Beyond AI Project
Analysis of materials’ quantum properties using AI(Quantum ID: Exploiting “Quantum Fingerprintings” of materials with AI)
Project Leader
Eiji Saitoh (Professor, School of Engineering, The University of Tokyo)

The goal of this project is to extract information hidden in complex quantum properties and quantum
fluctuations, which appear in microscopic physical systems governed by quantum mechanics, using
artificial intelligence (AI). The concrete research achievements are summarized below.

1. Deciphering quantum fingerprints in electric conductance using AI [1]
We have made the AI-assisted analysis of complex fluctuations in electric conductance (the reciprocalof resistance) that manifest in microscopic electric conduction in metals. In the minuscule metals with
the nanometer size, the electrons responsible for electrical conduction obey quantum mechanics,
demonstrating properties of both particles and waves, leading to quantum interference phenomena
similar to the interference of water waves. The atomic-level impurities and lattice defects in the micrometal lead to the interference between the wave functions, which are scattered from the impurities (ordefects) and reflected at the edges of the metal. As a result, when the magnitude of the magnetic field
applied to the metal changes, the electric conductance exhibits a highly complex pattern offluctuations in response. This complex pattern is essentially originated from quantum mechanics, andunlike the random thermal fluctuations of the classical world, it retains microscopic information suchas the positions of impurities in micro-metals, thus being termed as a 'quantum fingerprint'. However,
due to its complexity, the standard procedure has been to analyze these fluctuation patterns byaveraging, making it challenging to decode the hidden microscopic information. In this research, we
successfully extract information about quantum interference of wave functions in micro-metals fromthe quantum fingerprints using AI. More specifically, we dealt with micro-metals incorporating various
impurity arrangements by numerically solving the Schrödinger equation for electrons, allowing us todetermine interference patterns of the wave functions and derive the magnetic field-dependent
electric conductance. We start with the machine learning on image data of these interference patterns
based on a Variational Autoencoder (VAE), enabling us to extract their characteristic features in alatent space (Feature Extraction Network). Subsequently, we trained a deep neural network toestimate the characteristic features extracted by the VAE from the quantum fingerprints in electricconductance (Geometry Generative Network). This approach enabled us to successfully reconstructmicroscopic quantum information such as impurity positions and interference patterns from thequantum fingerprint in the micro-metals. (See Fig. 1)

Fig.1 : Schematic image of deciphering quantum fingerprints in electric conductance [1].

2. Quantum circuit distillation using AI [2]We utilize AI in research on fluctuations that appear in the output of quantum computations performedby quantum computers and lead to errors in computations. Quantum operations performed on
quantum bits (qubits), the basic units of a quantum computer, are governed by quantum mechanics,
and it is known to be extremely challenging to achieve precise quantum operations due to various
external disturbances. The frequency of errors increases with the number of quantum operations
required for quantum computation, leading to greater fluctuations in the output results, which makemeaningful computations impossible. In this research, we performed reinforcement learning in AI for
the ideal relationship between inputs and outputs for the quantum circuits (sequences of quantumoperations) used in quantum computations. This allowed us to discover new quantum circuits that
achieve (almost) the same outputs as well-known quantum circuits but are composed of fewer
quantum operations. The discovered quantum circuit, with fewer quantum operations compared toconventional ones, can exhibit smaller errors in the final output. Implementing this new quantum circuit

using superconducting qubits in an actual quantum computer has successfully led to output resultswith fewer errors compared to conventional circuits in quantum computations. (See Fig.2)

Fig.2 : Quantum circuit distillation of the inverse quantum Fourier transform of three qubits
by reinforcement learning [2].

3. Quantum state tomography for magnons [3, 4]
We are conducting research using AI not only for known physical systems that exhibit quantum
properties, but also exploring new quantum physical systems for the AI-assisted research in thisproject. One of these is the system of magnons, which are elementary excitations in magnetic
materials. Magnons are fluctuations in the quantum spins of electrons responsible for magnetismand have played a crucial role in the field of spintronics, where next-generation, low-powerconsumption devices utilizing spins are actively explored. To discern whether magnons exhibit
quantum properties, it is essential to investigate the statistical distribution followed by thefluctuations of magnons. This necessitates extensive data acquisition and analysis of magnon
fluctuations. In this research, we have successfully implemented a technique called state
tomography for the first time concerning magnons, allowing the determination of the presence orabsence of quantum properties in the states of magnons generated and controlled by magnetic
fields and microwaves [3, 4]. This advancement enables the acceleration of exploration into
various quantum states based on magnons and their potential applications in the future.

Selected papers :[1] S. Daimon, K. Tsunekawa, S. Kawakami, T. Kikkawa, R. Ramos, K. Oyanagi, T. Ohtsuki and
E. Saitoh, Nature Communications 13, 3160 (2022).
(https://doi.org/10.1038/s41467-022-30767-w)[2] S. Daimon, K. Tsunekawa, R. Takeuchi, T. Sagawa, N. Yamamoto and E. Saitoh,
arXiv:2309.01911[quant-ph]. (https://doi.org/10.48550/arXiv.2309.01911)[3] Tomosato Hioki, Hiroki Shimizu, Takahiko Makiuchi, and Eiji Saitoh, Physical Review B104,
L100419 (2021). (https://doi.org/10.1103/PhysRevB.104.L100419)[4] Tomosato Hioki and Eiji Saitoh, Journal of Applied Physics 132, 203901 (2022).
(https://doi.org/10.1063/5.0123221)