An Exact Quantum Polynomial-Time Algorithm for Simon's Problem

We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's problem can be solved in this way, whereas previous algorithms required quantum polynomial time in the expected sense only, without upper bounds on the worst-case running time. This is achieved by generalizing both Simon's and Grover's algorithms and combining them in a novel way. It follows that there is a decision problem that can be solved in exact quantum polynomial time, which would require expected exponential time on any classical bounded-error probabilistic computer if the data is supplied as a black box.Comment: 12 pages, LaTeX2e, no figures. To appear in Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems (ISTCS'97

Quantum Algorithm Animator

The design and development of quantum algorithms present a challenge, especially for inexperienced computer science students. Despite the numerous common concepts with classical computer science, quantum computation is still considered a branch of theoretical physics not commonly used by computer scientists. Experimental research into the development of a quantum computer makes the use of quantum mechanics in organizing computation more attractive, however the physical realization of a working quantum computer may still be decades away. This study introduces quantum computing to computer science students using a quantum algorithm animator called QuAL. QuAL\u27s design uses features common to classical algorithm animators guided by an exploratory study but refined to animate the esoteric and interesting aspects of quantum algorithms. In addition, this study investigates the potential for the animation of a quantum sorting algorithm to help novice computer science students understand the formidable concepts of quantum computing. The animations focus on the concepts required to understand enough about quantum algorithms to entice student interest and promote the integration of quantum computational concepts into computer science applications and curricula. The experimental case study showed no significant improvement in student learning when using QuAL\u27s initial prototype. Possible reasons include the animator\u27s presentation of concepts and the study\u27s pedagogical framework such as choice of algorithm (Wallace and Narayanan\u27s sorting algorithm), design of pre- and post tests, and the study\u27s small size (20 students) and brief duration (2 hours). Nonetheless, the animation system was well received by students. Future work includes enhancing this animation tool for illustrating elusive concepts in quantum computing