Step-by-Step HHL Algorithm Walkthrough to Enhance the Understanding of
  Critical Quantum Computing Concepts
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.
Hector Jose Morrell Jr Anika Zaman Hiu Yung Wong