Research memories

Figures, small discoveries, and things I remember.

A strongly correlated material is mapped to impurity sites coupled to bath sites. A solver computes the local Green’s function, which is used to update the bath in a self-consistency loop. — A quantum impurity model and the DMFT self-consistency loop. Click the figure to enlarge it.

2022

My first paper!

This picture connects a strongly correlated material to a small quantum impurity model and its surrounding bath. In this work, we explored a hybrid quantum–classical approach to computing the impurity model’s imaginary-time Green’s function.

R. Sakurai, W. Mizukami, and H. Shinaoka,
Hybrid quantum-classical algorithm for computing imaginary-time correlation functions.
Phys. Rev. Research 4, 023219 (2022). Figure: CC BY 4.0.

Four plots compare tensor-train methods in red and blue with Monte Carlo in green: option price and Vega versus volatility, and Delta and Gamma versus the initial asset price. The curves closely overlap, with visible Monte Carlo fluctuations in Gamma. — Price, Vega, Delta, and Gamma for a five-asset min-call option with random correlations. Red and blue: tensor trains; green: Monte Carlo. Click the figure to enlarge it.

2025

Prices and Greeks with tensor trains

Here we used tensor trains to compress Fourier-based option pricing and compute its sensitivities, the Greeks. The figure compares two tensor-train approaches with Monte Carlo: the curves track one another closely in these slices.

R. Sakurai, K. Miyamoto, and T. Okubo,
Tensor train representations of Greeks for Fourier-based option pricing of multi-asset options.
arXiv:2507.08482v1 (2025). Figure: CC BY 4.0.

CC BY-SA 4.0 Rihito Sakurai. Last modified: October 03, 2026. Website built with Franklin.jl and the Julia programming language.