Walsh transforms and efficient quantum algorithms

✍ Scribed by Takashi Mihara

• Book ID: 101294891
• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 220 KB
• Volume: 83
• Category: Article
• ISSN: 1042-0967
• DOI: 10.1002/(sici)1520-6440(200008)83:8<71::aid-ecjc8>3.0.co;2-c

✦ Synopsis

In this paper, we show structures of efficient quantum algorithms on a quantum Turing machine. First, we denote a relationship between Simons algorithm and Walsh transforms. Next, we also show that a quantum Turing machine can efficiently solve the DeutschJozsa problem by using interference among configurations instead of observation. Moreover, based on these results, we are led to structures of more general quantum algorithms. Finally, we show a problem that can be efficiently solved by using this type of algorithm and a Walsh transform.