arXiv subjects

Hiroshi Ueda

Publications and source records attributed to Hiroshi Ueda.

At least 37 records · Page 2Linked to original sources

arXiv2022

Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers

We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the system dimension, where the interactions between divided subsystems are taken as an effective Hamiltonian expanded by the reduced basis. Then the effective Hamiltonian is further solved by VQE, which we call deep VQE. Deep VQE allows us to apply quantum-classical hybrid algorithms on small-scale quantum computers to large systems with strong intra-subsystem interactions and weak inter-subsystem interactions, or strongly correlated spin models on large regular lattices. As proof-of-principle numerical demonstrations, we use the proposed method for quasi one-dimensional models, including one-dimensionally coupled 12-qubit Heisenberg anti-ferromagnetic models on Kagome lattices as well as two-dimensional Heisenberg anti-ferromagnetic models on square lattices. The largest problem size of 64 qubits is solved by simulating 20-qubit quantum computers with a reasonably good accuracy ~ a few %. The proposed scheme enables us to handle the problems of >1000 qubits by concatenating VQEs with a few tens of qubits. While it is unclear how accurate ground state energy can be obtained for such a large system, our numerical results on a 64-qubit system suggest that deep VQE provides a good approximation (discrepancy within a few percent) and has a room for further improvement. Therefore, deep VQE provides us a promising pathway to solve practically important problems on noisy intermediate-scale quantum computers.

quant-ph↗

arXiv2021

Automatic quantum circuit encoding of a given arbitrary quantum state

We propose a quantum-classical hybrid algorithm to encode a given arbitrarily quantum state $\vert Ψ\rangle$ onto an optimal quantum circuit $\hat{\mathcal{C}}$ with a finite number of single- and two-qubit quantum gates. The proposed algorithm employs as an objective function the absolute value of fidelity $F = \langle 0 \vert \hat{\mathcal{C}}^{\dagger} \vert Ψ\rangle$, which is maximized iteratively to construct an optimal quantum circuit $\hat{\mathcal{C}}$ with controlled accuracy. The key ingredient of the algorithm is the sequential determination of a set of optimal two-qubit unitary operators one by one via the singular value decomposition of the fidelity tensor. Once the optimal unitary operators are determined, including the location of qubits on which each unitary operator acts, elementary quantum gates are assigned algebraically. With noiseless numerical simulations, we demonstrate the algorithm to encode a ground state of quantum many-body systems, including the spin-1/2 antiferromagnetic Heisenberg model and the spin-1/2 XY model. The results are also compared with the quantum circuit encoding of the same quantum state onto a quantum circuit in a given circuit structure. Moreover, we demonstrate that the algorithm can also be applied to construct an optimal quantum circuit for classical data such as a classical image that is represented as a quantum state by the amplitude encoding. Finally, we also experimentally demonstrate that a quantum circuit generated by the AQCE algorithm can indeed represent the original quantum state reasonably on a noisy real quantum device.

quant-ph↗

arXiv2021

Quantum-inspired search method for low-energy states of classical Ising Hamiltonians

We develop a quantum-inspired numerical procedure for searching low-energy states of a classical Hamiltonian composed of two-body fully-connected random Ising interactions and a random local longitudinal magnetic field. In this method, we introduce infinitesimal quantum interactions that do not commute with the original Ising Hamiltonian, and repeatedly generate and truncate direct product states, inspired by the Krylov subspace method, to obtain the low-energy states of the original classical Ising Hamiltonian. The computational cost is controlled by the form of infinitesimal quantum interactions (e.g., one-body or two-body interactions) and the numbers of infinitesimal interaction terms introduced, different initial states considered, and low-energy states kept during the iteration. For a demonstrate of the method, here we introduce as the infinitesimal quantum interactions pair products of Pauli $X$ operators acting on different sites and on-site Pauli $X$ operators into the random Ising Hamiltonian, in which the numerical cost is $O(N^3)$ per iteration with the system size $N$. We consider 120 instances of the random coupling realizations for the random Ising Hamiltonian with $N$ up to 600 and search the 120 lowest-energy states for each instance. We find that the time-to-solution by the quantum-inspired method proposed here, with parallelization in terms of the different initial states, for searching the ground state of the random Ising Hamiltonian scales approximately as $N^5$ for $N$ up to 600. We also examine the basic physical properties such as the ensemble-averaged ground-state and first-excited energies and the ensemble-averaged number of states in the low-energy region of the random Ising Hamiltonian.

cond-mat.stat-mech↗

arXiv2021

Quantum spin solver near saturation: QS$^3_{~}$

We develop a program package named QS$^{3}$ [\textipa{kjú:-és-kjú:b}] based on the (thick-restart) Lanczos method for analyzing spin-1/2 XXZ-type quantum spin models on spatially uniform/non-uniform lattices near fully polarized states, which can be mapped to dilute hardcore Bose systems. All calculations in QS$^{3}$, including eigenvalue problems, expectation values for one/two-point spin operators, and static/dynamical spin structure factors, are performed in the symmetry-adapted bases specified by the number $N_{\downarrow}$ of down spins and the wave number $\boldsymbol{k}$ associated with the translational symmetry without using the bit representation for specifying spin configurations. Because of these treatments, QS$^{3}$ can support large-scale quantum systems containing more than 1000 sites with dilute $N_{\downarrow}$. We show the benchmark results of QS$^{3}$ for the low-energy excitation dispersion of the isotropic Heisenberg model on the $10\times10\times10$ cubic lattice, the static and dynamical spin structure factors of the isotropic Heisenberg model on the $10\times10$ square lattice, and the open-MP parallelization efficiency on the supercomputer (Ohtaka) based on AMD Epyc 7702 installed at the Institute for the Solid State Physics (ISSP). Theoretical backgrounds and the user interface of QS$^{3}$ are also described.

physics.comp-ph↗

arXiv2020

Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model

We investigate the phase transition of the dodecahedron model on the square lattice. The model is a discrete analogue of the classical Heisenberg model, which has continuous $O(3)$ symmetry. In order to treat the large on-site degree of freedom $q = 20$, we develop a massively parallelized numerical algorithm for the corner transfer matrix renormalization group method, incorporating EigenExa, the high-performance parallelized eigensolver. The scaling analysis with respect to the cutoff dimension reveals that there is a second-order phase transition at $T^{~}_{\rm c}=0.4398(8)$ with the critical exponents $ν=2.88(8)$ and $β=0.21(1)$. The central charge of the system is estimated as $c=1.99(6)$.

cond-mat.stat-mech↗

arXiv2020

Roles of easy-plane and easy-axis XXZ anisotropy and bond alternation on a frustrated ferromagnetic spin-$1/2$ chain

The spin-$1/2$ Heisenberg chain with a ferromagnetic first-neighbor exchange coupling $J_1$ and an antiferromagnetic second-neighbor $J_2$ has a Haldane dimer ground state with an extremely small spin gap. Thus, the ground state is readily altered by perturbations. Here, we investigate the effects of XXZ exchange magnetic anisotropy of both the easy-axis and easy-plane types and an alternation in $J_1$ on the ground state, the spin gap, and magnetic properties of the frustrated ferromagnetic spin-$1/2$ chain. It is found that there are two distinct dimerized spin-gap phases, in one of which the spin gap and the magnetic susceptibility are extremely small around the SU(2) symmetric case and in the other they are moderately large far away from the SU(2) symmetric case. A small alternation in the amplitude of $J_1$ rapidly shortens the pitch of spin correlations towards the four-spin periodicity, as in the limit of $J_1/J_2\to0$. These effects are not sufficient to quantitatively explain overall experimentally observed magnetic properties in the quasi-one-dimensional spin-gapped magnetoelectric cuprate Rb$_2$Cu$_2$Mo$_3$O$_{12}$ that exhibits ferroelectricity stabilized by a magnetic field. Our results are also relevant to Cs$_2$Cu$_2$Mo$_3$O$_{12}$, where the ferromagnetic intrachain and antiferromagnetic interchain order has recently been found, in a single chain level. We also reveal the nature of symmetry-protected topological phase transitions in the model by mapping onto effective spin-1 chain models.

cond-mat.str-el↗

arXiv2020

Finite-$m$ scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model

We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyses for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension $m$ at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the $c=1$ boundary conformal field theory associated with the effective $Z_6$ dual sine-Gordon model.

cond-mat.stat-mech↗

arXiv2020

Emergent spin-$1$ Haldane gap and ferroelectricity in a frustrated spin-$1/2$ ladder

We report experimental and theoretical evidence that Rb$_2$Cu$_2$Mo$_3$O$_{12}$ has a nonmagnetic tetramer ground state of a two-leg ladder comprising antiferromagnetically coupled frustrated spin-$1/2$ chains and exhibits a Haldane spin gap of emergent spin-1 pairs. Three spin excitations split from the spin-1 triplet by a Dzyaloshinskii-Moriya interaction are identified in inelastic neutron-scattering and electron spin resonance spectra. A tiny magnetic field generates ferroelectricity without closing the spin gap, indicating a novel class of ferroelectricity induced by a vector spin chirality order.

cond-mat.str-el↗

arXiv2018

Symmetry protected topological phases in two-orbital SU(4) fermionic atoms

We study one-dimensional systems of two-orbital SU(4) fermionic cold atoms. In particular, we focus on an SU(4) spin model [named SU(4) $e$-$g$ spin model] that is realized in a low-energy state in the Mott insulator phase at the filling $n_g=3, n_e=1$ ($n_g, n_e$: numbers of atoms in ground and excited states, respectively). Our numerical study with the infinite-size density matrix renormalization group shows that the ground state of SU(4) $e$-$g$ spin model is a nontrivial symmetry protected topological (SPT) phase protected by $Z_4 \times Z_4$ symmetry. Specifically, we find that the ground state belongs to an SPT phase with the topological index $2\in\mathbb{Z}_4$ and show sixfold degenerate edge states. This is topologically distinct from SPT phases with the index $1\in\mathbb{Z}_4$ that are realized in the SU(4) bilinear model and the SU(4) Affleck-Kennedy-Lieb-Tasaki (AKLT) model. We explore the phase diagram of SU(4) spin models including $e$-$g$ spin model, bilinear-biquadratic model, and AKLT model, and identify that antisymmetrization effect in neighboring spins (that we quantify with Casimir operators) is the driving force of the phase transitions. Furthermore, we demonstrate by using the matrix product state how the $\mathbb{Z}_4$ SPT state with six edge states appears in the SU(4) $e$-$g$ spin model.

cond-mat.str-el↗

arXiv2018

Infinite-size density matrix renormalization group with parallel Hida's algorithm

In this study, we report a parallel algorithm for the infinite-size density matrix renormalization group (iDMRG) that is applicable to one-dimensional (1D) quantum systems with $\ell$-site periods, where $\ell$ is an even number. It combines Hida's iDMRG applied to random 1D spin systems with a variant of McCulloch's wavefunction prediction. This allows us to apply $\ell/2$ times of computational power to accelerate the investigation of multi-leg frustrated quantum systems in the thermodynamic limit, which is a challenging simulation. We performed benchmark calculations for a spin-1/2 Heisenberg model on a Kagome cylinder YC8 using the parallel iDMRG, and found that the proposed iDMRG was efficiently parallelized for shared memory and distributed memory systems, and provided such bulk physical quantities as total energy, bond strength on nearest neighbor spins, and spin--spin correlation functions and their correlation lengths without finite-size effects. Moreover, the variant of the wavefunction prediction sped up Lanczos methods in the parallel iDMRG by approximately three times.

cond-mat.str-el↗

arXiv2017

Critical behavior of the two-dimensional icosahedron model

In the context of a discrete analogue of the classical Heisenberg model, we investigate critical behavior of the icosahedron model, where the interaction energy is defined as the inner product of neighboring vector spins of unit length pointing to vertices of the icosahedron. Effective correlation length and magnetization of the model are calculated by means of the corner-transfer matrix renormalization group (CTMRG) method. Scaling analysis with respect to the cutoff dimension $m$ in CTMRG reveals the second-order phase transition characterized by the exponents $ν= 1.62\pm0.02$ and $β= 0.12\pm0.01$. We also extract the central charge from the classical analogue of the entanglement entropy as $c = 1.90\pm0.02$, which cannot be explained by the minimal series of conformal field theory.

cond-mat.stat-mech↗

arXiv2017

Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation

Quantum magnetic phases near the magnetic saturation of triangular-lattice antiferromagnets with XXZ anisotropy have been attracting renewed interest since it has been suggested that a nontrivial coplanar phase, called the $π$-coplanar or $Ψ$ phase, could be stabilized by quantum effects in a certain range of anisotropy parameter $J/J_z$ besides the well-known 0-coplanar (known also as $V$) and umbrella phases. Recently, Sellmann $et$ $al$. [Phys. Rev. B {\bf 91}, 081104(R) (2015)] claimed that the $π$-coplanar phase is absent for $S=1/2$ from an exact-diagonalization analysis in the sector of the Hilbert space with only three down-spins (three magnons). We first reconsider and improve this analysis by taking into account several low-lying eigenvalues and the associated eigenstates as a function of $J/J_z$ and by sensibly increasing the system sizes (up to 1296 spins). A careful identification analysis shows that the lowest eigenstate is a chirally antisymmetric combination of finite-size umbrella states for $J/J_z\gtrsim 2.218$ while it corresponds to a coplanar phase for $J/J_z\lesssim 2.218$. However, we demonstrate that the distinction between 0-coplanar and $π$-coplanar phases in the latter region is fundamentally impossible from the symmetry-preserving finite-size calculations with fixed magnon number.} Therefore, we also perform a cluster mean-field plus scaling analysis for small spins $S\leq 3/2$. The obtained results, together with the previous large-$S$ analysis, indicate that the $π$-coplanar phase exists for any $S$ except for the classical limit ($S\rightarrow \infty$) and the existence range in $J/J_z$ is largest in the most quantum case of $S=1/2$.

cond-mat.str-el↗

arXiv2014

Z_3 symmetry-protected topological phases in the SU(3) AKLT model

We study $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases in one-dimensional spin systems with $Z_3 \times Z_3$ symmetry. We construct ground-state wave functions of the matrix product form for nontrivial $\mathbb{Z}_3$ phases and their parent Hamiltonian from a cocycle of the group cohomology $H^2(Z_3\times Z_3,U(1))$. The Hamiltonian is an SU(3) version of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, consisting of bilinear and biquadratic terms of su(3) generators in the adjoint representation. A generalization to the SU($N$) case, the SU($N$) AKLT Hamiltonian, is also presented which realizes nontrivial $\mathbb{Z}_N$ SPT phases. We use the infinite-size variant of the density matrix renormalization group (iDMRG) method to determine the ground-state phase diagram of the SU(3) bilinear-biquadratic model as a function of the parameter $θ$ controlling the ratio of the bilinear and biquadratic coupling constants. The nontrivial $\mathbb{Z}_3$ SPT phase is found for a range of the parameter $θ$ including the point of vanishing biquadratic term ($θ=0$) as well as the SU(3) AKLT point [$θ=\arctan(2/9)$]. A continuous phase transition to the SU(3) dimer phase takes place at $θ\approx -0.027π$, with a central charge $c\approx3.2$. For SU(3) symmetric cases we define string order parameters for the $\mathbb{Z}_3$ SPT phases in a similar way to the conventional Haldane phase. We propose simple spin models that effectively realize the SU(3) and SU(4) AKLT models.

cond-mat.str-el↗

arXiv2014

Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain

Frustrated spin-$1/2$ XXZ zigzag chains relevant to Rb$_2$Cu$_2$Mo$_3$O$_{12}$ are revisited in the light of symmetry-protected topological (SPT) phases. Using a density-matrix renormalization group method for infinite systems, we identify projective representations for four distinct time-reversal invariant SPT phases; two parity-symmetric dimer phases near the Heisenberg and XX limits and two parity-broken vector-chiral (VC) dimer phases in between. A small bond alternation in the nearest-neighbor ferromagnetic exchange coupling induces a direct SPT transition between the two distinct VC dimer phases. It is also found numerically that two Berezinskii-Kosterlitz-Thouless transitions from the gapless to the two distinct gapped VC phases meet each other at a Gaussian criticality of the same Tomonaga-Luttinger parameter value as in the SU(2)-symmetric case.

cond-mat.str-el↗

arXiv2014

Doubling of Entanglement Spectrum in Tensor Renormalization Group

We investigate the entanglement spectrum in HOTRG ---tensor renormalization group (RG) method combined with the higher order singular value decomposition--- for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by `doubling' of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to $D = 64$, where $D$ is the cut-off dimension of tensors. At the critical point, we also find that a non-trivial $D$ scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.

cond-mat.stat-mech↗

arXiv2013

Vector-spin-chirality order in a dimerized frustrated spin-1/2 chain

A frustrated spin-$1/2$ XXZ chain model comprising a ferromagnetic nearest-neighbor coupling with the bond alternation, $J_1(1\pmδ)<0$, and an antiferromagnetic second-neighbor exchange coupling $J_2>0$ is studied at zero and weak magnetic fields by means of density matrix renormalization group calculations of order parameters, correlation functions and the entanglement entropy as well as an Abelian bosonization analysis. At zero magnetic field, the bond alternation $δ>0$ suppresses the gapless phase characterized by a vector-chiral (VC) long-range order (LRO) and a quasi-LRO of an incommensurate spin spiral, whereas this phase occupies a large region in the space of $J_1/J_2$ and the easy-plane exchange anisotropy for $δ=0$ [S. Furukawa \textit{et al.}, Phys. Rev. Lett. \textbf{105}, 257205 (2010)]. Then, four gapped phases are found to appear as the exchange anisotropy varies from the SU(2)-symmetric case to the U(1)-symmetric case; the Haldane dimer (D$_+$) phase with the same sign of the $x,y$- and $z$-component dimer order parameters, two VC dimer (VCD$_+$/VCD$_-$) phases with the sign of the $z$-component dimer order parameter being unaltered/reversed, and the even-parity dimer (D$_-$) phase. At small magnetic fields, a field-induced ring-exchange interaction, which is proportional to a staggered scalar chirality and a magnetic flux penetrating the associated triangle, drives a transition from the D$_-$ phase into a VC-Neel-dimer (VCND) phase, but not from the D$_+$ phase. This VCND phase is stable up to the large magnetic field at which the Zeeman term closes the spin gap. A possible relevance to Rb$_2$Cu$_2$Mo$_3$O$_{12}$ is discussed.

cond-mat.str-el↗

arXiv2013

QCD phase diagram at finite baryon and isospin chemical potentials in Polyakov loop extended quark meson model with vector interaction

We investigate the QCD phase diagram of isospin asymmetric matter using the Polyakov loop extended quark meson (PQM) model with vector interaction. The critical point temperature is found to decrease in isospin asymmetric matter and disappear at large isospin chemical potential. We also discuss the QCD phase transition in the neutron star core. From comparison of the QCD phase diagram in PQM and corresponding baryon and isospin chemical potentials of neutron star matter in relativistic mean field models, we show that the order of the chiral phase transition in the neutron star core could be crossover because of large isospin chemical potential.

nucl-th↗

arXiv2013

Lattice QCD study for stringy excitation and role of UV gluons

In both cases of quark-antiquark (Q-Qbar) and three-quark (3Q) systems, we study ground-state and low-lying excited-state potentials in terms of the gluon-momentum component in the Coulomb gauge in SU(3) quenched lattice QCD. By introducing UV-cut in the gluon-momentum space, we investigate the "UV-gluon sensitivity" of the ground-state and excited-state potentials quantitatively. Such a non-quark-origin excitation is a purely gluonic excitation, which can be interpreted as a stringy excitation in the color flux-tube picture of hadrons. For both Q-Qbar and 3Q systems, the IR part of the ground-state potential is almost unchanged, even after cutting off high-momentum gluon component. On the other hand, we find more significant change of excited-state potential by the cut of UV-gluons. However, even after the removal of UV-gluons, the magnitude of the low-lying gluonic excitation remains to be of the order of 1GeV.

hep-lat↗