Time dynamics in chaotic manybody systems: can chaos destroy a quantum computer?
Abstract
Highly excited manyparticle states in quantum systems (nuclei, atoms, quantum dots, spin systems, quantum computers) can be ``chaotic'' superpositions of meanfield basis states (Slater determinants, products of spin or qubit states). This is a result of the very high energy level density of manybody states which can be easily mixed by a residual interaction between particles. We consider the time dynamics of wave functions and increase of entropy in such chaotic systems. As an example we present the time evolution in a closed quantum computer. A time scale for the entropy S(t) increase is t_c =t_0/(n log_2{n}), where t_0 is the qubit ``lifetime'', n is the number of qubits, S(0)=0 and S(t_c)=1. At t << t_c the entropy is small: S= n t^2 J^2 log_2(1/t^2 J^2), where J is the interqubit interaction strength. At t > t_c the number of ``wrong'' states increases exponentially as 2^{S(t)} . Therefore, t_c may be interpreted as a maximal time for operation of a quantum computer, since at t > t_c one has to struggle against the second law of thermodynamics. At t >>t_c the system entropy approaches that for chaotic eigenstates.
 Publication:

arXiv eprints
 Pub Date:
 November 1999
 arXiv:
 arXiv:quantph/9911061
 Bibcode:
 1999quant.ph.11061F
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Chaotic Dynamics;
 Nuclear Theory;
 Physics  Atomic Physics
 EPrint:
 9 pages, RevTex