VQE-generated quantum circuit dataset for machine learning

中山 昌勲*; 御手洗 光祐*; Placidi, L.*; 杉本 貴則*; 藤井 啓祐*

Physical Review Research (Internet), 7(3), p.033048_1 - 033048_9, 2025/07

https://doi.org/10.1103/c43x-9866

Quantum machine learning has the potential to computationally outperform classical machine learning, but it is not yet clear whether it will actually be valuable for practical problems. While some artificial scenarios have shown that certain quantum machine learning techniques may be advantageous compared to their classical counterpart, evidence does not yet suggest that quantum machine learning has surpassed conventional approaches in dealing with standard classical datasets, such as the MNIST dataset. In contrast, dealing with quantum data, such as quantum states or circuits, may be the task where we can benefit from quantum methods. Therefore, it is important to develop practically meaningful quantum datasets for which we expect quantum methods to be superior. In this paper, we propose a machine learning task that is likely to soon arise in the real world: clustering and classification of quantum circuits. We provide a dataset of quantum circuits optimized by the variational quantum eigensolver.

Diamond-shaped quantum circuit for real-time quantum dynamics in one dimension

宮腰 祥平*; 杉本 貴則*; 白川 知功*; 柚木 清司*; 上田 宏*

Physical Review Research (Internet), 6(4), p.043318_1 - 043318_14, 2024/12

https://doi.org/10.1103/PhysRevResearch.6.043318

In recent years, quantum computing has evolved as an exciting frontier, with the development of numerous algorithms dedicated to constructing quantum circuits that adeptly represent quantum many-body states. However, this domain remains in its early stages and requires further refinement to better understand the effective construction of highly entangled quantum states within quantum circuits. Here, we demonstrate that quantum many-body states can be universally represented using a quantum circuit comprising multiqubit gates. Furthermore, we evaluate the efficiency of a quantum circuit constructed with two-qubit gates in quench dynamics for the transverse-field Ising model.

Current numbers of qubits and their uses

市川 翼*; 箱嶋 秀昭*; 乾 幸地*; 伊藤 康介*; 松田 亮*; 御手洗 光祐*; 宮本 幸一*; 水上 渉*; 水田 郁*; 森 俊夫*; et al.

Nature Reviews Physics (Internet), 6(6), p.345 - 347, 2024/06

https://doi.org/10.1038/s42254-024-00725-0

Access to quantum computers has been democratized by the availability of cloud services from commercial providers, but the numbers of qubits users can exploit have remained modest, limited by noise and errors. What are these qubits used for and what can we expect next?

Confined states and topological phases in two-dimensional quasicrystalline -flux model

Ghadimi, R.*; Hori, Masahiro*; 杉本 貴則*; 遠山 貴己

Physical Review B, 108(12), p.125104_1 - 125104_18, 2023/09

https://doi.org/10.1103/PhysRevB.108.125104

Motivated by topological equivalence between an extended Haldane model and a chiral--flux model on a square lattice, we apply -flux models to two-dimensional bipartite quasicrystals with rhombus tiles in order to investigate topological properties in aperiodic systems. Topologically trivial -flux models in the Ammann-Beenker tiling lead to massively degenerate confined states whose energies and fractions differ from the zero-flux model. This is different from the -flux models in the Penrose tiling, where confined states only appear at the center of the bands as is the case of a zero-flux model. Additionally, Dirac cones appear in a certain -flux model of the Ammann-Beenker approximant, which remains even if the size of the approximant increases. Nontrivial topological states with nonzero Bott index are found when staggered tile-dependent hoppings are introduced in the -flux models. This finding suggests a direction in realizing nontrivial topological states without a uniform magnetic field in aperiodic systems.

Topological superconductivity in quasicrystals

Ghadimi, R.*; 杉本 貴則*; 田中 佳織*; 遠山 貴己

Physical Review B, 104(14), p.144511_1 - 144511_10, 2021/10

https://doi.org/10.1103/PhysRevB.104.144511

We propose realization of non-Abelian topological superconductivity in two-dimensional quasicrystals by the same mechanism as in crystalline counterparts. Specifically, we study a two-dimensional electron gas in Penrose and Ammann-Beenker quasicrystals with Rashba spin-orbit coupling, perpendicular Zeeman magnetic field, and conventional -wave superconductivity. We find that topological superconductivity with broken time-reversal symmetry is realized in both Penrose and Ammann-Beenker quasicrystals at low filling, where the Bott index is unity. The topological nature of this phase is confirmed by the existence of a zero-energy surface bound state and the chiral propagation of a wave packet projected onto the midgap bound state along the surfaces. Furthermore, we confirm the existence of a single Majorana zero mode each in a vortex at the center of the system and along the surfaces, signifying the non-Abelian character of the system when the Bott index is unity.

Mean-field study of the Bose-Hubbard model in the Penrose lattice

Ghadimi, R.*; 杉本 貴則*; 遠山 貴己

Physical Review B, 102(22), p.224201_1 - 224201_9, 2020/12

https://doi.org/10.1103/PhysRevB.102.224201

We examine the Bose-Hubbard model in the Penrose lattice based on inhomogeneous mean-field theory. Since the averaged coordination number in the Penrose lattice is four, the mean-field phase diagram consisting of the Mott insulator (MI) and superfluid (SF) phase is similar to that of the square lattice. However, the spatial distribution of the Bose condensate in the SF phase is significantly different from uniform distribution in the square lattice. We find a fractal structure in its distribution near the MI-SF phase boundary. The emergence of the fractal structure is a consequence of the cooperative effect between quasiperiodicity in the Penrose lattice and criticality at the phase transition.

Quasi-spin correlations in a frustrated quantum spin ladder

杉本 貴則*; 森 道康; 遠山 貴巳*; 前川 禎通

Physics Procedia, 75, p.861 - 867, 2015/12

https://doi.org/10.1016/j.phpro.2015.12.111

The quasi-spin correlations in a frustrated quantum spin ladder with one-half magnetization are theoretically studied by using the density-matrix renormalization-group method and the quasi- spin transformation. In this model, the frustration induces a gapless-to-gapful phase transition with a strong rung coupling. The gapful state is observed as the one-half magnetization plateau in the magnetization curve. In the magnetization-plateau state, we find that the quasi-spin dimer has a large expectation value with long-ranged correlations. This result does not only comes in useful to clarify the magnetization-plateau state, but gives a crucial information to understand the magnetization curve of the real compound BiCuPO, whose effective spin model corresponds to ours.

Magnetization plateaus by reconstructed quasispinons in a frustrated two-leg spin ladder under a magnetic field

杉本 貴則*; 森 道康; 遠山 貴巳*; 前川 禎通

Physical Review B, 92(12), p.125114_1 - 125114_6, 2015/09

AA2015-0451.pdf:0.43MB

https://doi.org/10.1103/PhysRevB.92.125114

The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCuPO.

Spin-spin correlation enhanced by impurities in a frustrated two-leg spin ladder

杉本 貴則*; 森 道康; 遠山 貴己*; 前川 禎通

JPS Conference Proceedings (Internet), 3, p.014016_1 - 014016_5, 2014/06

https://doi.org/10.7566/JPSCP.3.014016

We theoretically study a spin-spin correlation enhanced by non-magnetic impurities in a frustrated two-leg spin ladder. The frustration is introduced by the next-nearest-neighbor antiferromagnetic interaction in the leg direction in the antiferromagnetic two-leg spin ladder. The spin-spin correlation function around impurity site is calculated by the density-matrix renormalization-group method. We find that the spin-spin correlation is enhanced around impurity site with the wavenumber reflecting the frustration. As increasing the frustration, the wavenumber is shifted from commensurate to incommensurate. We discuss several experimental results on BiCuPO in the light of our theory.

Successive magnetic-phase transitions in a frustrated two-leg spin ladder

杉本 貴則; 森 道康; 遠山 貴己; 前川 禎通

no journal, , 

Recently, successive phase transitions induced by magnetic field have been observed in a frustrated two-leg spin ladder BiCuPO, in which the frustration is introduced by the next-nearest-neighbor antiferromagnetic exchange interaction in the leg direction. First, we calculate the magnetic-field dependence of magnetization by using density-matrix renormalization-group method. In this calculation, we find a phase transition induced by strong frustration, which does not appear in a non-frustrated two-leg spin ladder. The phase transition emerges as a jump of susceptibility with unsaturated finite magnetization. We also investigate the origin of the phase transition by using the bond-operator mean-field approximation. We conclude that the phase transition is the same type as the Lifshitz transition. Our study is useful to analyze experimental data of BiCuPO.