We quantify the intrinsic noise of the Single Electron Box arising from
stochastic cyclic electron tunnelling between a quantum dot and a resevoir
driven by a periodic gate voltage. We use both a master equation formalism and
Markov Monte Carlo simulations to calculate the gate noise current, and find it
to be generated by a cyclostationary process which displays significant
spectral correlations at large excitation amplitudes and high tunnel rates. We
model noise filtering through an electrical resonator and detection via
synchronous demodulation to evaluate the effective noise spectral density in
rf-reflectometry qubit readout applications, and determine the conditions under
which the intrinsic noise limit could be measured experimentally. Our results
have implications in the ultimate sensitivity of SEBs for fast, high-fidelity
readout of spin qubits.Comment: 6 pages, 4 figure