Open quantum systems can undergo dissipative phase transitions, and their critical behavior can be exploited in sensing applications. For example, it can be used to enhance the fidelity of superconducting qubit readout measurements, a central problem toward the creation of reliable quantum hardware. A recently introduced measurement protocol, named ``critical parametric quantum sensing'', uses the parametric (two-photon driven) Kerr resonator's driven-dissipative phase transition to reach single-qubit detection fidelity of 99.9\% [arXiv:2107.04503]. In this work, we improve upon the previous protocol by using machine learning-based classification algorithms to \textit{efficiently and rapidly} extract information from this critical dynamics, which has so far been neglected to focus only on stationary properties. These classification algorithms are applied to the time series data of weak quantum measurements (homodyne detection) of a circuit-QED implementation of the Kerr resonator coupled to a superconducting qubit. This demonstrates how machine learning methods enable a faster and more reliable measurement protocol in critical open quantum systems.
Open quantum systems can undergo dissipative phase transitions, and their critical behavior can be exploited in sensing applications. For example, it can be used to enhance the fidelity of superconducting qubit readout measurements, a central problem toward the creation of reliable quantum hardware. A recently introduced measurement protocol, named ``critical parametric quantum sensing'', uses the parametric (two-photon driven) Kerr resonator's driven-dissipative phase transition to reach single-qubit detection fidelity of 99.9% [arXiv:2107.04503]. In this work, we improve upon the previous protocol by using machine learning-based classification algorithms to \textit{efficiently and rapidly} extract information from this critical dynamics, which has so far been neglected to focus only on stationary properties. These classification algorithms are applied to the time series data of weak quantum measurements (homodyne detection) of a circuit-QED implementation of the Kerr resonator coupled to a superconducting qubit. This demonstrates how machine learning methods enable a faster and more reliable measurement protocol in critical open quantum systems.
Abstract Critical quantum systems are a promising resource for quantum metrology applications, due to the diverging susceptibility developed in proximity of phase transitions. Here, we assess the metrological power of parametric Kerr resonators undergoing driven-dissipative phase transitions. We fully characterize the quantum Fisher information for frequency estimation, and the Helstrom bound for frequency discrimination. By going beyond the asymptotic regime, we show that the Heisenberg precision can be achieved with experimentally reachable parameters. We design protocols that exploit the critical behavior of nonlinear resonators to enhance the precision of quantum magnetometers and the fidelity of superconducting qubit readout.
Quantum metrology, a cornerstone of quantum technologies, exploits entanglement and superposition to achieve higher precision than classical protocols in parameter-estimation tasks. When combined with critical phenomena such as phase transitions, the divergence of quantum fluctuations is predicted to enhance the performance of quantum sensors. Here, we implement a critical quantum sensor using a superconducting parametric (i.e., two-photon driven) Kerr resonator. The sensor, a linear resonator terminated by a superconducting quantum interference device, operates near the critical point of a finite-component second-order dissipative phase transition obtained by scaling the system parameters. We analyze the performance of a frequency-estimation protocol and show that quadratic precision scaling with respect to the system size can be achieved with finite values of the Kerr nonlinearity. Since each photon emitted from the cavity carries more information about the parameter to be estimated compared to its classical counterpart, our protocol opens up perspectives for faster or more precise metrological protocols. Our results demonstrate that quantum advantage in a sensing protocol can be achieved by exploiting a phase transition.
Josephson junctions are a fundamental building block of superconducting quantum circuits. They provide the nonlinearity required to realize quantum bits and enable a wide range of nonlinear phenomena central to quantum technologies. This thesis explores two superconducting systems in which this nonlinearity plays a central role. In the first part, we investigate a superconducting resonator terminated by a superconducting quantum interference device (SQUID), an arrangement of two Josephson junctions connected in parallel. The SQUID provides a tunable Kerr nonlinearity and allows the resonator to be driven parametrically. Under the combined action of the parametric drive, Kerr nonlinearity, and dissipation to the environment, the state of the resonator can undergo abrupt changes as the pump frequency or amplitude is varied. We interpret these changes within the framework of dissipative phase transitions (DPTs). By implementing a finite-component thermodynamic limit, we experimentally and theoretically investigate both first- and second-order DPTs in this system. We characterize their steady-state and dynamical signatures, including squeezing below vacuum, phase coexistence, hysteresis, spontaneous symmetry breaking, and critical slowing down. Finally, we exploit the enhanced susceptibility near the second-order critical point to implement a frequency-estimation protocol. We show that the estimation precision scales quadratically with the effective system size, demonstrating that finite-component DPTs can provide a quantum advantage in a sensing protocol. In the second part, we investigate a novel architecture for the readout of superconducting qubits. Conventional dispersive readout relies on a transverse interaction between a transmon and a resonator, which can lead to Purcell decay and measurement-induced state transitions, ultimately limiting the readout fidelity. To overcome these limitations, we implement a nonlinear coupling by galvanically connecting the transmon and resonator through a Josephson junction. This interaction provides a strong cross-Kerr coupling for clear state discrimination, but also introduces a detrimental transverse interaction. We experimentally show that the exchange part of the transverse interaction can be suppressed by adding a capacitor in parallel with the coupling junction while preserving the strong cross-Kerr coupling. In addition, we show that the same circuit acts as an intrinsic Purcell filter, protecting the qubit against Purcell decay. The coupling junction also induces a Kerr nonlinearity in the resonator, which we exploit to implement a bifurcation readout with a 99.4 % fidelity in a 68 ns integration time. This performance is achieved without a dedicated Purcell filter or a near-quantum-limited amplifier. Overall, this thesis demonstrates the engineering of nonlinear superconducting circuits to investigate dissipative phase transitions, exploit criticality for enhanced quantum sensing, and develop a novel qubit readout architecture enabling fast, high-fidelity measurement.
Two-level systems (TLS) in superconducting quantum devices are a dominant source of decoherence, noise, and device variability, ultimately limiting qubit performance and scalability. Efficient and reliable extraction of TLS parameters from spectroscopy measurements is therefore essential for both device characterization and materials optimization. In this thesis, machine learning methods are developed to accelerate and enhance TLS characterization from superconducting qubit spectroscopy data. The approach combines physics-based simulation of driven qubit–TLS dynamics with supervised learning models trained on synthetic datasets to infer underlying physical parameters from two-dimensional spectroscopy maps. Particular emphasis is placed on understanding how different parameters are encoded in observable features, and on evaluating the extent to which the inverse problem is well-posed. The results demonstrate that machine-learning-assisted inference can significantly reduce the computational cost of parameter estimation compared to conventional fitting-based approaches, while maintaining high accuracy for spectrally encoded parameters such as TLS frequency and coupling strength. In contrast, decoherence parameters are shown to be intrinsically more challenging to extract from short-time spectroscopy data, highlighting fundamental limitations of the measurement protocol rather than the learning model. Overall, this work establishes a data-driven framework for scalable TLS characterization and provides insight into the interplay between physical observability and machine learning-based inference in quantum systems.
In open quantum systems, dissipative phase transitions (DPTs) emerge from the interplay between unitary evolution, drive, and dissipation. While second-order DPTs have been predominantly investigated theoretically, first-order DPTs have been observed in single-photon-driven Kerr resonators. We present here an experimental and theoretical analysis of both first and second-order DPTs in a two-photon-driven superconducting Kerr resonator. We characterize the steady state at the critical points, showing squeezing below vacuum and the coexistence of phases with different photon numbers. Through time resolved measurements, we study the dynamics across the critical points and observe hysteresis cycles at the first-order DPT and spontaneous symmetry breaking at the second-order DPT. Extracting the timescales of the critical phenomena reveals slowing down across five orders of magnitude when scaling towards the thermodynamic limit. Our results showcase the engineering of criticality in superconducting circuits, advancing the use of parametric resonators for critically-enhanced quantum information applications.
Current methods for classifying measurement trajectories in superconducting qubit systems produce fidelities systematically lower than those predicted by experimental parameters. Here, we place current classification methods within the framework of machine learning (ML) algorithms and improve on them by investigating more sophisticated ML approaches. We find that nonlinear algorithms and clustering methods produce significantly higher assignment fidelities that help close the gap to the fidelity possible under ideal noise conditions. Clustering methods group trajectories into natural subsets within the data, which allows for the diagnosis of systematic errors. We find large clusters in the data associated with T1 processes and show these are the main source of discrepancy between our experimental and ideal fidelities. These error diagnosis techniques help provide a path forward to improve qubit measurements.