ShorVis: A Comprehensive Case Study of Quantum Computing Visualization

We introduce an open-source web-based platform that integrated multiple methods for visualizing Shor's algorithm. We mainly focus on three different approaches which are widely used in the field of visualizing qubit and quantum algorithms. These methods include Bloch sphere, quantum circuit and probability distribution map. We combine these geometrical methods and abstract the level of quantum circuit in order to introduce the well-known Shor's algorithm more explicitly. Our platform provides a direct and comprehensible perspective for better understanding the basic principles of quantum computation and how the features of quantum algorithms reduce the time complexity of certain problems. It also provides an interactive way for users to easily test the Shor's factoring algorithm. With further improvement and development, potential capacity can be proved in the field of visualization of quantum computation.

[1]  Franco Nori,et al.  QuTiP 2: A Python framework for the dynamics of open quantum systems , 2012, Comput. Phys. Commun..

[2]  R. Feynman Simulating physics with computers , 1999 .

[3]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[4]  C. Lavor,et al.  Shor's Algorithm for Factoring Large Integers , 2003, quant-ph/0303175.

[5]  Krysta Marie Svore,et al.  LIQUi|>: A Software Design Architecture and Domain-Specific Language for Quantum Computing , 2014, ArXiv.

[6]  R. Mosseri,et al.  Geometry of entangled states, Bloch spheres and Hopf fibrations , 2001, quant-ph/0108137.

[7]  Igor L. Markov,et al.  Constant-optimized quantum circuits for modular multiplication and exponentiation , 2012, Quantum Inf. Comput..

[8]  Matthias Troyer,et al.  ProjectQ: An Open Source Software Framework for Quantum Computing , 2016, ArXiv.

[9]  Diederik Aerts,et al.  The extended Bloch representation of quantum mechanics: Explaining superposition, interference, and entanglement , 2015, 1504.04781.

[10]  Tal Mor,et al.  Geometry of entanglement in the Bloch sphere , 2016, 1608.00994.

[11]  Scott N. Walck,et al.  Characterization and visualization of the state and entanglement of two spins , 2001 .

[12]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[13]  W. W.,et al.  The Nuclear Induction Experiment , 2022 .