Efficient circuits for exact-universal computation with qudits

被引：0

作者：

Brennen, G.K. ^{[1
,5
]}

Bullock, S.S. ^{[2
]}

O'Leary, D.P. ^{[3
,4
]}

机构：

[1] Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8420, United States

[2] Center for Computing Sciences, Institute for Defense Analyses, Bowie, MD 20715-4300, United States

[3] Department of Computer Science, Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, United States

[4] Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8910, United States

[5] Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020, Innsbruck, Austria

来源：

Quantum Information and Computation | 2006年 / 6卷 / 4-5期

关键词：

Quantum efficiency - Quantum theory;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper concerns the efficient implementation of quantum circuits for qudits. We show that controlled two-qudit gates can be implemented without ancillas and prove that the gate library containing arbitrary local unitaries and one two-qudit gate, CINC, is exact-universal. A recent paper [S.Bullock, D.O'Leary, and G.K. Brennen, Phys. Rev. Lett. 94, 230502 (2005)] describes quantum circuits for qudits which require O(dn) two-qudit gates for state synthesis and O(d2n) two-qudit gates for unitary synthesis, matching the respective lower bound complexities. In this work, we present the state-synthesis circuit in much greater detail and prove that it is correct. Also, the [(n-2)/(d-2)] ancillas required in the original algorithm may be removed without changing the asymptotics. Further, we present a new algorithm for unitary synthesis, inspired by the QR matrix decomposition, which is also asymptotically optimal. © Rinton Press.

引用

页码：436 / 454