  The Continuous Spontaneous Localization (CSL) model is an alternative
formulation of quantum mechanics which introduces a noise coupled non linearly
to the wave function to account for its collapse. We consider CSL effects on
quantum computers made of superconducting transmon qubits. As a direct effect
CSL reduces quantum superpositions of the computational basis states of the
qubits: we show the reduction rate to be negligibly small. However, an indirect
effect of CSL, dissipation induced by the noise, also leads transmon qubits to
decohere, by generating additional quasiparticles. Since the decoherence rate
of transmon qubits depends on the quasiparticle density, by computing their
generation rate induced by CSL, we can estimate the corresponding quasiparticle
density and thus the limit set by CSL on the performances of transmon quantum
computers. We show that CSL could spoil the quantum computation of practical
algorithms on large devices. We further explore the possibility of testing CSL
effects on superconducting devices.
