Jacobi fields in the Riemannian geometry of quantum computation

Howard E. Brandt

doi:10.1117/12.849648

16 April 2010 Jacobi fields in the Riemannian geometry of quantum computation

Howard E. Brandt

Proceedings Volume 7702, Quantum Information and Computation VIII; 770208 (2010) https://doi.org/10.1117/12.849648
Event: SPIE Defense, Security, and Sensing, 2010, Orlando, Florida, United States

Abstract

In the Riemannian geometry of quantum computation, the quantum evolution is described in terms of the special unitary group of n-qubit unitary operators with unit determinant. To elaborate on some aspects of the methodology, the generic Jacobi equation and lifted Jacobi equation, together with solutions on the group manifold, are explicitly derived. This is important for investigations of the global characteristics of geodesic paths in the group manifold, and the determination of optimal quantum circuits for carrying out a quantum computation.

Citation Download Citation

Howard E. Brandt "Jacobi fields in the Riemannian geometry of quantum computation", Proc. SPIE 7702, Quantum Information and Computation VIII, 770208 (16 April 2010); https://doi.org/10.1117/12.849648

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available