Quantum Computation of Quantum Chemistry
Study Session on Quantum Computation of Quantum Chemistry ( Chinese version)
10 unitsWe will go through four papers in great details to learn quantum computation of quantum chemistry.
The goal is to thoroughly examine the stateofart theories for quantum computing in Chemistry – true quantum advantage or not? – and to promote research in this direction.
This study session will focus on the following papers:
 I. Kassal, J. D. Whitfield, A. PerdomoOrtiz, M.H. Yung, and A. AspuruGuzik, Annu Rev Phys Chem 62, 185 (2011).
 P. J. J. O'Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Y. Mutus, M. Neeley, C. Neill, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, P. V. Coveney, P. J. Love, H. Neven, A. AspuruGuzik, and J. M. Martinis, Physical Review X 6, 361 (2016).
 R. Babbush, N. Wiebe, J. McClean, J. McClain, H. Neven, and G. K.L. Chan, Physical Review X 8, 011044 (2018).
 I. D. Kivlichan, J. McClean, N. Wiebe, C. Gidney, A. AspuruGuzik, G. K.L. Chan, and R. Babbush, Phys Rev Lett 120, 110501 (2018).
We will go through these papers in great details to learn quantum computation of quantum chemistry.
This course aims to provide a bridge for Chemistry majored students to appreciate recent advances of quantum computing methods for quantum chemistry problems.
Basic understanding of quantum mechanics & quantum chemistry will be needed.
 Brief Review of Quantum Computation for Quantum Chemistry
 Building Blocks of Quantum Computing and Quantum Fourier Transform
 Quantum Simulation and The Phase Estimation Algorithm
 Physical Realization of Qubits and Quantum Gates
 Encoding of Fermionic Problem
 The Unitary Coupled Cluster Ansatz and Variational Quantum Eigensolver
 Electronic Problem for Crystalline Solids
 Efficient Quantum Simulation with Linear Scaling(1)
 Efficient Quantum Simulation with Linear Scaling(2)
 Efficient Quantum Simulation with Linear Scaling(3)
Week  Topics  Reference 

1 
* General introduction * Critical overview of QCoQC 

2 
* Some key results in quantum computing * Quantum Fourier transform 

3  * Phase estimation  
4 
* Qubit implementations * Josephson junction & phase qubit * Quantum gates in superconducting quantum computer 

5 
* Secondedquantized molecular Hamiltonian * JordanWigner Transformation * BravyiKitaev Transformation * The case of minimabasis H_{2} problem 

6 
* Coupledcluster method * Unitary coupled cluster * UCC on the minimalbasis H_{2} problem 

7 
* Electronic Hamiltonian for crystalline solids * Plane waves and grids * Electronic Hamiltonian in the plane wave dual basis 

8 
* O(N) propagation in the plane wave dual basis * Preparation of meanfield state 

9 
* Fermionic Fast Fourier Transform * CooleyTukey Algorithm 
Lecture  Handout 

Lecture 1  Brief Review of Quantum Computation for Quantum Chemistry 
Lecture 2 
Some key results in quantum computing Quantum Fourier transform 
Lecture 4  Physical Realization of Qubits and Quantum Gates 
Lecture 6  The Unitary Coupled Cluster Ansatz and Variational Quantum Eigensolver 
Lecture 7  Electronic Problem for Crystalline Solids 
Lecture  Topic  length 

Lecture 1  Brief Review of Quantum Computation for Quantum Chemistry  1:34:05 
Lecture 2  Building Blocks of Quantum Computing and Quantum Fourier Transform  1:38:21 
Lecture 3  Quantum Simulation and The Phase Estimation Algorithm  1:21:51 
Lecture 4  Physical Realization of Qubits and Quantum Gates  1:10:43 
Lecture 5  Encoding of Fermionic Problem  1:35:36 
Lecture 6  The Unitary Coupled Cluster Ansatz and Variational Quantum Eigensolver  1:25:35 
Lecture 7  Electronic Problem for Crystalline Solids  1:32:08 
Lecture 8  Efficient Quantum Simulation with Linear Scaling(1)  57:12 
Lecture 9  Efficient Quantum Simulation with Linear Scaling(2)  1:08:37 
Lecture 10  Efficient Quantum Simulation with Linear Scaling(3)  41:35 
Lecture  Topics  Reference 

Lecture 1 


Lecture 2 


Lecture 4 


Lecture 5 


Lecture 6 


Lecture 7  
Lecture 8 
2019© YuanChung Cheng's Research Group  鄭原忠老師理論物理化學研究室
國立臺灣大學化學系  Department of Chemistry, National Taiwan University