Measuring effective temperatures of qubits using correlations

Initialization of a qubit in a pure state is a prerequisite for quantum computer operation. A plethora of ways to achieve this has been proposed in the last decade, from active reset protocols to advances in materials and shielding. An instrumental tool to evaluate those methods and develop new ones is the ability to measure the population of excited states with high precision and in a short period of time. In this Letter, we propose a new technique of fording the excited state population of a qubit using correlations between two sequential measurements. We experimentally implement the proposed technique using a circuit QED platform and compare its performance with previously developed ones. Unlike other techniques, our method does not require high-fidelity readout and does not involve the excited levels of the system outside of the qubit subspace. We experimentally demonstrated measurement of the spurious qubit population with accuracy of up to 0.01%. This accuracy enabled us to perform "temperature spectroscopy" of the qubit, which helps to shed light on decoherence sources.