Protocol for temperature sensing using a three-level transmon circuit

We present a method for in situ temperature measurement of superconducting quantum circuits, by using the first three levels of a transmon device to which we apply a sequence of π gates. Our approach employs projective dispersive readout and utilizes the basic properties of the density matrix associated with thermal states. This method works with an averaging readout scheme and does not require a single-shot readout setup. We validate this protocol by performing thermometry in the range of 50 mK 200 mK, corresponding to a range of residual populations 1%− 20% for the first excited state and 0.02%− 3% for the second excited state. Superconducting qubits are one of the most promising candidates as the basic element of future quantum computers. The progress of the last decade has resulted in a significant increase of their coherence times to tens of microseconds, in a reduction of errors caused by interaction with the environment through the implementation of reset protocols and error-correction protocols, and in an enhancement in readout fidelity up to 99.6%. However, the exact mechanisms that limits further improvements in superconducting qubit systems are still not fully understood; one possibility is the spurious excitations caused by microwave noise, infrared radiation from hotter stages of the dilution refrigerators or poisoning by quasiparticles. To mitigate these effects, a range of experimental techniques have been deployed – the use of cryogenic filters and attenuators, infrared absorbers, radiation and magnetic shielding of samples, with the goal of reducing the temperature of the electromagnetic environment and the quasiparticle population. Here we introduce a protocol for evaluating the effective temperature of a superconducting qubit. Our method can be readily used as a diagnostic tool for qubit thermalization and line integrity in quantum computing applications. An important application is quantum thermodynamics, where controlling the effective temperature of the circuit can be used to drive quantum engines. The state of the electromagnetic environment of the qubit is described by an effective temperature, which characterizes the thermal equilibrium between the qubit and the environment and thus defines residual populations of former. There are several ways to estimate this effective temperature from the residual populations of qubit’s states, assuming a MaxwellBoltzmann distribution. A straightforward method is to use a single-shot readout. In this case the residual probabilities can be directly calculated from measurement statistics, provided that the states can be discriminated with sufficiently good precision. However, the implementation of a single-shot readout scheme requires a good quantum limited parametric ampliElectronic mail: sorin.paraoanu@aalto.fi fier and additional components. An alternative approach, which does not use single-shot readout, is based on the measurement of correlations between responses corresponding to the ground and excited states. Another technique uses a three level system, where the Rabi oscillation amplitude between the first and the second excited state depends on the residual population of the first excited state. However, this method is highly sensitive to the readout signal parameters. Finally, a thermometry technique for propagating waves in open-waveguides can be used to characterize the temperature of the electromagnetic field, but this method requires a dedicated sample design. Here we propose an in situ method for measuring the effective temperature, which utilizes only π pulses and requires measuring only the average responses in the dispersive readout limit. Therefore this method could be implemented without a specialized setup or sophisticated measurement techniques. In addition, determining the temperature does not rely on qubit state tomography: In our protocol, we measure the cavity responses after applying six different drive sequences that swap the populations of the three-level system, in our case defined by the first levels in a transmon device. A simple linear relationship is found between some of these responses, and the coefficient of proportionality is determined only by the thermal level occupations. Therefore, as the method does not rely on full state tomography or on the knowledge of the pure state responses, it is more resilient to noise and drifts which are commonly present in superconducting artificial atom experiments. Moreover, since only π pulses are utilized, the proposed method is robust against dephasing and, if the pulses are much shorter with respect to the relaxation time, also against decay. Consider a three-level system in thermal equilibrium with its environment at a temperature T . The density matrix reads ρ̂ = pg |g〉 〈 g|+ pe |e〉 〈e| + p f | f 〉 〈 f | , (1) where |g〉 , |e〉 , | f 〉 are respectively the ground, the first excited and the second excited state, with corresponding populations pg, pe, and p f . Thermal equilibrium means that ρ̂