  We model an isolated quantum computer as a two-dimensional lattice of qubits
(spin halves) with fluctuations in individual qubit energies and residual
short-range inter-qubit couplings. In the limit when fluctuations and couplings
are small compared to the one-qubit energy spacing, the spectrum has a band
structure and we study the quantum computer core (central band) with the
highest density of states. Above a critical inter-qubit coupling strength,
quantum chaos sets in, leading to quantum ergodicity of eigenstates in an
isolated quantum computer. The onset of chaos results in the interaction
induced dynamical thermalization and the occupation numbers well described by
the Fermi-Dirac distribution. This thermalization destroys the noninteracting
qubit structure and sets serious requirements for the quantum computer
operability.
