Simon's Algorithm Research Articles

QUANTUM-STATISTICAL SIMULATIONS FOR QUANTUM CIRCUITS

Using a Hubbard–Stratonovich like decomposition technique, we implemented simulations for the quantum circuits of Simon's algorithm for the detection of the periodicity of a function and Shor's algorithm for the factoring of prime numbers on a classical computer. Our approach has the advantage that the dimension of the problem does not grow exponentially with the number of qubits.

Walsh transforms and efficient quantum algorithms

In this paper, we show structures of efficient quantum algorithms on a quantum Turing machine. First, we denote a relationship between Simon's algorithm and Walsh transforms. Next, we also show that a quantum Turing machine can efficiently solve the Deutsch–Jozsa 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. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(8): 71–80, 2000