Engineering functional quantum algorithms

2003/01/17 by Andreas Klappenecker, Martin Rötteler · 1 citation
Computer Science · Mathematics · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Computability, Logic, AI Algorithms #Quantum Fourier transform #Quantum algorithm #Unitary matrix #Quantum gate #Quantum computer #Quantum circuit #Integer (computer science) #Unitary state #Quantum phase estimation algorithm #Quantum #Mathematics #Algorithm #Simple (philosophy) #Discrete mathematics #Matrix (chemical analysis) #Electronic circuit #Quantum mechanics #Physics #Computer science #Quantum error correction

paper · doi:10.1103/physreva.67.010302

openalex publication_date 2003/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most O(mK+m²lnm) elementary gates. The functions of U are realized by a generic quantum circuit, which has a particularly simple structure. Among other results, we obtain efficient circuits for the fractional Fourier transform.

Citations

• Elementary gates for quantum computation
• Quantum computations: algorithms and error correction

Cited by

• Fractional Fourier transform [wikipedia]