Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A Study of Linear Joint and Tool Models in Spindle-Holder-Tool Receptance Coupling

Published

Author(s)

Timothy J. Burns, T L. Schmitz

Abstract

As a qubit is a two-level system whose state space is spanned by and , so a qudit is a -level system whose state space is spanned by ,..., . Quantum computation has stimulated much recent interest in algorithms factoring unitary evolutions of an -qubit state space into component two-particle unitary evolutions. In the absence of symmetry, Shende, Markov, and Bullock use Sard's theorem to prove that at least two-qubit unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa (VMS) use the matrix factorization and Gray codes in an optimal order construction involving two-particle evolutions. In this work, we note that Sard's theorem demands two-qudit unitary evolutions to construct a generic (symmetry-less) -qudit evolution. However, the VMS result applied to virtual qubits only recovers optimal order in the case that is a power of two. We further construct a decomposition for multi-level quantum logics, proving a sharp asymptotic of two-qudit gates and thus closing the complexity question for all -level systems ( finite). Gray codes are not required.
Proceedings Title
Proceedings of the Fifth ASME International Conference on Multibody Systems Nonlinear Dynamics and Control
Volume
Long Beach, CA
Conference Dates
September 24-28, 2005
Conference Title
ASME 2005 International Design Engineering Technical Conferences

Keywords

coupling, high-speed machining, receptance, stability lobes, tool length turning

Citation

Burns, T. and Schmitz, T. (2005), A Study of Linear Joint and Tool Models in Spindle-Holder-Tool Receptance Coupling, Proceedings of the Fifth ASME International Conference on Multibody Systems Nonlinear Dynamics and Control (Accessed December 13, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created October 1, 2005, Updated February 19, 2017