A quantum Fourier transform algorithm
Chris Lomont
TL;DR
This paper presents a quantum Fourier transform algorithm over cyclic groups, providing a rigorous correctness proof and precise bounds on qubit requirements for desired accuracy, enhancing the understanding of quantum algorithm efficiency.
Contribution
It introduces a new quantum Fourier transform algorithm with improved performance bounds and detailed qubit requirement analysis, correcting previous claims.
Findings
Algorithm correctness is rigorously proven.
Exact qubit bounds are established for specific tolerances.
Performance bounds are tightened compared to earlier claims.
Abstract
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds given earlier. Exact bounds are given for the number of qubits needed to achieve a desired tolerance, allowing simulation of the algorithm.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications