The association of a quantum bit and a harmonic mode dispersively coupled is one of the most studied systems in the field of quantum electrodynamics of superconducting circuits. It offers one of the most reliable current methods for measuring the state of a quantum bit in a non-destructive manner and has enabled numerous quantum information experiments, studying the information obtained through this measurement and the dynamics of the qubit when subjected to it. It also provides the ability to prepare and manipulate the quantum state of the harmonic mode via the qubit, allowing information to be stored and processed in this mode, which is fundamental to building a quantum processor. This thesis presents two experiments based on this architecture. The first demonstrates how to use qubit fluorescence to non-destructively read the number of photons contained in a microwave cavity in a single shot, that is, before the cavity has relaxed. This makes it possible to measure photon number trajectories and observe them leave the cavity one by one. The analysis of this experiment relies on a fluorescence analysis in terms of propagating modes and addresses a number of questions about the information that these modes may contain. The second is a demonstration of the use of a neural network for quantum state preparation in the cavity. Here, the goal is to accelerate the optimization of control electromagnetic pulses at the frequencies of the cavity and qubit to create a quantum state in the cavity with high fidelity, and this for a broad class of states. To evaluate the efficiency of this new optimization protocol over this class of states, an optimal method to assess the fidelity of the prepared states using a Wigner function measurement protocol was experimentally implemented for the first time.
The association of a quantum bit and a harmonic mode dispersively coupled is one of the most studied systems in the field of quantum electrodynamics of superconducting circuits. It offers one of the most reliable current methods for measuring the state of a quantum bit in a non-destructive manner and has enabled numerous quantum information experiments, studying the information obtained through this measurement and the dynamics of the qubit when subjected to it. It also provides the ability to prepare and manipulate the quantum state of the harmonic mode via the qubit, allowing information to be stored and processed in this mode, which is fundamental to building a quantum processor. This thesis presents two experiments based on this architecture. The first demonstrates how to use qubit fluorescence to non-destructively read the number of photons contained in a microwave cavity in a single shot, that is, before the cavity has relaxed. This makes it possible to measure photon number trajectories and observe them leave the cavity one by one. The analysis of this experiment relies on a fluorescence analysis in terms of propagating modes and addresses a number of questions about the information that these modes may contain. The second is a demonstration of the use of a neural network for quantum state preparation in the cavity. Here, the goal is to accelerate the optimization of control electromagnetic pulses at the frequencies of the cavity and qubit to create a quantum state in the cavity with high fidelity, and this for a broad class of states. To evaluate the efficiency of this new optimization protocol over this class of states, an optimal method to assess the fidelity of the prepared states using a Wigner function measurement protocol was experimentally implemented for the first time.
After years of academic development, the circuit quantum electrodynamics is entering the age of applications. This thesis was realized in this context of creating tools to bridge the gap between an astounding academic quantum system, superconducting circuits, and a grand goal, the universal quantum computer. A likely blueprint for quantum processors consists in the assembly of a large number of elementary modules arranged in a network.In this experimental thesis, a possible node for such a network, the quantum node, was developed and fabricated using state-of-the-art techniques for 2D superconducting microwave circuits. This node was first used to implement a novel sequential readout method for a superconducting qubit. This experiment, first proposed in 2013 by Sete et al., potentially allows for faster, more accurate read out of superconducting qubits. The read out of qubits is one of the several bottlenecks limiting the development of fault-tolerant superconducting quantum computers, which made this project both useful as a demonstration of the quantum node and for applications. This novel readout method achieves readout performances close to state-of-the-art of superconducting qubit readout even though the chip was not optimized for that purpose.During this work, we also contributed to two other experiments engineering quantum measurement and dissipation with superconducting circuits. First, a dedicated circuit was developed to demonstrate a new form of quantum measurement: the multiplexed photon number measurement. In that experiment led by A. Essig and Q. Ficheux, a superconducting transmon quantum bit is read out at multiple frequencies simultaneously to extract more than one bit of information about the number of photons contained in a microwave resonator coupled to that quantum bit.Second, we contributed to the experimental demonstration of the exponential suppression of bit-flips in a qubit encoded in a Schrödinger Cat state of a microwave mode. This experiment led by R. Lescanne and Z. Leghtas, demonstrates the improvement by a factor 300 of the lifetime of a qubit thanks to the autonomous error correction realized through the engineering of the dissipation of a microwave mode.
In this thesis, experimentally relevant aspects and open questions of quantum information processing and measurement in circuit quantum electrodynamics have been investigated theoretically. Circuit quantum electrodynamics is a relatively young field combining superconducting transmission line resonators on-chip with superconducting quantum bits which serve as artificial atoms. Remarkable experiments have underlined the prospects of circuit QED as a possible architecture for quantum information processing as well as a framework within which quantum optics experiments can be performed. In contrast to their optical counterparts, these experiments reach the ultra-strong coupling limit and allow e.g. the generation of Fock states, the study of decoherence and the observation of quantum jumps. We present the physics of superconducting circuits based on the Josephson junction as a non-linear circuit element. We discuss the various types of quantum bits (qubits) before turning to an introduction on cavity QED and conclude the introduction with a brief presentation of the most relevant experiments and a short introduction to the principles and prospects of quantum information processing. Building on the pioneering theoretical and experimental work in which up to three qubits have been integrated on a chip and successfully coupled via a cavity mode, we propose a scheme to overcome the natural limits concerning scalability in these systems. Usually, scalability is severely limited by the resonance width of the qubit transitions and the attainable frequency range for both qubit transition and cavity resonance frequencies. This limits the present setups to at most ten qubits. As a possible solution, we propose and investigate a cross-bar grid layout of cavities with qubits at the intersections. It turns out that this setup, allowing for up to about 1000 qubits, offers significant advantages over e.g. nearest-neighbor coupling schemes. In addition, it can serve as a building block for a truly scalable scheme for fault-tolerant quantum information processing with superconducting circuits by combining 7x7 arrays in a staircase manner. Furthermore, we discuss and simulate different possibilities to improve upon the suggested scheme by e.g. using resonant gates and optimal control theory. Another focus of the present thesis is measurement physics. In order to investigate e.g. the possibilities of using a circuit QED system to dispersively detect single microwave photons or to generate multi-qubit entangled states, we introduce in a pedagogical manner the basics of stochastic master equations which generate quantum trajectories before turning to concrete applications. Quantum trajectories have proven to be a state-of-the-art tool to analyze measurement situations in a very realistic manner by giving access to both the measurement record as well as the internal quantum dynamics conditioned on this record. Using the method of quantum trajectories as generated by stochastic master equations, we discuss a scheme to efficiently generate multi-qubit entangled states in a very flexible way. The method is based on a collective, dispersive qubit readout. By this measurement, a suitable product state of N qubits can be reliably converted into e.g. an N-qubit Greenberger-Horne-Zeilinger or W state. We propose and discuss the scheme and investigate the effects of decoherence and parameter spread as they would be encountered in experiment. Last but not least, we propose and fully analyze a scheme to dispersively detect single itinerant microwave photons. While experiments to generate single microwave photons have already been successfully performed, their single-shot quantum non-demolition detection has not been possible so far. The scheme presented in this thesis closes this gap in the circuit QED toolbox and reaches detection efficiencies of 30% only limited by fundamental quantum mechanics in this case the Quantum Zeno effect. This detection scheme could be used in quantum communication or quantum cryptography applications.
Circuit quantum electrodynamics (cQED), exemplified by a coupled system of a superconducting qubit and a microwave cavity, is a powerful framework for the quantum control and measurement of macroscopic quantum states in solid-state circuits. Quantum circuits based on superconducting qubits have emerged as one of the leading platforms in the pursuit of fault-tolerant quantum computing. Despite significant progress in extending qubit lifetimes, refining experimental protocols, and scaling up quantum processors, errors arising from the control and measurement of superconducting qubits continue to hinder the realization of a universal quantum computer. To investigate the error mechanisms for state-of-the-art qubits, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, with an average of 0.2 ms and a maximum exceeding 0.4 ms. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments. We also present a novel scheme for operating a cQED system in a regime where the cavity is largely displaced. We find that a qubit drive at the bare cavity frequency can effectively displace the cavity field while minimizing the cavity-drive-induced dephasing and the ac Stark shift. Furthermore, we demonstrate that standard cQED protocols, such as qubit control, readout, and cavity single-photon generation, remain compatible with largely displaced cavity fields, even beyond the critical photon number. These findings open new pathways for exploring cQED dynamics in large-photon-number regimes, including the study of nonlinear phenomena in microwave cavities, the saturation of two-level system baths for extending the coherence of microwave quantum states, and the acceleration of the dispersive readout. Finally, mechanical resonators have emerged as integral components in quantum computing for storing and transducing quantum information. Low-frequency mechanical resonators, with extremely low energy dissipation rates, are particularly interesting for extending the lifetimes of stored quantum information. However, integrating low-frequency mechanical resonators with qubits is challenging because their small energy gaps make coherent energy exchange and ground-state preparation difficult. In this thesis, we report the first steps towards the characterization of a hybrid quantum device, consisting of a Transmon qubit and a circuit optomechanical system, both coupled to a 3D microwave cavity.
Mesure et contrôle assisté par réseau de neurones de modes micro-ondes quantiques avec des circuits supraconducteurs L'association d'un bit quantique et d'un mode harmonique couplé dispersivement est l'un des systèmes les plus étudiés dans le domaine de l'électrodynamique quantique de circuits supraconducteurs. Il offre un des moyens actuels les plus fiables pour mesurer l'état d'un bit quantique de manière non-destructive, et a permis nombre d'expériences d'information quantique étudiant l'information obtenue via cette mesure et la dynamique du qubit lorsqu'il y est soumis. Il offre également la possibilité de préparer et de manipuler l'état quantique du mode harmonique grâce au qubit, ce qui permet de stocker et de manipuler de l'information dans ce mode. C'est notamment crucial pour des applications telles que la construction d'un ordinateur quantique. Dans cette thèse sont présentées deux expériences reposant sur cette architecture. La première démontre comment utiliser la fluorescence du qubit pour lire le nombre de de photons contenus dans le mode de manière non-destructive et en un seul coup, c'est-à-dire avant que les photons soient dissipés. Cela permet de mesurer des trajectoires du nombre de photons, et de les voir quitter la cavité un par un. L'analyse de cette expérience repose sur une analyse de la fluorescense en termes de modes propageants, et permet d'aborder un certain nombre de questionnements sur l'information que peuvent contenir ces modes. La seconde constitue une démonstration de l'utilisation d'un réseau de neurones dans le cadre de la préparation d'états quantiques dans le mode. Il s'agit ici d'accélérer l'optimisation des impulsions électromagnétiques de contrôle du mode et du qubit pour créer un état quantique dans le mode avec une grande fidélité, et ce pour une grande classe d'états. Pour évaluer l'efficacité de ce nouveau protocole d'optimisation sur l'ensemble de cette classe, une manière optimale d'évaluer la fidélité des états préparés à partir d'un protocole de mesure de la fonction de Wigner du mode a été pour la première fois implémentée expérimentalement.
In this paper, the coherent interaction of individual microwave photons with superconducting qubits is presented both for quantum information processing and for novel quantum optics experiments in the circuit quantum electrodynamics (QED) architecture. In the resonant regime we observe the vacuum Rabi mode splitting. In the non-resonant regime we use the dispersive coupling between the qubit and the cavity field to perform high visibility quantum non-demolition (QND) measurements of the qubit state. In the strong dispersive limit we also perform measurements of the cavity state from which the photon number statistics of the field can be extracted. Generally, the circuit QED architecture is attractive for quantum information processing and as an interface in hybrid quantum systems.
In the early 1980’s, it was suggested that a computer obeying the laws of quantum mechanics would be able to solve problems beyond the capabilities of a classical computer. The novel ways in which such a quantum computer works relies on the quantum properties of the quantum bits (qubits) used to store the information. Any candidate for a quantum computer must thus be able to sustain these properties and offer means to manipulate and read-out the information. One such candidate are quantum mechanical, superconducting circuits, where the logical bit is encoded in the energy eigenstates of the system. In circuit quantum electrodynamics, such a qubit is coupled to a microwave cavity allowing the qubit to be coherently controlled and read-out by probing the cavity. In this thesis, we theoretically investigate the destructive effects of noise which couple to the system as one tries to measure and control the qubits. We study the so called quantum capacitance read-out scheme, where the state of the qubit is mapped onto an equivalent capacitance of the circuit. It is shown that this is quantum limited, in the sense that the state of the qubit can be determined while simultaneously adding a minimum amount of noise to the system. Apart from the added noise, a measurement on a qubit will perturb it, causing the state to collapse to one of the measurement eigenstates. Such a state collapse can be utilized to generate entanglement between qubits by measuring on the cavity. We show that high-fidelity entangled states can be produced in this way and discuss the potential of the measurement to violate a bound given by local hidden variable theories. The possibility to prolong the life-time of the quantum state by active error correction is also investigated and we discuss limits on gate operation times to benefit from such a code, given realistic values for the error probabilities. This work was supported by the European Commission through IST-015708 EuroSQIP integrated pro ject, and by the Swedish Research Council.