Abstract
AbstractThe ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete logarithm over Abelian groups, solving systems of linear equations, and phase estimation, to name a few. The standard fault-tolerant implementation of an n-qubit unitary QFT approximates the desired transformation by removing small-angle controlled rotations and synthesizing the remaining ones into Clifford+T gates, incurring the T-count complexity of $$O(n\,{\mathrm{log}}^{2}\,(n))$$
O
(
n
log
2
(
n
)
)
. In this paper, we show how to obtain approximate QFT with the T-count of $$O(n\,{\mathrm{log}}\,(n))$$
O
(
n
log
(
n
)
)
. For brevity, the above figures omit the dependence on the approximation error ε, assuming the error is fixed. Our approach relies on quantum circuits with measurements and feedforward, and on reusing a special quantum state that induces the phase gradient transformation. We report asymptotic analysis as well as concrete circuits, demonstrating significant advantages in both theory and practice.
Funder
United States Department of Defense | United States Army | U.S. Army Research, Development and Engineering Command | Army Research Office
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Computer Networks and Communications,Statistical and Nonlinear Physics,Computer Science (miscellaneous)
Reference38 articles.
1. Shor, P. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997).
2. Kitaev, A. Quantum measurements and the Abelian Stabilizer Problem. Preprint at https://arxiv.org/abs/quant-ph/9511026 (1995).
3. Brassard G. & Hoyer P. An exact quantum polynomial-time algorithm for Simon’s Problem. In Proc. of Fifth Israeli Symposium on Theory of Computing and Systems, 12–23 (IEEE, Ramat-Gan, Israel, 1997). https://arxiv.org/quant-ph/9704027.
4. Grover, L. Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80, 4329 (1998).
5. Kassal, I., Whitfield, J. D., Perdomo-Ortiz, A., Yung, M.-H. & Aspuru-Guzik, A. Simulating chemistry using quantum computers. Annu. Rev. Phys. Chem. 62, 185 (2011).
Cited by
47 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献