arXiv subjects

Naoyuki Takeda

Publications and source records attributed to Naoyuki Takeda.

12 recordsLinked to original sources

arXiv2024

Analysis of Parameterized Quantum Circuits: on The Connection Between Expressibility and Types of Quantum Gates

Expressibility is a crucial factor of a Parameterized Quantum Circuit (PQC). In the context of Variational Quantum Algorithms (VQA) based Quantum Machine Learning (QML), a QML model composed of highly expressible PQC and sufficient number of qubits is theoretically capable of approximating any arbitrary continuous function. While much research has explored the relationship between expressibility and learning performance, as well as the number of layers in PQCs, the connection between expressibility and PQC structure has received comparatively less attention. In this paper, we analyze the connection between expressibility and the types of quantum gates within PQCs using a Gradient Boosting Tree model and SHapley Additive exPlanations (SHAP) values. Our analysis is performed on 1,615 instances of PQC derived from 19 PQC topologies, each with 2-18 qubits and 1-5 layers. The findings of our analysis provide guidance for designing highly expressible PQCs, suggesting the integration of more RX or RY gates while maintaining a careful balance with the number of CNOT gates. Furthermore, our evaluation offers an additional evidence of expressibility saturation, as observed by previous studies.

quant-ph↗

arXiv2021

Linear Regression by Quantum Amplitude Estimation and its Extension to Convex Optimization

Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the regression coefficients as classical data, the complexity of the existing quantum algorithms can be larger than the classical method. This is because it depends strongly on the tolerance error $ε$: the best one among the existing proposals is $O(ε^{-2})$. In this paper, we propose the new quantum algorithm for linear regression, which has the complexity of $O(ε^{-1})$ and keeps the logarithmic dependence on the number of data points $N_D$. In this method, we overcome bottleneck parts in the calculation, which take the form of the sum over data points and therefore have the complexity proportional to $N_D$, using quantum amplitude estimation, and other parts classically. Additionally, we generalize our method to some class of convex optimization problems.

quant-ph↗

arXiv2021

Quantum Speedup of Monte Carlo Integration with respect to the Number of Dimensions and its Application to Finance

Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a smaller number of iterative calls of the quantum circuit which calculates the integrand, than classical methods call the integrand subroutine. However, the issues about the iterative operations in the integrand circuit have not been discussed so much. That is, in the high-dimensional integration, many random numbers are used for calculation of the integrand and in some cases similar calculations are repeated to obtain one sample value of the integrand. In this paper, we point out that we can reduce the number of such repeated operations by a combination of the nested QAE and the use of pseudorandom numbers (PRNs), if the integrand has the separable form with respect to contributions from distinct random numbers. The use of PRNs, which the authors originally proposed in the context of the quantum algorithm for Monte Carlo, is the key factor also in this paper, since it enables parallel computation of the separable terms in the integrand. Furthermore, we pick up one use case of this method in finance, the credit portfolio risk measurement, and estimate to what extent the complexity is reduced.

quant-ph↗

arXiv2020

Quantum Pricing with a Smile: Implementation of Local Volatility Model on Quantum Computer

Applications of the quantum algorithm for Monte Carlo simulation to pricing of financial derivatives have been discussed in previous papers. However, up to now, the pricing model discussed in such papers is Black-Scholes model, which is important but simple. Therefore, it is motivating to consider how to implement more complex models used in practice in financial institutions. In this paper, we then consider the local volatility (LV) model, in which the volatility of the underlying asset price depends on the price and time. We present two types of implementation. One is the register-per-RN way, which is adopted in most of previous papers. In this way, each of random numbers (RNs) required to generate a path of the asset price is generated on a separated register, so the required qubit number increases in proportion to the number of RNs. The other is the PRN-on-a-register way, which is proposed in the author's previous work. In this way, a sequence of pseudo-random numbers (PRNs) generated on a register is used to generate paths of the asset price, so the required qubit number is reduced with a trade-off against circuit depth. We present circuit diagrams for these two implementations in detail and estimate required resources: qubit number and T-count.

quant-ph↗

arXiv2017

Flavor structure, Higgs boson mass and dark matter in supersymmetric model with vector-like generations

We study a supersymmetric model in which the Higgs mass, the muon anomalous magnetic moment and the dark matter are simultaneously explained with extra vector-like generation multiplets. For the explanations, non-trivial flavor structures and a singlet field are required. In this paper, we study the flavor texture by using the Froggatt-Nielsen mechanism, and then find realistic flavor structures which reproduce the Cabbibo-Kobayashi-Maskawa matrix and fermion masses at low energy. Furthermore, we find that the fermion component of the singlet field becomes a good candidate of dark matter. In our model, flavor physics and dark matter are explained with moderate size couplings through renormalization group flows, and the presence of dark matter supports the existence of just three generations in low energy scales. We analyze the parameter region where the current thermal relic abundance of dark matter, the Higgs boson mass and the muon $g-2$ can be explained simultaneously.

hep-ph↗

arXiv2016

Cosmological relaxation and high scale inflation

We study whether the relaxion mechanism solves the Higgs hierarchy problem against a high scale inflation or a high reheating temperature. To accomplish the mechanism, we consider the scenario that the Higgs vacuum expectation value is determined after inflation. We take into account the effects of the Hubble induced mass and thermal one in the dynamics of the relaxion.

hep-ph↗

arXiv2015

Adiabatic Invariance of Oscillons/I-balls

Real scalar fields are known to fragment into spatially localized and long-lived solitons called oscillons or $I$-balls. We prove the adiabatic invariance of the oscillons/$I$-balls for a potential that allows periodic motion even in the presence of non-negligible spatial gradient energy. We show that such potential is uniquely determined to be the quadratic one with a logarithmic correction, for which the oscillons/$I$-balls are absolutely stable. For slightly different forms of the scalar potential dominated by the quadratic one, the oscillons/$I$-balls are only quasi-stable, because the adiabatic charge is only approximately conserved. We check the conservation of the adiabatic charge of the $I$-balls in numerical simulation by slowly varying the coefficient of logarithmic corrections. This unambiguously shows that the longevity of oscillons/$I$-balls is due to the adiabatic invariance.

hep-th↗

arXiv2015

Inflatonic baryogenesis with large tensor mode

We consider the complex inflaton field with a CP asymmetric term for its potential. This CP asymmetric term produces the global charge of the inflaton after inflation. With the assignment of the baryon number to the inflaton, the baryon asymmetry of the universe is produced by inflaton's decay. In addition to this, the $U(1)$ breaking term modulates the curvature of the inflaton radial direction depending on its phase, which affects the tensor to scalar ratio. In this paper, we have studied the relation between the baryon asymmetry and the tensor to scalar ratio, then verified that the future CMB observation could test this baryogenesis scenario with large tensor mode.

astro-ph.CO↗

arXiv2015

I-ball formation with logarithmic potential

A coherently oscillating real scalar field with potential shallower than quadratic one fragments into spherical objects called I-balls. We study the I-ball formation for logarithmic potential which appears in many cosmological models. We perform lattice simulations and find that the I-balls are formed when the potential becomes dominated by the quadratic term. Furthermore, we estimate the I-ball profile assuming that the adiabatic invariant is conserved during formation and obtain the result that agrees to the numerical simulations.

astro-ph.CO↗

arXiv2015

Consistent generation of magnetic fields in axion inflation models

There has been a growing evidence for the existence of magnetic fields in the extra-galactic regions, while the attempt to associate their origin with the inflationary epoch alone has been found extremely challenging. We therefore take into account the consistent post-inflationary evolution of the magnetic fields that are originated from vacuum fluctuations during inflation. In the model of our interest, the electromagnetic (EM) field is coupled to a pseudo-scalar inflaton $ϕ$ through the characteristic term $ϕF\tilde F$, breaking the conformal invariance. This interaction dynamically breaks the parity and enables a continuous production of only one of the polarization states of the EM field through tachyonic instability. The produced magnetic fields are thus helical. We find that the dominant contribution to the observed magnetic fields in this model comes from the modes that leave the horizon near the end of inflation, further enhanced by the tachyonic instability right after the end of inflation. The EM field is subsequently amplified by parametric resonance during the period of inflaton oscillation. Once the thermal plasma is formed (reheating), the produced helical magnetic fields undergo a turbulent process called inverse cascade, which shifts their peak correlation scales from smaller to larger scales. We consistently take all these effects into account within the regime where the perturbation of $ϕ$ is negligible and obtain $B_{\rm eff} \sim 10^{-19}$G, indicating the necessity of additional mechanisms to accommodate the observations.

astro-ph.CO↗

arXiv2014

No quasi-stable scalaron lump forms after $R^2$ inflation

In the Einstein frame picture of Starobinky's $R^2$ inflation model, cosmic inflation is driven by a slowly rolling inflaton field, called scalaron, and followed by a coherently oscillating scalaron phase. Since the scalaron oscillates excessively many times in its potential, which has a quadratic minimum and is a little shallower than quadratic on the positive side, it may fragment into long-living localized objects, called oscillons or I-balls, due to nonlinear growth of fluctuations before reheating of the universe. We show that while parametric self-resonances amplify scalaron fluctuations in the Minkowski background, the growth cannot overcome the decay due to expansion in the Friedmann background after $R^2$ inflation. By taking into account back-reaction from the metric of spacetime, modes that are larger than a critical scale are indeed amplified and become non-decaying. However, those non-decaying modes are not growing enough to form spatially localized lumps of the scalaron. Thus, reheating processes are unaltered by oscillons/I-balls and they proceed through perturbative decay of the scalaron as studied in the original work.

astro-ph.CO↗

arXiv2013

Gravitational waves from smooth hybrid new infation

We calculate the production of the gravitational waves from a double inflation model with lattice simulations. Between the two inflationary stages, gravitational waves with a characteristic frequency are produced by fluctuations of the scalar fields enhanced through parametric resonance. The wavelength of the produced gravitational waves gets extra redshift during the second inflationary stage and it can be in the observable range for the direct gravitational wave detectors. It is found that there is a possibility for the produced gravitational waves to be detected in the planned experiments.

astro-ph.CO↗