High-fidelity and rapid readout of a qubit state is key to quantum computing and communication,
and it is a prerequisite for quantum error correction. We present a readout scheme for superconducting
qubits that combines two microwave techniques: applying a shelving technique to the qubit
that effectively increases the energy-relaxation time, and a two-tone excitation of the readout resonator
to distinguish among qubit populations in higher energy levels. Using a machine-learning
algorithm to post-process the two-tone measurement results further improves the qubit-state assignment
fidelity. We perform single-shot frequency-multiplexed qubit readout, with a 140 ns readout
time, and demonstrate 99.5% assignment fidelity for two-state readout and 96.9% for three-state
readout—without using a quantum-limited amplifier.