ua nt - p h / 99 11 06 1 v 1 1 5 N ov 1 99 9 Time dynamics in chaotic many - body systems : can chaos destroy a quantum computer ?

Highly excited many-particle states in quantum systems (nuclei, atoms, quantum dots, spin systems, quantum computers) can be " chaotic " superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is a result of the very high energy level density of many-body 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 ∼ τ 0 /(n log 2 n), where τ 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 ∼ nt 2 J 2 log 2 (1/t 2 J 2), where J is the inter-qubit 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.