arXiv subjects

Shohei Watabe

Publications and source records attributed to Shohei Watabe.

At least 37 records · Page 2Linked to original sources

arXiv2021

Boltzmann machine learning with a variational quantum algorithm

Boltzmann machine is a powerful tool for modeling probability distributions that govern the training data. A thermal equilibrium state is typically used for Boltzmann machine learning to obtain a suitable probability distribution. The Boltzmann machine learning consists of calculating the gradient of the loss function given in terms of the thermal average, which is the most time consuming procedure. Here, we propose a method to implement the Boltzmann machine learning by using Noisy Intermediate-Scale Quantum (NISQ) devices. We prepare an initial pure state that contains all possible computational basis states with the same amplitude, and apply a variational imaginary time simulation. Readout of the state after the evolution in the computational basis approximates the probability distribution of the thermal equilibrium state that is used for the Boltzmann machine learning. We actually perform the numerical simulations of our scheme and confirm that the Boltzmann machine learning works well by our scheme.

quant-ph↗

arXiv2021

Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers

The Gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. There are several proposals to calculate the partition functions on near-team quantum computers. However, the existing schemes require many copies of the Gibbs states to perform an extrapolation for the calculation of the partition function, and these could be costly performed on the near-term quantum computers. Here, we propose an efficient scheme to calculate the Gibbs function with the imaginary time evolution. To calculate the Gibbs function of $N$ qubits, only $2N$ qubits are required in our scheme. After preparing Gibbs states with different temperatures by using the imaginary time evolution, we measure the overlap between them on a quantum circuit, and this allows us to calculate the Gibbs partition function.

quant-ph↗

arXiv2021

Propagation of phase-imprinted solitons from superfluid core to Mott-insulator shell and superfluid shell

We study phase-imprinted solitons of ultracold bosons in an optical lattice with a harmonic trap, which shows the superfluid (SF) and Mott-insulator (MI) shell structures. The earlier study [Konstantin V. Krutitsky, J. Larson, and M. Lewenstein, Phys. Rev. A 82, 033618 (2010).] reported three types of phase-imprinted solitons in the Bose-Hubbard model: in-phase soliton, out-of-phase soliton, and wavelet. In this paper, we uncover the dynamical phase diagram of these phase-imprinted solitons, and find another type of the phase-imprinted soliton namely, the hybrid soliton. In the harmonically trapped system, the solitonic excitations created at the SF core cannot penetrate into the outer SF shell. This repulsion at the surface of the outer SF shell can be cured by inposing a repulsive potential at the center of the trap. These results can be interpreted as a kind of the impedance matching of excitations in BECs in terms of the effective chemical potentials or the local particle numbers in the shell, and the analogous results can be observed also in the sound wave created by the local single-shot pulse potential.

cond-mat.quant-gas↗

arXiv2021

Variational secure cloud quantum computing

Variational quantum algorithms (VQAs) have been considered to be useful applications of noisy intermediate-scale quantum (NISQ) devices. Typically, in the VQAs, a parametrized ansatz circuit is used to generate a trial wave function, and the parameters are optimized to minimize a cost function. On the other hand, blind quantum computing (BQC) has been studied in order to provide the quantum algorithm with security by using cloud networks. A client with a limited ability to perform quantum operations hopes to have access to a quantum computer of a server, and BQC allows the client to use the server's computer without leakage of the client's information (such as input, running quantum algorithms, and output) to the server. However, BQC is designed for fault-tolerant quantum computing, and this requires many ancillary qubits, which may not be suitable for NISQ devices. Here, we propose an efficient way to implement the NISQ computing with guaranteed security for the client. In our architecture, only N+ 1 qubits are required, under an assumption that the form of ansatzes is known to the server, where N denotes the necessary number of the qubits in the original NISQ algorithms. The client only performs single-qubit measurements on an ancillary qubit sent from the server, and the measurement angles can specify the parameters for the ansatzes of the NISQ algorithms. No-signaling principle guarantees that neither parameters chosen by the client nor the outputs of the algorithm are leaked to the server. This work paves the way for new applications of NISQ devices.

quant-ph↗

arXiv2021

Hugenholtz-Pines theorem for multicomponent Bose-Einstein condensates

The Hugenholtz-Pines (HP) theorem is derived for Bose-Einstein condensates (BECs) with internal degrees of freedom. The low-energy Ward-Takahashi identity is provided in the system with the linear and quadratic symmetry breaking terms. This identity serves to organize the HP theorem for multicomponent BECs, such as the binary BEC as well as the spin-$f$ spinor BEC in the presence of a magnetic field with broken U$(1)$$\times$SO$(3)$ symmetry. The experimental method based on the Stern-Gerlach experiment is proposed for studying the Ward-Takahashi identity.

cond-mat.quant-gas↗

arXiv2020

Strong connection between single-particle and density excitations in Bose-Einstein condensates

Strong connection between the single-particle and collective excitations stands out as one of the features of Bose-Einstein condensates (BECs). We discuss theoretically these excitations of BECs focusing on the exact properties of the one-body and two-body Green's functions developed by Gavoret and Nozières. We also investigate these excitations by using the many-body approximation theory at nonzero temperatures. First, we revisited the earlier study presented by Gavoret and Nozières, involving the subsequent results given by Nepomnyashchii and Nepomnyashchii, in terms of the matrix formalism representation. This formalism is an extension of the Nambu representation for the single-particle Green's function of BECs to discuss the density and current response functions efficiently. We describe the exact low-energy properties of the correlation functions and the vertex functions, and discuss the correspondence of the spectra between the single-particle and density excitations in the low-energy and low-momentum limits at $T=0$. After deriving the exact low-energy structures of the one-body and two-body Green's functions, we develop a many-body approximation theory of BECs using the matrix formalism for describing the single-particle Green's function and the density response function at nonzero temperatures. We show how the peaks of the single-particle spectral function and the density response function behave with an increasing temperature. Many-body effect on the single-particle spectral function and the density response function is included within a random phase approximation, where satellite structures emerge because of beyond-mean-field effects. Criticisms are also made on recent theories casting doubt upon the conventional wisdom of the BEC: the equivalence of the dispersion relations between the single-particle and collective excitations in the low-energy and low-momentum regime.

cond-mat.quant-gas↗

arXiv2020

Dipole Mode of Trapped Bose--Fermi Mixture Gas

We investigate dipole modes in a trapped Bose--Fermi mixture gas in the normal phase, composed of single-species bosons and single-species fermions with $s$-wave scattering. In the extremely low temperature regime, Bose--Einstein statistics and Fermi--Dirac statistics may give rise to an interesting temperature dependence of collective modes. Applying the moment method to the linearized Boltzmann equation, we study the transition of the dipole modes between the hydrodynamic regime and the collisionless regime.

cond-mat.quant-gas↗

arXiv2020

Dipole oscillation of a trapped Bose--Fermi-mixture gas in collisionless and hydrodynamic regimes

Dipole oscillation is studied in a normal phase of a trapped Bose--Fermi-mixture gas composed of single-species bosons and single-species fermions. Applying the moment method to the linearized Boltzmann equation, we derive a closed set of equations of motion for the center-of-mass position and momentum of both components. By solving the coupled equations, we reveal the behavior of dipole modes in the transition between the collisionless regime and the hydrodynamic regime. We find that two oscillating modes in the collisionless regime have distinct fates in the hydrodynamic regime: one collisionless mode shows a crossover to a hydrodynamic in-phase mode, and the other collisionless mode shows a transition to two purely damped modes. The temperature dependence of these dipole modes are also discussed.

cond-mat.quant-gas↗

arXiv2020

Scaling Hypothesis of Spatial Search on Fractal Lattice Using Quantum Walk

We investigate a quantum spatial search problem on fractal lattices, such as Sierpinski carpets and Menger sponges. In earlier numerical studies of the Sierpinski gasket, the Sierpinski tetrahedron, and the Sierpinski carpet, conjectures have been proposed for the scaling of a quantum spatial search problem finding a specific target, which is given in terms of the characteristic quantities of a fractal geometry. We find that our simulation results for extended Sierpinski carpets and Menger sponges support the conjecture for the ${\it optimal}$ number of the oracle calls, where the exponent is given by $1/2$ for $d_{\rm s} > 2$ and the inverse of the spectral dimension $d_{\rm s}$ for $d_{\rm s} < 2$. We also propose a scaling hypothesis for the ${\it effective}$ number of the oracle calls defined by the ratio of the ${\it optimal}$ number of oracle calls to a square root of the maximum finding probability. The form of the scaling hypothesis for extended Sierpinski carpets is very similar but slightly different from the earlier conjecture for the Sierpinski gasket, the Sierpinski tetrahedron, and the conventional Sierpinski carpet.

quant-ph↗

arXiv2019

Enhancing quantum annealing performance by a degenerate two-level system

Quantum annealing is an innovative idea and method for avoiding the increase of the calculation cost of the combinatorial optimization problem. Since the combinatorial optimization problems are ubiquitous, quantum annealing machine with high efficiency and scalability will give an immeasurable impact on many fields. However, the conventional quantum annealing machine may not have a high success probability for finding the solution because the energy gap closes exponentially as a function of the system size. To propose an idea for finding high success probability is one of the most important issues. Here we show that a degenerate two-level system provides the higher success probability than the conventional spin-1/2 model in a weak longitudinal magnetic field region. The physics behind this is that the quantum annealing in this model can be reduced into that in the spin-1/2 model, where the effective longitudinal magnetic field may open the energy gap, which suppresses the Landau--Zener tunneling providing leakage of the ground state. We also present the success probability of the $Λ$-type system, which may show the higher success probability than the conventional spin-1/2 model.

cond-mat.stat-mech↗

arXiv2019

Identities and Many-Body Approaches in Bose-Einstein Condensates

This paper discusses exact relations in Bose--Einstein condensates (BECs), starting from basic properties of an ideal Bose gas. In particular, focused on are the Hugenholtz--Pines relation, Nepomnyashchii--Nepomnyashchii identity, and identities for the density response function. After introducing these exact relations, a few approaches of many-body approximations are discussed, which satisfy the exact relations in BECs. This paper will serve as a bridge between theories on exact relations and those on approximations in BECs.

cond-mat.quant-gas↗

arXiv2018

Spatial Search on Sierpinski Carpet Using Quantum Walk

We investigate a quantum spatial search problem on a fractal lattice. A recent study for the Sierpinski gasket and tetrahedron made a conjecture that the dynamics of the search on a fractal lattice is determined by spectral dimension. We tackle this problem for the Sierpinski carpet, and our simulation result supports the conjecture. We also propose a scaling hypothesis of oracle calls for the quantum amplitude amplification.

quant-ph↗

arXiv2018

Hidden multiparticle excitation in weakly interacting Bose-Einstein Condensate

We investigate multiparticle excitation effect on a collective density excitation as well as a single-particle excitation in a weakly interacting Bose--Einstein condensate (BEC). We find that although the weakly interacting BEC offers weak multiparticle excitation spectrum at low temperatures, this multiparticle excitation effect may not remain hidden, but emerges as bimodality in the density response function through the single-particle excitation. Identification of spectra in the BEC between the single-particle excitation and the density excitation is also assessed at nonzero temperatures, which has been known to be unique nature in the BEC at absolute zero temperature.

cond-mat.quant-gas↗

arXiv2018

Density and spin modes in imbalanced normal Fermi gases from collisionless to hydrodynamic regime

We study mass and population imbalance effect on density (in-phase) and spin (out-of-phase) collective modes in a two-component normal Fermi gas. By calculating eigenmodes of the linearized Boltzmann equation as well as the density/spin dynamic structure factor, we show that mass and population imbalance effects offer a variety of collective mode crossover behaviors from collisionless to hydrodynamic regimes. The mass imbalance effect shifts the crossover regime to the higher-temperature, and a significant peak of the spin dynamic structure factor emerges only in the collisionless regime. This is in contrast to the case of mass and population balanced normal Fermi gases, where the spin dynamic response is always absent. Although the population imbalance effect does not shift the crossover regime, the spin dynamic structure factor survives both in the collisionless and hydrodynamic regimes.

cond-mat.quant-gas↗

arXiv2017

Decay of phase-imprinted dark soliton in Bose-Einstein condensate at non-zero temperature

We study relaxation dynamics of dark soliton, created by a phase-imprinted method, in a two-dimensional trapped Bose-Einstein condensate at non-zero temperatures by using the projected Gross-Pitaevskii equation. At absolute zero temperature, a dark soliton is known to decay with a snake instability. At non-zero temperature, as we expected, we find that this snake instability cannot be clearly seen as in the absolute zero temperature case because of the presence of thermal fluctuations. However, we find that the decay rate, the half width of the overlap integral with respect to the phase-imprinted initial state, shows a power low decay as a function of the energy and finally remains a non-zero value.

cond-mat.quant-gas↗

arXiv2017

Nonlinear Mixing of Collective Modes in Harmonically Trapped Bose-Einstein Condensates

We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function for the Gross-Pitaevskii equation, we find that mode mixing selectively occurs. Our perturbative approach is useful in gaining qualitative understanding of the recent experiment [Yamazaki et al., J. Phys. Soc. Japan 84, 44001 (2015)], exhibiting a beating phenomenon of the scissors mode as well as a modulation phenomenon of the low-lying quadrupole mode by the high-lying quadrupole mode frequency. Within the second-order treatment of the nonlinear mode coupling terms, our approach predicts all the spectral peaks obtained by the numerical simulation of the Gross-Pitaevskii equation.

cond-mat.quant-gas↗

arXiv2014

Green's function formalism for a condensed Bose gas consistent with infrared-divergent longitudinal susceptibility and Nepomnyashchii-Nepomnyashchii identity

We present a Green's function formalism for an interacting Bose-Einstein condensate (BEC) satisfying the two required conditions: (i) the infrared-divergent longitudinal susceptibility with respect to the BEC order parameter, and (ii) the Nepomnyashchii-Nepomnyashchii identity stating the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. These conditions cannot be described by the ordinary mean-field Bogoliubov theory, the many-body $T$-matrix theory, as well as the random-phase approximation with the vertex correction. In this paper, we show that these required conditions can be satisfied, when we divide many-body corrections into singular and non-singular parts, and separately treat them as different self-energy corrections. The resulting Green's function may be viewed as an extension of the Popov's hydrodynamic theory to the region at finite temperatures. Our results would be useful in constructing a consistent theory of BECs satisfying various required conditions, beyond the mean-field level.

cond-mat.quant-gas↗

arXiv2013

Stability Criterion for Superfluidity based on the Density Spectral Function

We study a stability criterion hypothesis for superfluids in terms of the the local density spectral function $I_n (r, ω)$ applicable both to homogeneous and inhomogeneous systems. We evaluate the local density spectral function in the presence of a one-dimensional repulsive/attractive external potential within the Bogoliubov theory using solutions of the tunneling problem. We also evaluate the local density spectral function using an orthogonal basis, and calculate the autocorrelation function $C_n (r,t)$. When superfluids flow below a threshold, we find that in the $d$-dimensional system, $I_n (r, ω) \propto ω^{d}$ in the low-energy regime and $C_n (r, t) \propto 1/t^{d+1}$ in the long-time regime hold. When superfluids flow with the critical current, on the other hand, we find $I_n (r, ω) \propto ω^β$ in the low-energy regime and $C_n (r,t) \propto 1/t^{β+1}$ in the long-time regime with $β< d$. These results support the stability criterion hypothesis recently proposed.

cond-mat.quant-gas↗