DLAP online Seminar - PowerPoint PPT Presentation

吉岡信行（理研） 量子多体系の表現 DLAP online Seminar ニューラルネットワークで探る ������ ������� ���������� Zoom Webinar, 2020.07.09

博論タイトル「ニューラルネットワークによる物理状態の判定と表現」 自己紹介 ・非平衡量子ダイナミクス 主な研究内容：量子物理・情報科学の境界から生まれる高速アルゴリズムの探索 共同研究者のみなさま ・ニューラルネットワークによる量子多体状態の効率的表現 吉岡 信行 (Nobuyuki Yoshioka) 2015.03 東京大学理学部物理学科 卒 2017.03 東大理物 修士課程修了 ( 桂研 ) 2020.03 東大理物 博士課程修了 ( 桂研 ) Dr. Ryusuke Dr. Franco Nori Hamazaki 現在 理化学研究所 開拓研究本部 Nori 理論量子物理研究室 Dr. Ravindra 
 Dr. Clemens 
 Chhajlany Gneiting Today ・ NIQS アルゴリズム開発 e.g. 物理量の Error bound Prof. Wataru e.g. オンサーガー代数による Perfect Scar の構築 Mizukami 2

▸ Introduction to Neural Quantum States Restricted Boltzmann Machine as a quantum state Variational calculation Relationship with tensor networks ▸ Application to open quantum system Steady state as “ground state” of Lindbladian Results by RBM ansatz 3

Machine Learning Simulation of “Probability Distribution” Quantum Many-body 
 Computing Problems

Simulation of “Probability distribution” Data-driven learning Model-driven learning Obtained via fitting into measurements Obtained via optimization of No access to “ground truth” model-based well-defined cost function - Mathematical programming - Machine learning Classical data e.g. combinatorial optimization e.g. image recognition Probability distribution 
 e.g. data science - Recommendation for Monte Carlo Single computational basis - Variational simulation - Quantum tomography Quantum data - Reproduce quantum state, - Costless simulation of 
 Wave function 
 Hamiltonian, Liouvilllian etc. eigenvectors, density mat. Unitary/non-unitary mapping - Tensor Nets, Neural Nets, 
 - Error mitigation Quantum circuits, etc. 5

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<latexit sha1_base64="y4oNMBQD4Q+MCZJv/jSeXzDG5uk=">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</latexit> <latexit sha1_base64="cg0hK924sD/BmEpfULMW9SV2mvY=">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</latexit> <latexit sha1_base64="R10YyoAuJjD7iUruIGMwGeJgxg=">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</latexit> <latexit sha1_base64="yUqCZV/HAQfzyrALVxdix0XcIsU=">AC+HichVFNaxQxGH5n/KrR1e9CB4cXCr1smRLwQ8QSkXocdu6baEpQyZ9dxuayQyZ7EI7nT/g1UMPXlSQUrz5F7z4Bz0J4jHClLowXdnR6S26huSvHnyPG+eJFGqVeYO/D8c+cvXLw0drl25eq16+P1GzeXsqRvJXZkohO7EokMtTLYcpXEktijSuBxtPhvuLw/QZioxL9xWimux6BnVI4gsL6q+dhzm0cDGJZPOV9s05cdDl3G+hEkfMkRStcYo2IMRe2FytTFAHvWiFzroXpaeTtTIW/FDtzO8EJgNuSVJzNPpMa1husycoITietKmlAFe2kvgc1iEBCX2IAcGAo1yDgIzaKrSAQUrYGuSEWcpUuY9QI20fWIhMQShmzT2aLVaoYbWw5pZqZ0iqZuSRnABPvC9tkh+8w+sK/s+K+18rLG0MsWzdFIi2k4/vL24o/qmKaHWz8Vv3Ts4MuPCq9KvKelsjwFnKkH2zvHi4+WZjI7N37Bv5f8sO2Ce6gRl8l+/nceE1OgDWn8+9+lkarZm4+np9uzMxWXzEGd+AeTNJ7P4QZmIM2dOjcI+uN+k98Lf9N/6evz+i+l6luQUnwv/4E4jzx2Y=</latexit> Variational simulation Optimize the ansatz w.r.t target depending on what you want to do Ψ θ e.g. Hamiltonian e.g. Product of Liouvillian L † ˆ hh ρ θ | ˆ h Ψ θ | H | Ψ θ i L| ρ θ ii E vmc = argmin 0 = argmin h Ψ θ | Ψ θ i hh ρ θ | ρ θ ii θ θ Model Minimize GS approximant Ψ θ energy Static property X { Symmetry breaking H = h q P q Ordering Parametrized model q Minimize “energy” “Ground truth” accessible by (super)-exponential cost Non-equilibrium Steady state ρ θ property Appropriate ansatz, “cost function”, optimization needed 7

Simulation/Estimation of “Probability distribution” Data-driven Model-driven Obtained via fitting into measurements Obtained via optimization of No access to “ground truth” model-based well-defined cost function - Mathematical programming - Machine learning Classical data e.g. combinatorial optimization e.g. image recognition Probability distribution 
 e.g. data science - Recommendation for Monte Carlo Single computational basis - Variational simulation - Quantum tomography Quantum data - Reproduce quantum state, - Costless simulation of 
 Wave function 
 Hamiltonian, Liouvilllian etc. eigenvectors, density mat. Unitary/non-unitary mapping - Tensor Nets, Neural Nets, 
 - Error mitigation Quantum circuits, etc. 8