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Recent advancements in quantum computing have opened new avenues for tackling long-standing complex combinatorial optimization problems that are intractable for classical computers. Predicting secondary structure of mRNA is one such notoriously difficult problem that can benefit from the ever-increasing maturity of quantum computing technology. Accurate prediction of mRNA secondary structure is critical in designing RNA-based therapeutics as it dictates various steps of an mRNA life cycle, including transcription, translation, and decay. The current generation of quantum computers have reached utility-scale, allowing us to explore relatively large problem sizes. In this paper, we examine the feasibility of solving mRNA secondary structures on a quantum computer with sequence length up to 60 nucleotides representing problems in the qubit range of 10 to 80. We use Conditional Value at Risk (CVaR)-based VQE algorithm to solve the optimization problems, originating from the mRNA structure prediction problem, on the IBM Eagle and Heron quantum processors. To our encouragement, even with ``minimal'' error mitigation and fixed-depth circuits, our hardware runs yield accurate predictions of minimum free energy (MFE) structures that match the results of the classical solver CPLEX. Our results provide sufficient evidence for the viability of solving mRNA structure prediction problems on a quantum computer and motivate continued research in this direction., Comment: 12 pages, 12 figures

In gravitational wave astronomy, non-Gaussian noise, such as scattered light noise disturbs stable interferometer operation, limiting the interferometer's sensitivity, and reducing the reliability of the analyses. In scattered light noise, the non-Gaussian noise dominates the sensitivity in a low frequency range of less than a few hundred Hz, which is sensitive to gravitational waves from compact binary coalescence. This non-Gaussian noise prevents reliable parameter estimation, since several analysis methods are optimized only for Gaussian noise. Therefore, identifying data contaminated by non-Gaussian noise is important. In this work, we extended the conventional method to evaluate non-Gaussian noise, Rayleigh statistic, by using a statistical hypothesis test to determine a threshold for non-Gaussian noise. First, we estimated the distribution of the Rayleigh statistic against Gaussian noise, called the background distribution, and validated that our extension serves as the hypothetical test. Moreover, we investigated the detection efficiency by assuming two non-Gaussian noise models. For example, for the model with strong scattered light noise, the true positive rate was always above 0.7 when the significance level was 0.05. The results showed that our extension can contribute to an initial detection of non-Gaussian noise and lead to further investigation of the origin of the non-Gaussian noise., Comment: 18 pages, 11 figures

The search for subsolar mass primordial black holes (PBHs) poses a challenging problem due to the low signal-to-noise ratio, extended signal duration, and computational cost demands, compared to solar mass binary black hole events. In this paper, we explore the possibility of investigating the mass range between subsolar and planetary masses, which is not accessible using standard matched filtering and continuous wave searches. We propose a systematic approach employing the Viterbi algorithm, a dynamic programming algorithm that identifies the most likely sequence of hidden Markov states given a sequence of observations, to detect signals from small mass PBH binaries. We formulate the methodology, provide the optimal length for short-time Fourier transforms, and estimate sensitivity. Subsequently, we demonstrate the effectiveness of the Viterbi algorithm in identifying signals within mock data containing Gaussian noise. Our approach offers the primary advantage of being agnostic and computationally efficient., Comment: 14 pages, 8 figures. Expanded the analysis to include a more detailed look into the distribution of the detection statistics, and also added further comments and references

The subsolar mass primordial black hole (PBH) attracts attention as robust evidence of its primordial origin against the astrophysical black hole. Not only with themselves, PBHs can also form binaries with ordinary astrophysical objects, catching them by gravitational wave (GW) bremsstrahlung. We discuss the detectability of the inspiral GWs from binaries consisting of a PBH and a white dwarf (WD) by using space-borne gravitational wave interferometers like DECIGO. The conservative assessment shows the expected event number in three years by DECIGO is $\mathcal{O}(10^{-6})$ for $M_\mathrm{PBH} \sim 0.1M_\odot$. Possible enhancement mechanisms of WD-PBH binary formation may amplify this event rate. We discuss how large enhancement associated with WDs is required to detect WD-PBH merger events without violating the existing constraints on the PBH-PBH merger by the ground-based detector., Comment: 13 pages, 10 figures

Financial services is a prospect industry where unlocked near-term quantum utility could yield profitable potential, and, in particular, quantum machine learning algorithms could potentially benefit businesses by improving the quality of predictive models. Quantum kernel methods have demonstrated success in financial, binary classification tasks, like fraud detection, and avoid issues found in variational quantum machine learning approaches. However, choosing a suitable quantum kernel for a classical dataset remains a challenge. We propose a hybrid, quantum multiple kernel learning (QMKL) methodology that can improve classification quality over a single kernel approach. We test the robustness of QMKL on several financially relevant datasets using both fidelity and projected quantum kernel approaches. We further demonstrate QMKL on quantum hardware using an error mitigation pipeline and show the benefits of QMKL in the large qubit regime.

We propose a simple theoretical model referred to as the {\it two-band model} to realize both a large Seebeck coefficient and high electrical conductivity, resulting in a high thermoelectric (TE) power factor ($PF$). Using the Kubo--Luttinger linear response theory, we apply this model to the TE response of an FeSe thin film reported by Shimizu {\it et al.} to show a high $PF$ with strong temperature dependence. The effects of superconducting fluctuations and excitonic correlations are found to not be critical.

Sparse connectivity of a superconducting quantum computer results in the large experimental overheads of SWAP gates. In this study, we consider employing a virtual two-qubit gate (VTQG) as an error suppression technique. The VTQG enables a non-local operation between a pair of distant qubits using only single qubit gates and projective measurements. Here, we apply the VTQG to the digital quantum simulation of the transverse-field Ising model on an IBM quantum computer to suppress the errors due to the noisy two-qubit operations. We present an effective use of VTQG, where the reduction of multiple SWAP gates results in increasing the fidelity of the output states. The obtained results indicate that the VTQG can be useful for suppressing the errors due to the additional SWAP gates. Additionally, by combining a pulse-efficient transpilation method with the VTQG, further suppression of the errors is observed. In our experiments, we have observed one order of magnitude improvement in accuracy for the quantum simulation of the transverse-field Ising model with 8 qubits., Comment: 5 pages, 6 figures

The ensemble of unresolved compact binary coalescences is a promising source of the stochastic gravitational wave (GW) background. For stellar-mass black hole binaries, the astrophysical stochastic GW background is expected to exhibit non-Gaussianity due to their intermittent features. We investigate the application of deep learning to detect such non-Gaussian stochastic GW background and demonstrate it with the toy model employed in Drasco \& Flanagan (2003), in which each burst is described by a single peak concentrated at a time bin. For the detection problem, we compare three neural networks with different structures: a shallower convolutional neural network (CNN), a deeper CNN, and a residual network. We show that the residual network can achieve comparable sensitivity as the conventional non-Gaussian statistic for signals with the astrophysical duty cycle of $\log_{10}\xi \in [-3,-1]$. Furthermore, we apply deep learning for parameter estimation with two approaches, in which the neural network (1) directly provides the duty cycle and the signal-to-noise ratio (SNR) and (2) classifies the data into four classes depending on the duty cycle value. This is the first step of a deep learning application for detecting a non-Gaussian stochastic GW background and extracting information on the astrophysical duty cycle., Comment: 13 pages, 11 figures, minor corrections

Transient noise appearing in the data from gravitational-wave detectors frequently causes problems, such as instability of the detectors and overlapping or mimicking gravitational-wave signals. Because transient noise is considered to be associated with the environment and instrument, its classification would help to understand its origin and improve the detector's performance. In a previous study, an architecture for classifying transient noise using a time-frequency 2D image (spectrogram) is proposed, which uses unsupervised deep learning combined with variational autoencoder and invariant information clustering. The proposed unsupervised-learning architecture is applied to the Gravity Spy dataset, which consists of Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO) transient noises with their associated metadata to discuss the potential for online or offline data analysis. In this study, focused on the Gravity Spy dataset, the training process of unsupervised-learning architecture of the previous study is examined and reported., Comment: 17 pages, 10 figures, Matches version published in Annalen der Physik

We present a convolutional neural network that is capable of searching for continuous gravitational waves, quasi-monochromatic, persistent signals arising from asymmetrically rotating neutron stars, in $\sim 1$ year of simulated data that is plagued by non-stationary, narrow-band disturbances, i.e., lines. Our network has learned to classify the input strain data into four categories: (1) only Gaussian noise, (2) an astrophysical signal injected into Gaussian noise, (3) a line embedded in Gaussian noise, and (4) an astrophysical signal contaminated by both Gaussian noise and line noise. In our algorithm, different frequencies are treated independently; therefore, our network is robust against sets of evenly-spaced lines, i.e., combs, and we only need to consider perfectly sinusoidal line in this work. We find that our neural network can distinguish between astrophysical signals and lines with high accuracy. In a frequency band without line noise, the sensitivity depth of our network is about $\mathcal{D}^{95\%} \simeq 43.9$ with a false alarm probability of $\sim 0.5\%$, while in the presence of line noise, we can maintain a false alarm probability of $\sim 10\%$ and achieve $\mathcal{D}^\mathrm{95\%} \simeq 3.62$ when the line noise amplitude is $h_0^\mathrm{line}/\sqrt{S_\mathrm{n}(f_k)} = 1.0$. We evaluate the computational cost of our method to be $O(10^{19})$ floating point operations, and compare it to those from standard all-sky searches, putting aside differences between covered parameter spaces. Our results show that our method is more efficient by one or two orders of magnitude than standard searches. Although our neural network takes about $O(10^8)$ sec to employ using our current facilities (a single GPU of GTX1080Ti), we expect that it can be reduced to an acceptable level by utilizing a larger number of improved GPUs., Comment: 17 pages, 11 figures; v2: Virgo's contribution appropriately mentioned, typos fixed

The speedup of heavy numerical tasks by quantum computing is now actively investigated in various fields including data analysis in physics and astronomy. In this paper, we propose a new quantum algorithm for matched filtering in gravitational wave (GW) data analysis based on the previous work by Gao et al., Phys. Rev. Research 4, 023006 (2022) [arXiv:2109.01535]. Our approach uses the quantum algorithm for Monte Carlo integration for the signal-to-noise ratio (SNR) calculation instead of the fast Fourier transform used in Gao et al. and searches signal templates with high SNR by quantum amplitude amplification. In this way, we achieve an exponential reduction of the qubit number compared with Gao et al.'s algorithm, keeping a quadratic speedup over classical GW matched filtering with respect to the template number., Comment: 29 pages, 2 figures

On the basis of the Kubo-Luttinger linear response theory combined with the scaling theory of Anderson localization predicting the energy dependence of localization length near the mobility edge, we have studied the thermoelectric response of a disordered system exhibiting Mott variable-range hopping (VRH). We found that the low-tempetature Seebeck coefficient for VRH conduction in a $d$-dimensional system varies as $S\propto T^{d/(d+1)}$, which is different from the widely used expression, $S\propto T^{(d-1)/(d+1)}$, based on the energy-independent localization length. It is seen that the low-$T$ behavior of $S(T)$ of the thiospinel CuCrTiS$_4$ is in full agreement with the new scheme., Comment: 4 pages, 2 figures

In positive characteristic, there exist counterexamples to the statement corresponding to Batyrev's theorem concerning the McKay correspondence. In this paper, we give another computation of the counterexamples by using stringy-point count for some sequences of quotient varieties. There is a proof of the Serre-Bhagava's mass formula, which is important formula in the number theory, from the computation of stringy-point count of a quotient variety associated to a representation of symmetric group. Our computation of the stringy-point count in this paper is regarded as a variation of this proof to give different versions of mass formula.

In this work, we present a Gauss-Newton based quantum algorithm (GNQA) for combinatorial optimization problems that, under optimal conditions, rapidly converges towards one of the optimal solutions without being trapped in local minima or plateaus. Quantum optimization algorithms have been explored for decades, but more recent investigations have been on variational quantum algorithms, which often suffer from the aforementioned problems. Our approach mitigates those by employing a tensor product state that accurately represents the optimal solution, and an appropriate function for the Hamiltonian, containing all the combinations of binary variables. Numerical experiments presented here demonstrate the effectiveness of our approach, and they show that GNQA outperforms other optimization methods in both convergence properties and accuracy for all problems considered here. Finally, we briefly discuss the potential impact of the approach to other problems, including those in quantum chemistry and higher order binary optimization., Comment: 21 pages, 8 figures

In the data obtained by laser interferometric gravitational wave detectors, transient noise with non-stationary and non-Gaussian features occurs at a high rate. This often results in problems such as detector instability and the hiding and/or imitation of gravitational-wave signals. This transient noise has various characteristics in the time--frequency representation, which is considered to be associated with environmental and instrumental origins. Classification of transient noise can offer clues for exploring its origin and improving the performance of the detector. One approach for accomplishing this is supervised learning. However, in general, supervised learning requires annotation of the training data, and there are issues with ensuring objectivity in the classification and its corresponding new classes. By contrast, unsupervised learning can reduce the annotation work for the training data and ensure objectivity in the classification and its corresponding new classes. In this study, we propose an unsupervised learning architecture for the classification of transient noise that combines a variational autoencoder and invariant information clustering. To evaluate the effectiveness of the proposed architecture, we used the dataset (time--frequency two-dimensional spectrogram images and labels) of the Laser Interferometer Gravitational-wave Observatory (LIGO) first observation run prepared by the Gravity Spy project. The classes provided by our proposed unsupervised learning architecture were consistent with the labels annotated by the Gravity Spy project, which manifests the potential for the existence of unrevealed classes., Comment: 18 pages, 9 figures. Matches version published in Scientific Reports

In multi-objective optimization, designing good benchmark problems is an important issue for improving solvers. Controlling the global location of Pareto optima in existing benchmark problems has been problematic, and it is even more difficult when the design space is high-dimensional since visualization is extremely challenging. As a benchmarking with explicit local Pareto fronts, we introduce a benchmarking based on basin connectivity (3BC) by using basins of attraction. The 3BC allows for the specification of a multimodal landscape through a kind of topological analysis called the basin graph, effectively generating optimization problems from this graph. Various known indicators measure the performance of a solver in searching global Pareto optima, but using 3BC can make us localize them for each local Pareto front by restricting it to its basin. 3BC's mathematical formulation ensures the accurate representation of the specified optimization landscape, guaranteeing the existence of intended local and global Pareto optima.

The \(v\)-function appears in the wild McKay correspondence and it is an invariant of a Galois extension over a local field which measures about the ramification of extension. The ramification filtration is also such invariant. Yasuda presented the problem whether the \(v\)-function is determined by ramification filtration. In this paper, we give a formula for the \(v\)-function for 2-dimensional representations of the bicyclic group of order \(p^2\) with \(p\) the characteristic of our base field. Using this formula, we construct an example of \(v\)-function not determined by the ramification filtration.

In characteristic zero, if a quotient variety has a crepant resolution, the Euler characteristic of the crepant resolution is equal to the number of conjugacy classes of the acting group, by Batyrev's theorem. This is one of the McKay correspondence. It is natural to consider the analogue statement in the positive characteristic. In this paper, we present sequences of crepant resolutions of quotient varieties in the positive characteristic and show that one of the sequences gives a counterexample to the analogue statement of Batyrev's theorem., Comment: 27 pages, 2 figures

We have theoretically investigated thermoelectric (TE) effects of narrow-gap single-walled carbon nanotubes (SWCNTs) with randomly substituted nitrogen (N) impurities, i.e., N-substituted (20,0) SWCNTs with a band gap of 0.497 eV. For such a narrow-gap system, the thermal excitation from the valence band to the conduction band contributes to its TE properties even at the room temperature. In this study, the N-impurity bands are treated with both conduction and valence bands taken into account self-consistently. We found the optimal N concentration per unit cell, $c_{\rm opt}$, which gives the maximum power factor ($PF$) for various temperatures, e.g., $PF=$0.30$\rm{W/K^2m}$ with $c_{\rm opt}=3.1\times 10^{-5}$ at 300K. In addition, the electronic thermal conductivity has been estimated, which turn out to be much smaller than the phonon thermal conductivity, leading to the figure of merit as $ZT\sim 0.1$ for N-substituted (20,0) SWCNTs with $c_{\rm opt}=3.1\times 10^{-5}$ at 300K.

To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. We show the main concepts of Qulacs, explain how to use its features via examples, describe numerical techniques to speed-up simulation, and demonstrate its performance with numerical benchmarks., Comment: 34 pages, 12 figures

The signal of continuous gravitational waves has a longer duration than the observation period. Even if the waveform in the source frame is monochromatic, we will observe the waveform with modulated frequencies due to the motion of the detector. If the source location is unknown, a lot of templates having different sky positions are required to demodulate the frequency, and the required huge computational cost restricts the applicable parameter region of coherent search. In this work, we propose and examine a new method to select candidates, which reduces the cost of coherent search by following-up only the selected candidates. As a first step, we consider an idealized situation in which only a single-detector having 100\% duty cycle is available and its detector noise is approximated by the stationary Gaussian noise. Also, we assume the signal has no spindown and the polarization angle, the inclination angle, and the initial phase are fixed to be $\psi=0$, $\cos\iota=1$, and $\phi_0=0$, and they are treated as known parameters. We combine several methods: 1) the short-time Fourier transform with the re-sampled data such that the Earth motion for the source is canceled in some reference direction, 2) the excess power search in the Fourier transform of the time series obtained by picking up the amplitude in a particular frequency bin from the short-time Fourier transform data, and 3) the deep learning method to further constrain the source sky position. The computational cost and the detection probability are estimated. The injection test is carried out to check the validity of the detection probability. We find that our method is worthy of further study for analyzing $O(10^7)$sec strain data., Comment: 14 pages, 7 figures

Recently, several deep learning methods are proposed for the gravitational wave data analysis. One is conditional variational auto encoder (CVAE), proposed by Gabbard et al. [1]. We study the accuracy of a CVAE in the context of the estimation of the QNM frequency of the ringdown. We show that the accuracy of the estimation by the CVAE is better than the matched filtering. The areas of confidence regions are also compared and it is shown that the CVAE can return smaller confidence regions. Also, we assess the reliability of the confidence regions estimated by the CVAE. Our work confirms that the deep learning method has ability to compete with or overcome the matched filtering., Comment: 9 pages, 5 figures

Variational quantum eigensolver (VQE) is an appealing candidate for the application of near-term quantum computers. A technique introduced in [Higgot et al., Quantum 3, 156 (2019)], which is named variational quantum deflation (VQD), has extended the ability of the VQE framework for finding excited states of a Hamiltonian. However, no method to evaluate transition amplitudes between the eigenstates found by the VQD without using any costly Hadamard-test-like circuit has been proposed despite its importance for computing properties of the system such as oscillator strengths of molecules. Here we propose a method to evaluate transition amplitudes between the eigenstates obtained by the VQD avoiding any Hadamard-test-like circuit. Our method relies only on the ability to estimate overlap between two states, so it does not restrict to the VQD eigenstates and applies for general situations. To support the significance of our method, we provide a comprehensive comparison of three previously proposed methods to find excited states with numerical simulation of three molecules (lithium hydride, diazene, and azobenzene) in a noiseless situation and find that the VQD method exhibits the best performance among the three methods. Finally, we demonstrate the validity of our method by calculating the oscillator strength of lithium hydride, comparing results from numerical simulations and real-hardware experiments on the cloud enabled quantum computer IBMQ Rome. Our results illustrate the superiority of the VQD to find excited states and widen its applicability to various quantum systems., Comment: 12 pages, 7 figures