  Fault-tolerant quantum computing requires initializing the quantum register
in a well-defined fiducial state. In solid-state systems, this is typically
achieved through thermalization to a cold reservoir, such that the
initialization fidelity is fundamentally limited by temperature. Here, we
present a method of preparing a fiducial quantum state with a confidence beyond
the thermal limit. It is based on real time monitoring of the qubit through a
negative-result measurement -- the equivalent of a `Maxwell's demon' that
triggers the experiment only upon the appearance of a qubit in the
lowest-energy state. We experimentally apply it to initialize an electron spin
qubit in silicon, achieving a ground-state initialization fidelity of 98.9(4)%,
corresponding to a 20$\times$ reduction in initialization error compared to the
unmonitored system. A fidelity approaching 99.9% could be achieved with
realistic improvements in the bandwidth of the amplifier chain or by slowing
down the rate of electron tunneling from the reservoir. We use a nuclear spin
ancilla, measured in quantum nondemolition mode, to prove the value of the
electron initialization fidelity far beyond the intrinsic fidelity of the
electron readout. However, the method itself does not require an ancilla for
its execution, saving the need for additional resources. The quantitative
analysis of the initialization fidelity reveals that a simple picture of
spin-dependent electron tunneling does not correctly describe the data. Our
digital `Maxwell's demon' can be applied to a wide range of quantum systems,
with minimal demands on control and detection hardware.
