This is the third quantum computing gathering hold by quantum computing study group.

This is a lecture series by Prof. Mark Alford (Washington University in St. Louis) on the structure of neutron stars.

Oct. 7 (Tues), 15:30-17:00
Lecture I : Quark matter: the high-density frontier
The densest predicted state of matter is color-superconducting quark matter, which has some affinities to electrical superconductors, but a much richer phase structure because quarks come in many varieties. This form of matter may well exist in the core of compact stars, and the search for signatures of its presence is currently proceeding. I will review the nature of color-superconducting quark matter, and discuss some ideas for finding it in nature.

Oct. 14 (Tues), 15:30-17:00
Lecture II: Solid quark matter
I will review three ways in which quark matter can occur in a solid phase, where translational invariance is broken by some sort of crystalline structure. These include a color superconductor of the Fulde-Ferrell-Larkin-Ovchinnikov type, mixed phases that can arise at a nuclear/quark matter interface, and the strangelet crystal crust of a strange star.

Oct. 21 (Tues), 15:30-17:00
Lecture III: Dissipation in neutron star mergers
In a neutron star merger, nuclear matter experiences dramatic changes in temperature and density that happen in milliseconds. Mergers therefore probe dynamical properties that may help us uncover the phase structure of ultra-dense matter. I will describe some of the relevant material properties, focusing on flavor equilibration and its consequences such as bulk viscosity and damping of oscillations.

Oct. 28 (Tues), 15:30-17:00
Lecture IV: Neutrinos in dense matter: beyond modified Urca
Neutrino absorption and emission (the "Urca process") is an essential aspect of the formation and cooling of neutron stars and of the dynamics of neutron star mergers. In this talk I will describe the traditional way of calculating Urca rates, explain its shortfalls, and propose an alternative approach, the nucleon width approximation.

In this talk I will cover our recent preprint arXiv:2509.12323 where we propose a neural network approach to finding the ground state wavefunction of SU(2) lattice gauge theory. Specifically, we demonstrate that the use of bespoke SU(2)-gauge-equivariant neural network layers increases the extent to which our variational ansatz can represent the ground state of this system. During this talk I will contrast the Hamiltonian and Euclidean formalisms of lattice gauge theories, highlighting the promises that the former offers but also the difficulties: noting briefly the issues of parameterising the continuous Hilbert space that plague tensor network and quantum simulation approaches and how our approach alleviates this. I will try and present our method pedagogically as we are very interested in learning its uses but also the limits of its validity, before closing with some remarks on scaling to larger systems and different gauge groups.

This workshop will serve as the first meeting of the collaboration between the Leinweber Institute for Theoretical Physics (LITP) at the University of California Berkeley and the RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS). Participation is open and researchers from other institutions are welcome to attend. The workshop will feature talks on recent developments in the field of Quantum Gravity and other relevant topics.

The joint general meeting is scheduled to be held at Okochi Hall from 13:20 to 17:45.
The networking reception is scheduled to be held at the RIKEN Cafeteria from 18:00 to 19:40.

A theorem prover is a tool for the formalization of mathematics, that is, for rigorously expressing and verifying theorems and proofs on a computer. In recent years, the Lean theorem prover has seen progress in the formalization of a wide range of areas of mathematics. In this talk, I will explain formalization of mathematics in Lean from the basics and survey the formalized results achieved to date.

I will introduce the recent development of a method to calculate the (anti)symmetrized wave functions and energies of the ground and low-lying excited states using the unsupervised machine learning technique. I will also introduce the recent attempts to consider the spin-isospin degrees of freedom and extend them to the Dirac equation.

This seminar is co-hosted by GWX-EOS Working Group and iTHEMS-ABBL Joint Astro Study Group.

Abstract:
In the first part of my talk, I will review recent work on Bose-Fermi mixtures with an attractive interaction inducing pairing between bosons and fermions. After discussing a recent experiment on this system [1], which has confirmed predictions obtained by us some time ago within a many-body diagrammatic approach [2], I will present novel results for the compressibility [3] that suggest a metastable nature for the many-body phase observed in [1]. Then, I will discuss the extension of our calculations to two-dimensional Bose-Fermi mixtures [4,5]. The results obtained in 2D challenge previous beliefs formulated for 3D systems.
In the second part, I will discuss attractive polarized Fermi systems, for which the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase was proposed many years ago as a possible superfluid phase. I will discuss how significant precursor FFLO fluctuation effects appear already in the normal phase of polarized Fermi gases at finite temperature [6], and how they could be experimentally detected with ultracold gases. At zero temperature [7], I will discuss how the quasi-particle parameters of the normal Fermi gas change when approaching an FFLO quantum critical point, with a complete breakdown of the quasi-particle picture analogous to what found in heavy-fermion materials at an antiferromagnetic quantum critical point.
Finally, I will discuss a recent joint experimental-theoretical work on the motion of a vortex orbiting a pinned anti-vortex in a strongly interacting Fermi gas [8], highlighting the interplay between Andreev bound states in the vortex core and delocalized thermal excitations in shaping the vortex dynamics.

Recently some researchers gave many studies toward algebro-geometric foundation for tropical geometry. I focused on rational function semifields of tropical curves and characterized them. With this characterization, in this talk, I suggest a definition of ``rational function semifield of dimension one". This definition can write out weight in the term of $\boldsymbol{T}$-algebra homomorphism, and can write balancing condition together with harmonic functions, where both weight and balancing condition are fundamental concepts for tropical varieties and $\boldsymbol{T}$ is the tropical semifield $(\boldsymbol{R} \cup \{-\infty\}, \operatorname{max}, +)$.

Large language models such as ChatGPT are based on deep learning architectures known as Transformers. Owing to their remarkable performance and broad applicability, Transformers have become indispensable in modern AI development. However, it still remains an open question why Transformers perform so well and what the essential meaning of their unique structure is. One possible clue lies in the mathematical correspondence between Hopfield Networks and Transformers.

In this talk, I will first introduce the major developments over the past decade that have significantly increased the storage capacity of Hopfield Networks. I will then review the theoretical correspondence between Hopfield Networks and Transformers. Building on this background, I will present our recent findings: by extending this correspondence to include the hidden-state dynamics of Hopfield Networks, we discovered a new class of Transformers that can recursively propagate attention-score information across layers. Furthermore, we found, both theoretically and experimentally, that this new Transformer architecture resolves the “rank collapse” problem often observed in conventional multi-layer attention. As a result, when applied to language generation and image recognition tasks, it achieves performance surpassing that of existing Transformer-based models.

Topological insulators are materials which do not conduct current inside but do conduct at the surface or the edge. The name "topological" comes from the fact that the "shape" of the wavefunction of electrons in topological insulators show non-trivial twist, which can be mathematically characterized by the language of topology. Alongside the development of the study of topological insulators in solids, analogous phenomena were found to exist also in other systems such as photonics, mechanics, geophysics, and active matter. In this seminar, I discuss how the underlying concept of "topology of states" can have a broad impact applicable to various areas in physics, with some emphasis on my own contribution to the field. I aim to structure the first half of my seminar to be accessible to those outside physics, and latter half to be more specialized, covering cutting-edge results.

The ninth installment of the Intensive Lecture Series, organized by the Quantum Gravity Gatherings (QGG) study group at RIKEN iTHEMS, will feature Prof. Norio Kawakami from the Fundamental Quantum Science Program (FQSP) under RIKEN's Transformative Research Innovative Platform (TRIP). Over the course of two days, Prof. Kawakami will deliver a lecture series on quantum many-body systems.

In recent years, insights from quantum many-body physics have become central to research in quantum gravity, where correlation effects induced by gravity play nontrivial roles. By bridging perspectives from gravitational physics and quantum many-body dynamics, one hopes to understand how macroscopic spacetime and its geometric properties emerge from the collective behavior of quantum constituents at microscopic scales.

In this lecture series, Prof. Kawakami will introduce the fundamental properties of correlation effects through representative examples in condensed matter physics. A distinctive aspect of this event is its joint organization with the Fundamental Quantum Science Program (FQSP) at RIKEN. The goal is to further strengthen connections between the quantum gravity, condensed matter, and quantum information communities.

The lectures will be delivered in a blackboard-style format (in English), designed to foster interaction, active participation, and in-depth Q&A discussions. In addition, short talk sessions will be held, giving participants the opportunity to present briefly on topics of their choice. Through this informal and dynamic setting, we hope to spark active interactions among participants and create an environment where ideas can be shared openly and enthusiastically.

Abstract:
Some examples of theoretical methods to treat strongly correlated systems in condensed matter physics are explained. We start with the Kondo effect, which is one of the most fundamental quantum many-body problems and has been intensively studied to date in a wide variety of topics such as dilute magnetic alloys, heavy fermion systems, quantum dot systems, etc. Dynamical mean-field theory (DMFT) is then introduced, which enables us to systematically treat strongly correlated materials such as a Mott insulator. It is shown that the essence of DMFT is closely related to the Kondo effect. Furthermore, we explain how to apply conformal field theory (CFT) to treat correlation effects in one-dimensional electron systems.

Accurate prediction of quantum Hamiltonian dynamics and identification of Hamiltonian parameters are crucial for advancements in quantum simulations, error correction, and control protocols. This talk introduces a machine learning model with dual capabilities: it can deduce time-dependent Hamiltonian parameters from observed changes in local observables within quantum many-body systems, and it can predict the evolution of these observables based on Hamiltonian parameters. The model’s validity was confirmed through theoretical simulations across various scenarios and further validated by two experiments. Initially, the model was applied to a Nuclear Magnetic Resonance quantum computer, where it accurately predicted the dynamics of local observables. The model was then tested on a superconducting quantum computer with initially unknown Hamiltonian parameters, successfully inferring them. We believe that machine learning techniques hold great promise for enhancing a wide range of quantum computing tasks, including parameter estimation, noise characterization, feedback control, and quantum control optimization.