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) similar to tau (o)/(n 1og(2)n), where to is the qubit 'lifetime', n is the number of qubits, S(0) = 0 and S(t(c)) = 1. At t much less than 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. At t much greater thant(c) the system entropy approaches that for chaotic eigenstates.