Introduction to Quantum Computing

The Most Important Step to Understand Quantum Computing.- First Impression.- Basis, Basis Vectors, and Inner Product.- Orthonormal Basis, Bra-Ket Notation, and Measurement.- Changing Basis, Uncertainty Principle, and Bra-ket Operations.- Observables, Operators, Eigenvectors, and Eigenvalues.- Pauli Spin Matrices, Adjoint Matrix, and Hermitian Matrix.- Operator Rules, Real Eigenvalues, and Projection Operator.- Eigenvalue and Matrix Diagonalization; Unitary Matrix.- Unitary Transformation, Completeness, and Construction of Operator.- Hilbert Space, Tensor Product, and Multi-Qubit.- Tensor Product of Operators, Partial Measurement, and Matrix Representation in a Given Basis.- Quantum Register and Data Processing, Entanglement and the Bell States.- Concepts Review, Density Matrix, and Entanglement Entropy.- Quantum Gate Introduction; NOT and C-NOT Gates.- SWAP, Phase Shift and CC-NOT (Toffoli) Gates.- Walsh-Hadamard Gate and its Properties.- Two Quantum Circuit Examples.- No-Cloning Theorem and Quantum Teleportation I.- Quantum Teleportation II and Entanglement Swapping.- Deutsch Algorithm.- Quantum Oracles and Construction of Quantum Gate.- Grover's Algorithm: I.- Grover's Algorithm: II.- Quantum Fourier Transform I.- Quantum Fourier Transform II.- Bloch Sphere and Single-Qubit Arbitrary Unitary Gate.- Quantum Phase Estimation.- Shor's Algorithm.- The Last But Not the Least..

Hiu Yung Wong is an Associate Professor and Silicon Valley AMDT Endowed Chair in Electrical Engineering, at San Jose State University (SJSU). He received his Ph.D. degree in EECS from UC Berkeley in 2006. From 2006 to 2009, he worked as a Technology Integration Engineer at Spansion. From 2009 to 2018, he was a TCAD Senior Staff Engineer at Synopsys.

Given the important role of electrical engineers in the quantum computing industry, he created a new master's specialization in quantum computing at SJSU. He is also one of the founding faculties of the MS degree program in Quantum Technology at SJSU, sponsored by NSF. Based on his quantum computing teaching experience to electrical engineers, he authored the book "Introduction to Quantum Computing: From a Layperson to a Programmer in 30 Steps" with teaching videos available on Youtube (@quantum_computing). He also created a class on Quantum Computing Architectures (available on YouTube) and Cryogenic Nanoelectronics to train the next generation of electrical engineers in quantum computing. He is an organizer and speaker in the Real-World Quantum Computing Workshop with Lawrence Livermore National Lab to orient engineering students to work on superconducting quantum computers.

Dr. Wong has given numerous tutorials to promote quantum computing. He was invited to give a tutorial at the ISQED conference and IEEE Quantum Week 2023, and a public seminar for FormFactor, Inc. in 2022 (> 300 attendees). He has also given quantum computing talks in companies such as Fujitsu Research of America, eBay Inc, and Synopsys Inc. and study groups such as Zen4Quantum and Washington DC Quantum Computing Meetup. He gives yearly quantum computing workshops for socially-disadvantaged high school students sponsored by NSF funding.

He received the McGraw Research Award from ASEE in 2022, the NSF CAREER award and the Newnan Brothers Award in 2021, and Synopsys Excellence Award in 2010.



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