arXiv subjects

Gota Tanaka

Publications and source records attributed to Gota Tanaka.

10 recordsLinked to original sources

arXiv2026

Mutation and crossover of simplicial complexes

Color graphs and their subgraphs, referred to as bubble graphs, correspond bijectively to the simplicial complexes of pseudomanifolds and their subsimplices, respectively. In this paper, we introduce matrix representations for colored graphs and their associated bubble graphs. By using this correspondence, we define simplicial-complex matrices and subsimplex matrices that encode the simplicial complexes of pseudomanifolds and their subsimplices. Moreover, we formulate mutation and crossover operations on colored graphs. Through the established correspondence among simplicial complexes, colored graphs, and simplicial-complex matrices, we extend these operations to simplicial complexes and simplicial-complex matrices. We further implement an algorithm generating simplicial-complex matrices and a genetic algorithm performing mutation and crossover of them to produce pseudomanifolds exhibiting diverse topologies. In addition, we implement procedures for decomposing the generated simplicial-complex matrices into simplex matrices, reconstructing the simplicial complexes of the associated pseudomanifolds from this information, and computing geometric quantities such as the volume, circumcenter, and dual-simplex volume of each simplex.

hep-th↗

arXiv2025

Quantum Reversibility Meets Classical Reverse Diffusion

Bayes' rule connects forward and reverse processes in classical probability theory, and its quantum analogue has been discussed in terms of the Petz (transpose) map. For quantum dynamics governed by the Lindblad equation, the corresponding Petz map can also be written in Lindblad form. In classical stochastic systems, the analogue of the Lindblad equation is the Fokker-Planck equation, and applying Bayes' rule to it yields the reverse diffusion equation underlying modern diffusion-based generative models. It is known that a semiclassical approximation of the Lindblad equation yields the Fokker-Planck equation for the Wigner function, which is a quasiprobability distribution defined on phase space as the Wigner transform of the density operator. Here we demonstrate that applying the same approximation to the Lindblad equation associated with the Petz map produces an equation that coincides with that obtained from the Fokker-Planck equation via Bayes' rule. This finding establishes a direct correspondence between the Petz map and Bayes' rule, unifying quantum reversibility with classical reverse diffusion.

quant-ph↗

arXiv2025

Tensor renormalization group approach to entanglement entropy

We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a $d$-dimensional quantum system is represented as a $(d+1)$-dimensional tensor network. We develop an explicit algorithm for $d=1$ that enables the calculation of EE for single-interval subsystems of arbitrary size. We test our method in two-dimensional tensor network of the Ising model. The central charge is obtained as $c=0.49997(8)$ for $D=96$, which agrees with the theoretical prediction within an error, demonstrating the accuracy and reliability of our proposed method.

hep-lat↗

arXiv2025

Entanglement entropy by tensor renormalization group approach

We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a $1 + 1$-dimensional tensor network, which is analogous to the tensor network representation of the partition function. The HOTRG method is used to approximate the reduced density matrix for arbitrary subsystem sizes, from which we obtain the entanglement entropy. We test our method in the quantum Ising model and obtain the entanglement entropy of the ground state by taking the size of time direction to infinity. The central charge $c$ is obtained as $c = 0.49997(8)$ for a bond dimension $D=96$, which agrees with the theoretical value $c=1/2$ within the error.

hep-lat↗

arXiv2024

Quantum error correction realized by the renormalization group in scalar field theories

We demonstrate that quantum error correction is realized by the renormalization group in scalar field theories. We construct $q$-level states by using coherent states in the IR region. By acting on them the inverse of the unitary operator $U$ that describes the renormalization group flow of the ground state, we encode them into states in the UV region. We find the situations in which the Knill-Laflamme condition is satisfied for operators that create coherent states. We verify this to the first order in the perturbation theory. This result suggests a general relationship between the renormalization group and quantum error correction and should give insights into understanding the role played by them in the gauge/gravity correspondence.

hep-th↗

arXiv2024

Gauge invariant discretization of Chern-Simons couplings

We discretize Chern-Simons couplings in gauge invariant way. We obtain (p+q)-forms representing Chern-Simons couplings on (p + q)-simplexes from wedge products of p- and q-forms on p- and q-simplexes, respectively, where p- and q-simplexes form (p+q)-simplexes by having a common vertex. We show that the Chern-Simons couplings on simplicial complexes reduce to Chern-Simons couplings on the manifolds in a continuum limit. Moreover, we prove that a typical discretized Chern-Simons term that has the Chern-Simons coupling is gauge invariant.

hep-lat↗

arXiv2023

The perturbative vacua in string geometry theory

String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, in the bosonic closed sector of string geometry theory, we completely identify the perturbative vacua, which include general string backgrounds in bosonic closed string theory. From fluctuations around these configurations, we derive the path-integrals of perturbative strings on the string backgrounds up to any order.

hep-th↗

arXiv2023

Exact renormalization group for wave functionals

Motivated by the construction of the cMERA for interacting field theories, we derive a non-perturbative functional differential equation for wave functionals in scalar field theories from the exact renormalization group equation. We check the validity of the equation using the perturbation theory. We calculate the wave functional up to the first-order perturbation and verify that it satisfies the equation.

hep-th↗

arXiv2022

Higher derivative extension of the functional renormalization group

We study higher derivative extension of the functional renormalization group (FRG). We consider FRG equations for a scalar field that consist of terms with higher functional derivatives of the effective action and arbitrary cutoff functions. We show that the epsilon expansion around the Wilson-Fisher fixed point is indeed reproduced by the local potential approximation of the FRG equations.

hep-th↗

arXiv2021

Renormalization group and diffusion equation

We study the relationship between the renormalization group and the diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed action. As a generalization of the result obtained by Sonoda and Suzuki, we find that the correlation functions of diffused fields with respect to the bare action agree with those of bare fields with respect to the effective action, where the diffused field obeys a generalized diffusion equation determined by the cutoff function and the seed action and agrees with the bare field at the initial time.

hep-th↗