a Computational Role for the OneDimensional Lieb ShultzMattis Spin Model
Abstract
Regarding individual quantummechanical degrees of freedom as elements of a parallel computation, a simple but fully interacting quantum manybody system is analyzed in order to derive a fundamental quantummechanical limit to massively parallel computation. Exact solutions for all eigenvalues and eigenvectors of an operator Gamma that the characterizes parallel computational velocity are found. A symmetry between the Hamiltonian and Gamma is described, and its consequences investigated. The largest eigenvalue of the computational velocity operator is found to scale with system size, N, as gamma _{rm max} ~ 2N/pi < N, a result which implies the impossibility of using additional quantummechanical parallel processors to obtain the same ideal speedup as in the classical case. A variational argument shows that this is a special case of a more fundamental limit to parallel quantum computation. (Copies available exclusively from MIT Libraries, Rm. 140551, Cambridge, MA 021394307. Ph. 6172535668; Fax 617253 1690.).
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT........88B
 Keywords:

 NANOELECTRONICS;
 Engineering: Electronics and Electrical; Computer Science; Physics: Condensed Matter