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We show that, in a system with defects, two-particle states may experiencedestructive quantum interference, or antiresonance. It prevents an excitationlocalized on a defect from decaying even where the decay is allowed by energyconservation. The system studied is a qubit chain or an equivalent spin chainwith an anisotropic ($XXZ$) exchange coupling in a magnetic field. The chainhas a defect with an excess on-site energy. It corresponds to a qubit with thelevel spacing different from other qubits. We show that, because of theinteraction between excitations, a single defect may lead to multiple localizedstates. The energy spectra and localization lengths are found fortwo-excitation states. The localization of excitations facilitates theoperation of a quantum computer. Analytical results for strongly anisotropiccoupling are confirmed by numerical studies.Comment: Updated version, 13 pages, 5 figures To appear in Phys. Rev. B (2003

Two-particle localization and antiresonance in disordered spin and qubit chains