After learning basic quantum computing concepts, it is desirable to reinforce the learning using an important and relatively complex algorithm through which the students can observe and appreciate how the qubits evolve and interact with each other. Harrow-Hassidim-Lloyd (HHL) quantum algorithm, which can solve Linear System Problems with exponential speed-up over the classical method and is the basic of many important quantum computing algorithms, is used to serve this purpose. The HHL algorithm is explained analytically followed by a 4-qubit numerical example in bra-ket notation. Matlab code corresponding to the numerical example is available for students to gain a deeper understanding of the HHL algorithm from a pure matrix point of view. A quantum circuit programmed using qiskit is also provided which can be used for real hardware execution in IBM quantum computers. After going through the material, students are expected to have a better appreciation of the concepts such as basis transformation, bra-ket and matrix representations, superposition, entanglement, controlled operations, measurement, Quantum Fourier Transformation, Quantum Phase Estimation, and quantum programming. To help readers review these basic concepts, brief explanations augmented by the HHL numerical examples in the main text are provided in the Appendix.
Solving Linear Systems of Equations with the Quantum HHL Algorithm: A Tutorial on the Physical and Mathematical Foundations for Undergraduate Students
Latin America Quantum Computing Center, SENAI CIMATEC（拉丁美洲量子计算中心，SENAI CIMATEC）；QuIIN - Quantum Industrial Innovation, Centro de Competência Embrapii Cimatec. SENAI CIMATEC（QuIIN - 量子工业创新中心，Embrapii Cimatec能力中心。SENAI CIMATEC）；Centro de Ciências Exatas e das Tecnologias, Universidade Federal do Oeste da Bahia - Campus Reitor Edgard Santos（理学院与技术学院，巴伊亚联邦大学雷托尔·埃德加多·桑托斯校区）
Pritzker School of Molecular Engineering, The University of Chicago（芝加哥大学普利兹克分子工程学院）；qBraid Co.（qBraid公司）；Kadanoff Center for Theoretical Physics, The University of Chicago（芝加哥大学卡达诺夫理论物理中心）；Chicago Quantum Exchange（芝加哥量子交易所）；Department of Computer Science, The University of Chicago（芝加哥大学计算机科学系）；Department of Mathematics, University of Surrey（萨里大学数学系）；Lab for Information & Decision Systems (LIDS), Massachusetts Institute of Technology（麻省理工学院信息与决策系统实验室）
Quantum Decoding Algorithms: Quantum Speedups in Optimization
University of Copenhagen（哥本哈根大学）；New York University Shanghai（纽约大学上海分校；纽约大学上海NYU-ECNU物理研究所）；NYU-ECNU Institute of Physics at NYU Shanghai（阿布扎比纽约大学研究中心（CQTS）量子与拓扑系统中心）；Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University Abu Dhabi（纽约大学物理系）；Department of Physics, New York University
Towards identifying possible fault-tolerant advantage of quantum linear system algorithms in terms of space, time and energy
The University of Pittsburgh（匹兹堡大学）；The University of Chicago（芝加哥大学）；Mason Experimental Geometry Lab（梅森实验几何实验室）；Lehigh University（理海大学）；The University of Portland（波特兰大学）；Charles Schwab Corporation（嘉信理财公司）
