two BMS (46.2% vs. 25.0%, p=0.597). Histology demonstrated various patterns after SES including thrombus, fibrin, inflammatory infiltrate, and collagen-matrix rich tissue, while thrombus component was not detected in BMS. Thrombus and fibrin deposition detected by either CAS or histopathology were observed more frequently in SES than in BMS group (92.3% vs. 25.0%, p=0.007). CONCLUSIONS: Restenosis after SES and BMS have different clinical and histological patterns. SES restenosis may be frequently associated with thrombus component.

Clinical outcomes after percutaneous peripheral intervention for chronic total occlusion of superficial femoral arteries: comparison between self-expandable nitinol stent and stainless steel stent.

BACKGROUND: It has been reported that nitinol stents provide higher patency in chronic phase than stainless steel stents after intervention to superficial femoral artery (SFA). However, there are few reports about stent patency for chronic total occlusion of SFA (SFA CTO). OBJECTIVE: To compare clinical outcomes of self-expanding nitinol stents and stainless steel stents after percutaneous peripheral intervention (PPI) for SFA CTO. METHODS AND RESULTS: Between April 2004 and August 2007, a total of 25 SFA CTO lesions (nitinol stent group, 13; stainless steel stent group, 12) in 21 patients were treated with PPI, all patients were followed clinically, and 21 lesions (nitinol, 9; stainless steel, 12) received follow-up angiography. There was no significant difference in baseline characteristics, mean stent diameter (7.3+/-0.7 mm vs. 6.9+/-1.2 mm, p=0.32), pre-ankle-brachial index (ABI), and Fontaine stage between groups. Mean occlusion length and stent length were significantly longer (129.5+/-54.9 mm vs. 39.0+/-20.6 mm, 250.8+/-90.0 mm vs. 145.2+/-64.6 mm, respectively, p<0.01) and number of stents was significantly larger (2.8+/-0.9 vs. 1.6+/-0.5, p<0.01) in the nitinol stent group. At follow-up, ABI was significantly lower (0.73+/-0.20 vs. 0.95+/-0.13, p=0.04), restenosis rate and target lesion revascularization was significantly higher (58.3% vs. 15.4%, p=0.03; 50.0% vs. 7.7%, p=0.02, respectively) in the stainless steel stent group. CONCLUSION: Our study demonstrates the superiority of nitinol stent implantation compared with stainless steel stent implantation for SFA CTO.

The potential of RF backscattered IVUS data and multidetector-row computed tomography images for tissue characterization of human coronary atherosclerotic plaques.

The aim is to compare virtual histology which uses spectral analysis of backscattered intravascular ultrasound (VH-IVUS) and multidetector-row computed tomography (MDCT) for the characterization of coronary atherosclerotic plaques obtained by directional coronary atherectomy (DCA). We performed DCA in 15 de novo native coronary stenotic lesions (15 patients) and selected one or two segments within the plaque from each patient (total 29 segments). Then, we evaluated the accuracy of the VH-IVUS findings in 50 sites among the 29 segments compared with the histopathology findings. MDCT was performed in all patients before percutaneous coronary intervention (PCI), and CT density values were measured. VH-IVUS data analysis correlated well with histopathological examination (predictive accuracy: 66.7% for fibrous, 100% for fibro-fatty, 100% for necrotic core, and 100% for dense calcium regions, respectively). In addition, CT density values between fibrous and fibro-fatty plaques classified by histopathology were 100.0 +/- 26.0 HU versus 110.4 +/- 67.9 HU, there were no difference among them (P = 0.594). These findings indicated that the validation of plaque characteristics using VH-IVUS correlates well with histopathology. While tissue characterization using CT density could be difficult to distinguish between fibro-fatty and fibrous tissue.

Short- or long-term outcomes of coronary artery aneurysms occurring after directional coronary atherectomy.

Coronary artery aneurysm (CAA) often occurs after percutaneous coronary intervention, and it could be recognized more often in coronary intervention with directional coronary atherectomy (DCA). However, it has been uncertain and the natural history of CAA after DCA remains obscure. Thus, we examined the clinical course after DCA. This study included 792 lesions in which a follow-up angiogram was completed at mid- or long-term (3 months [mos.] or more than 1 year after DCA). The mean average of the angiographic follow-up period was 24.8 mos. (range 3-128 mos.), and clinical follow-up period was 45.6 mos. (range 3-144 mos.). CAA was defined as 1.5 > DCA site diameter/reference diameter by quantitative coronary angiography (QCA). CAAs were detected in 21 lesions (2.7%). There was no significant difference in the target lesion revascularization rate between CAA and non-CAA lesion (19.0% vs. 24.6%). More than twice as many follow-up coronary angiograms were performed in 15 lesions among 21 CAA lesions. The mean duration of the follow-up angiograms was 19.6 mos. There was no significant difference in lumen diameter between the value of QCA at first and final follow-up coronary angiography (3.9 +/- 0.9 vs. 4.0 +/- 0.8 mm). Acute coronary events or coronary perforations did not occur at all. This study showed the frequency of DCA-related CAA and revealed acceptable short- or long-term prognosis. DCA-related CAA had not been progressing during the follow-up period. We concluded that almost all CAAs should be managed conservatively.