Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication

Topics

Quantum State Preparation Representation

The Minimum Number of Rotations About Two Axes for Constructing an Arbitrary Fixed Rotation

arXiv
Authors: Mitsuru Hamada

Year

2013

Paper ID

2220

Status

Preprint

Abstract Read

~2 min

Abstract Words

120

Citations

N/A

Abstract

For any pair of three-dimensional real unit vectors hat{m} and hat{n} with |hat{m}rm T hat{n}| < 1 and any rotation U, let N_{hat{m},hat{n}}(U) denote the least value of a positive integer k such that U can be decomposed into a product of k rotations about either hat{m} or hat{n}. This work gives the number N_{hat{m},hat{n}}(U) as a function of U. Here a rotation means an element D of the special orthogonal group {rm SO}(3) or an element of the special unitary group {rm SU}(2) that corresponds to D. Decompositions of U attaining the minimum number N_{hat{m},hat{n}}(U) are also given explicitly.

Why This Paper Matters

  • This paper contributes to the Quantum State Preparation & Representation research area in the Quantum Articles archive.
  • It adds a 2013 reference point for readers tracking recent quantum research.
  • For any pair of three-dimensional real unit vectors hatm and hatn with |hatm^rm T hatn| < 1 and any rotation U, let N_hatm,hatn(U) denote the least value of a positive integer...

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in
Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/arXiv:1401.0153 [2] arXiv https://arxiv.org/abs/1401.0153 [3] Publisher https://arxiv.org/abs/1401.0153

Local Citation Graph (Related-Paper Links)

Current Paper #2220

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.