arXiv subjects

Tsuyoshi Okubo

Publications and source records attributed to Tsuyoshi Okubo.

At least 19 recordsLinked to original sources

arXiv2026

Matrix Product Evolution: A Method for Simulating Quantum Circuits Using Tensor Networks

Classical simulation of quantum circuits is an essential tool in quantum information science, but its applicability is constrained by the exponential growth of the Hilbert space and the entanglement structure of quantum states. In this work, we introduce Matrix Product Evolution (MPE), a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index. Within this formulation, the simulation of a quantum circuit is modeled as the contraction of multiple MPE tensors. We develop an efficient contraction strategy based on a zip-up procedure to carry out this contraction in practice. We investigate the numerical behavior of this MPE-based contraction framework through simulations of random quantum circuits and the time evolution of a quantum many-body state. Our results characterize the growth of temporal bond dimensions, clarify how post-selection modifies the contraction cost and approximation accuracy, and identify regimes in which depth-oriented tensor-network contractions provide a useful complement to standard MPS-based simulation approaches.

quant-ph↗

arXiv2026

Clifford Circuits Augmented Grassmann Matrix Product States

Recent progress in combining Clifford circuits with tensor-network (TN) methods has shown that local Clifford disentanglers can reduce bipartite entanglement across TN bonds prior to tensor compression, thereby improving the efficiency of TN simulations. In this work, we embed local Clifford disentanglers in the Grassmann-tensor language to define a Clifford-augmented Grassmann matrix product state (CAGMPS) ansatz, and develop a density-matrix renormalization group (DMRG) framework based on this ansatz while preserving locality and fermion-parity structure. We benchmark the resulting CAGMPS--DMRG method on representative fermionic lattice systems, including the tight-binding, $t$-$V$, and $t$-$V$-$V'$ models. In all cases, Clifford augmentation systematically suppresses bipartite entanglement and improves the accuracy of the ground-state energy at a fixed bond dimension. We further show that the Grassmann-evenness condition, together with equivalence under entangling action, restricts the relevant two-site Clifford candidates to 12 inequivalent representatives, enabling a more economical disentangling search than approaches based on the standard two-qubit Clifford gate set. Our results suggest that the CAGMPS--DMRG method provides a scalable and efficient variational tool for strongly correlated fermionic systems.

quant-ph↗

arXiv2026

Simplification of tensor updates toward performance-complexity balanced quantum computer simulation

Matrix Product States (MPS) provide a powerful framework for simulating quantum circuits. In practical simulations, tensor updates are typically performed in the canonical form (CF), which corresponds to the Schmidt decomposition and improves approximation accuracy. However, maintaining the canonical form introduces significant computational overhead. An alternative approach, known as the Simple Update (SU), does not enforce the Schmidt decomposition and is expected to reduce computational complexity. In this work, we systematically compare the performance and computational cost of SU and CF in quantum circuit simulations. We benchmark both methods on highly entangled circuits and on a QASM benchmark suite covering a wide range of circuit types. Our results show that SU achieves accuracy comparable to CF while reducing computational complexity, indicating that SU provides an efficient alternative for practical quantum circuit simulations.

quant-ph↗

arXiv2026

Efficient tomography of microwave photonic cluster states

Entanglement among a large number of qubits is a crucial resource for many quantum algorithms. Such many-body states have been efficiently generated by entangling a chain of itinerant photonic qubits in the optical or microwave domain. However, it has remained challenging to fully characterize the generated many-body states by experimentally reconstructing their exponentially large density matrices. Here, we develop an efficient tomography method based on the matrix-product-operator formalism and demonstrate it on a cluster state of up to 35 microwave photonic qubits by reconstructing its $2^{35} \times 2^{35}$ density matrix. The full characterization enables us to detect the performance degradation of our photon source which occurs only when generating a large cluster state. This tomography method is generally applicable to various physical realizations of entangled qubits and provides an efficient benchmarking method for guiding the development of high-fidelity sources of entangled photons.

quant-ph↗

arXiv2025

Thermal Hall transport in Kitaev spin liquids

We investigate the thermal Hall conductivity in the Kitaev model with additional interactions under a magnetic field, employing a finite-temperature tensor network method benchmarked by a thermal pure quantum state technique. We find that the thermal Hall conductivity divided by temperature, $κ_{xy}/T$, significantly overshoots the value of the half-integer quantization and exhibits a pronounced hump while decreasing temperature. Moreover, we show that the field-direction dependence of $κ_{xy}/T$ is consistent with the sign of the Chern number associated with the Majorana fermions across a wide range of magnetic fields. We also demonstrate that the additional off-diagonal interactions, known as the $Γ$ and $Γ^{\prime}$ terms, considerably affect $κ_{xy}/T$. In particular, we show that positive $Γ$ and negative $Γ^{\prime}$ lead to a remarkable enhancement in the intermediate temperature region. From the comparison with the classical counterpart, we reveal that the effects of the $Γ$ term go beyond the classical picture, indicating significant quantum fluctuation effects, while those of the $Γ^\prime$ term are well captured at the classical level. These comprehensive analyses indicate that the enhanced thermal Hall response is consistently explained by dominant contributions from topological Majorana fermions, even within the polarized regime beyond the critical field. Our approach not only establishes a robust theoretical framework for understanding the thermal Hall transport in Kitaev materials such as $α$-RuCl$_{3}$, but also offers a promising pathway to bridge the gap between theories and experiments across a wide range of strongly correlated materials.

cond-mat.str-el↗

arXiv2025

Tensor train representations of Greeks for Fourier-based pricing of multi-asset options

Efficient computation of Greeks for multi-asset options remains a key challenge in quantitative finance. While Monte Carlo (MC) simulation is widely used, it suffers from the large sample complexity for high accuracy. We propose a framework to compute Greeks in a single evaluation of a tensor train (TT), which is obtained by compressing the Fourier transform (FT)-based pricing function via TT learning using tensor cross interpolation. Based on this TT representation, we introduce two approaches to compute Greeks: a numerical differentiation (ND) approach that applies a numerical differential operator to one tensor core and an analytical (AN) approach that constructs the TT of closed-form differentiation expressions of FT-based pricing. Numerical experiments on a five-asset min-call option in the Black-Sholes model show significant speed-ups of up to about $10^{5} \times$ over MC while maintaining comparable accuracy. The ND approach matches or exceeds the accuracy of the AN approach and requires lower computational complexity for constructing the TT representation, making it the preferred choice.

q-fin.CP↗

arXiv2025

Plastic tensor networks for interpretable generative modeling

A structural optimization scheme for a single-layer nonnegative adaptive tensor tree (NATT) that models a target probability distribution is proposed as an alternative paradigm for generative modeling. The NATT scheme, by construction, automatically searches for a tree structure that best fits a given discrete dataset whose features serve as inputs, and has the advantage that it is interpretable as a probabilistic graphical model. We consider the NATT scheme and a recently proposed Born machine adaptive tensor tree (BMATT) optimization scheme and demonstrate their effectiveness on a variety of generative modeling tasks where the objective is to infer the hidden structure of a provided dataset. Our results show that in terms of minimizing the negative log-likelihood, the single-layer scheme has model performance comparable to the Born machine scheme, though not better. The tasks include deducing the structure of binary bitwise operations, learning the internal structure of random Bayesian networks given only visible sites, and a real-world example related to hierarchical clustering where a cladogram is constructed from mitochondrial DNA sequences. In doing so, we also show the importance of the choice of network topology and the versatility of a least-mutual information criterion in selecting a candidate structure for a tensor tree, as well as discuss aspects of these tensor tree generative models including their information content and interpretability.

cs.LG↗

arXiv2025

Universal Scaling Laws of Absorbing Phase Transitions in Artificial Deep Neural Networks

We demonstrate that conventional artificial deep neural networks operating near the phase boundary of the signal propagation dynamics, also known as the edge of chaos, exhibit universal scaling laws of absorbing phase transitions in non-equilibrium statistical mechanics. We exploit the fully deterministic nature of the propagation dynamics to elucidate an analogy between a signal collapse in the neural networks and an absorbing state (a state that the system can enter but cannot escape from). Our numerical results indicate that the multilayer perceptrons and the convolutional neural networks belong to the mean-field and the directed percolation universality classes, respectively. Also, the finite-size scaling is successfully applied, suggesting a potential connection to the depth-width trade-off in deep learning. Furthermore, our analysis of the training dynamics under the gradient descent reveals that hyperparameter tuning to the phase boundary is necessary but insufficient for achieving optimal generalization in deep networks. Remarkably, nonuniversal metric factors associated with the scaling laws are shown to play a significant role in concretizing the above observations. These findings highlight the usefulness of the notion of criticality for analyzing the behavior of artificial deep neural networks and offer new insights toward a unified understanding of the essential relationship between criticality and intelligence.

stat.ML↗

arXiv2025

Tensor tree learns hidden relational structures in data to construct generative models

Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST handwritten digits, (iii) Bayesian networks, and (iv) the pattern of stock price fluctuation pattern in S&P500. In (i) and (ii), the strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and in (iv), a structure corresponding to the eleven sectors emerged.

cs.LG↗

arXiv2025

Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids

Quantum entanglement in strongly correlated electron systems often leads to exotic elementary excitations. Quantum spin liquids (QSLs) provide a paradigmatic example, where the elementary excitations are described by fractional quasiparticles such as spinons. However, such fractional quasiparticles behave differently from electrons, making their experimental identification challenging. Here, we theoretically investigate the spin Seebeck effect, which is a thermoelectric response via a spin current, as an efficient probe of the fractional quasiparticles in QSLs, focusing on the Kitaev honeycomb model. By comprehensive studies using the real-time dynamics, the perturbation theory, and the linear spin-wave theory based on the tunnel spin-current theory, we find that the spin current is induced by thermal gradient in the Kitaev spin liquid, via the low-energy fractional Majorana excitations. This underscores the ability of Majorana fermions to carry spin current, despite lacking spin angular momentum. Furthermore, we find that the induced spin current changes its sign depending on the sign of the Kitaev interaction, indicating that the Majorana fermions contribute to the spin current with (up-)down-spin like nature when the exchange coupling is (anti)ferromagnetic. Thus, in contrast to the negative spin current already found in a one-dimensional QSL, our finding reveals that the spin Seebeck effect can exhibit either positive or negative signals, contingent upon the nature of fractional excitations in the QSLs. We also clarify contrasting field-angle dependence between the Kitaev spin liquid in the low-field limit and the high-field ferromagnetic state, which is useful for the experimental identification. Our finding suggests that the spin Seebeck effect could be used not only to detect fractional quasiparticles emerging in QSLs but also to generate and control them.

cond-mat.str-el↗

arXiv2025

Embedding of Tree Tensor Networks into Shallow Quantum Circuits

Variational Quantum Algorithms (VQAs) are being highlighted as key quantum algorithms for demonstrating quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices, which are limited to executing shallow quantum circuits because of noise. However, the barren plateau problem, where the gradient of the loss function becomes exponentially small with system size, hinders this goal. Recent studies suggest that embedding tensor networks into quantum circuits and initializing the parameters can avoid the barren plateau. Yet, embedding tensor networks into quantum circuits is generally difficult, and methods have been limited to the simplest structure, Matrix Product States (MPSs). This study proposes a method to embed Tree Tensor Networks (TTNs), characterized by their hierarchical structure, into shallow quantum circuits. TTNs are suitable for representing two-dimensional systems and systems with long-range correlations, which MPSs are inadequate for representing. Our numerical results show that embedding TTNs provides better initial quantum circuits than MPS. Additionally, our method has a practical computational complexity, making it applicable to a wide range of TTNs. This study is expected to extend the application of VQAs to two-dimensional systems and those with long-range correlations, which have been challenging to utilize.

quant-ph↗

arXiv2025

TeNeS-v2: Enhancement for Real-Time and Finite Temperature Simulations of Quantum Many-Body Systems

Quantum many-body systems are challenging targets for computational physics due to their large degrees of freedom. The tensor networks, particularly Tensor Product States (TPS) and Projected Entangled Pair States (PEPS), effectively represent these systems on two-dimensional lattices. However, the technical complexity of TPS/PEPS-based coding is often too much for researchers to handle. To reduce this problem, we developed TeNeS (Tensor Network Solver). This paper introduces TeNeS-v2, which extends TeNeS with real-time and finite temperature simulations, providing deeper insights into quantum many-body systems. We detail the new algorithms, input/output design, and application examples, demonstrating TeNeS-v2's applicability to various quantum spin and Bose models on two-dimensional lattices.

cond-mat.str-el↗

arXiv2024

Nuclear norm regularized loop optimization for tensor network

We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)] for the critical 2D Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion.

cond-mat.stat-mech↗

arXiv2024

Quantum spin state stabilized by coupling with classical spins

We introduce a model compound featuring a spin-1/2 frustrated square lattice partially coupled by spin-5/2. A significant magnetization plateau exceeding 60 T could be observed, indicating a quantum state formed by $S$ = 1/2 spins in the square lattice. The remaining $S$ = 5/2 spins exhibited paramagnetic behavior in the low-field regions. The numerical analysis confirmed that the observed quantum state is a many-body entangled state based on the dominant AF interactions and is strongly stabilized by coupling with spin-5/2. The stabilization of this quantum state can be attributed to a compensation effect similar to magnetic field-induced superconductivity, which serves as a strategy to control the stability of quantum spin states in magnetic fields.

cond-mat.str-el↗

arXiv2024

Quantum phase transition between spin liquid and spin nematics in spin-1 Kitaev honeycomb model

Besides the exactly solvable spin-1/2 Kitaev model, higher spin-$S$ ones, not exactly solvable, are promising playgrounds for researches on the quantum spin liquid as well. One of the main interests in higher spin-S cases is the interplay between the Kitaev spin liquid (KSL) and spin nematics. We probe this interplay in a spin-1 model on the honeycomb lattice with competing bilinear-biquadratic and Kitaev interactions. Utilizing the 2D infinite projected entangled-pair state (iPEPS), we map out the phase diagram for the ferro-biquadratic interaction. In the phase diagram, we discover the direct KSL--spin-nematics transitions in the vicinity of pure Kitaev limits. It has been revealed that the ferro KSL exhibits robustness against perturbations from ferro-quadrupolar interactions. Also, the spin-nematic phase is extended to the parameter region near the antiferro-Kitaev limit.

cond-mat.stat-mech↗

arXiv2024

Hunting for quantum-classical crossover in condensed matter problems

The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: {\it When and how will quantum computers outperform classical computers?} The next milestone is undoubtedly the realization of quantum acceleration in practical problems. Here we provide a clear evidence and arguments that the primary target is likely to be condensed matter physics. Our primary contributions are summarized as follows: 1) Proposal of systematic error/runtime analysis on state-of-the-art classical algorithm based on tensor networks; 2) Dedicated and high-resolution analysis on quantum resource performed at the level of executable logical instructions; 3) Clarification of quantum-classical crosspoint for ground-state simulation to be within runtime of hours using only a few hundreds of thousand physical qubits for 2d Heisenberg and 2d Fermi-Hubbard models, assuming that logical qubits are encoded via the surface code with the physical error rate of $p=10^{-3}$. To our knowledge, we argue that condensed matter problems offer the earliest platform for demonstration of practical quantum advantage that is order-of-magnitude more feasible than ever known candidates, in terms of both qubit counts and total runtime.

quant-ph↗

arXiv2023

Possibility of a Topological Phase Transition in Two-dimensional $RP^3$ Model

We study by large-scale Monte Carlo simulation the $RP^3$ model, which can be regarded as an effective low-energy model of a triangular lattice Heisenberg antiferromagnet. $Z_2$ vortices appear as elementary excitations in the triangular lattice Heisenberg antiferromagnet. Such $Z_2$ vortices are ubiquitous in other frustrated Heisenberg spin systems that have noncollinear long-range orders. In this study, we investigate a possible topological phase transition driven by the binding--unbinding of $Z_2$ vortices. By extracting important degrees of freedom, we map a frustrated spin system to an effective $RP^3$ model. From large-scale Monte Carlo simulation, we obtain an order parameter and a correlation length of up to $L=16384$. Concerning the existence of a $Z_2$-vortex transition, by extrapolating the order parameter to the thermodynamics limit assuming the $Z_2$-vortex transition, we obtain a finite transition temperature as $T_v/\tilde{J} \simeq 0.25$. Our estimate of the correlation length at $T_v$ is much larger than $L=16384$, which is beyond the previous estimate obtained with the triangular lattice Heisenberg model.

cond-mat.stat-mech↗

arXiv2022

TeNeS: Tensor Network Solver for Quantum Lattice Systems

TeNeS (Tensor Network Solver) is a free/libre open-source software program package for calculating two-dimensional many-body quantum states based on the tensor network method and the corner transfer matrix renormalization group (CTMRG) method. This package calculates ground-state wavefunctions for user-defined Hamiltonians and evaluates user-defined physical quantities such as magnetization and correlation functions. For certain predefined models and lattices, there is a tool that makes it easy to generate input files. TeNeS uses an OpenMP/MPI hybrid parallelized tensor operation library and thus can perform large-scale calculations using massively parallel machines.

cond-mat.str-el↗