Autoparametric resonance extending the bit-flip time of a cat qubit up to 0.3 s

Cat qubits, for which logical $|0\rangle$ and $|1\rangle$ are coherent states $|\pm\alpha\rangle$ of a harmonic mode, offer a promising route towards quantum error correction. Using dissipation to our advantage so that photon pairs of the harmonic mode are exchanged with single photons of its environment, it is possible to stabilize the logical states and exponentially increase the bit-flip time of the cat qubit with the photon number $|\alpha|^2$. Large two-photon dissipation rate $\kappa_2$ ensures fast qubit manipulation and short error correction cycles, which are instrumental to correct the remaining phase-flip errors in a repetition code of cat qubits. Here we introduce and operate an autoparametric superconducting circuit that couples a mode containing the cat qubit to a lossy mode whose frequency is set at twice that of the cat mode. This passive coupling does not require a parametric pump and reaches a rate $\kappa_2/2\pi\approx 2~\mathrm{MHz}$. With such a strong two-photon dissipation, bit-flip errors of the autoparametric cat qubit are prevented for a characteristic time up to 0.3 s with only a mild impact on phase-flip errors. Besides, we illustrate how the phase of a quantum superposition between $|\alpha\rangle$ and $|-\alpha\rangle$ can be arbitrarily changed by driving the harmonic mode while keeping the engineered dissipation active

Quantum control of a cat-qubit with bit-flip times exceeding ten seconds

Binary classical information is routinely encoded in the two metastable states of a dynamical system. Since these states may exhibit macroscopic lifetimes, the encoded information inherits a strong protection against bit-flips. A recent qubit - the cat-qubit - is encoded in the manifold of metastable states of a quantum dynamical system, thereby acquiring bit-flip protection. An outstanding challenge is to gain quantum control over such a system without breaking its protection. If this challenge is met, significant shortcuts in hardware overhead are forecast for quantum computing. In this experiment, we implement a cat-qubit with bit-flip times exceeding ten seconds. This is a four order of magnitude improvement over previous cat-qubit implementations, and six orders of magnitude enhancement over the single photon lifetime that compose this dynamical qubit. This was achieved by introducing a quantum tomography protocol that does not break bit-flip protection. We prepare and image quantum superposition states, and measure phase-flip times above 490 nanoseconds. Most importantly, we control the phase of these superpositions while maintaining the bit-flip time above ten seconds. This work demonstrates quantum operations that preserve macroscopic bit-flip times, a necessary step to scale these dynamical qubits into fully protected hardware-efficient architectures

Observation of Josephson Harmonics in Tunnel Junctions

Superconducting quantum processors have a long road ahead to reach fault-tolerant quantum computing. One of the most daunting challenges is taming the numerous microscopic degrees of freedom ubiquitous in solid-state devices. State-of-the-art technologies, including the world's largest quantum processors, employ aluminum oxide (AlO$_x$) tunnel Josephson junctions (JJs) as sources of nonlinearity, assuming an idealized pure $\sin\varphi$ current-phase relation (C$\varphi$R). However, this celebrated $\sin\varphi$ C$\varphi$R is only expected to occur in the limit of vanishingly low-transparency channels in the AlO$_x$ barrier. Here we show that the standard C$\varphi$R fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunneling through an inhomogeneous AlO$_x$ barrier predicts %-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The reality of Josephson harmonics transforms qubit design and prompts a reevaluation of models for quantum gates and readout, parametric amplification and mixing, Floquet qubits, protected Josephson qubits, etc. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and the associated errors in transmon qubits by an order of magnitude, while preserving anharmonicity

Observation of Josephson harmonics in tunnel junctions

Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminium oxide (AlO$_x$) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current–phase relation. However, this relation is expected to hold only in the limit of vanishingly low-transparency channels in the AlO$_x$ barrier. Here we show that the standard current–phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunnelling through an inhomogeneous AlO$_x$ barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlOx-based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity

Réalisation d’une dissipation multi-photonique grâce aux circuitssupraconducteurs pour la correction d’erreur quantique

Quantum systems can occupy peculiar states, such as superposition or entangled states. These states are intrinsically fragile and eventually get wiped out by inevitable interactions with the environment. Protecting quantum states against decoherence is a fundamental problem in physics and is pivotal for the future of quantum computing. In this thesis, we discuss experiments on superconducting circuits that investigate a new kind of qubit: the Schrödinger cat qubit. It belongs to the class of bosonic codes that store quantum information in the infinite dimensional Hilbert space of a microwave resonator. By carefully tailoring the dissipation of the resonator, we are able to stabilize the two basis states of the cat-qubit without affecting their superposition. In terms of errors, this translates into a reduced bit-flip rate while keeping a native phase-flip rate. This approach challenges the intuition that a qubit must be isolated from its environment. Instead, the dissipation acts as a feedback loop which continuously and autonomously corrects against errors. This enabling dissipation is known as two-photon dissipation and was engineered by the general method of parametric pumping. In our case, it is used to selectively intensify a two-to-one photon exchange interaction between the cat-qubit resonator and a dissipative resonator. To demonstrate error correction with cat-qubits, experimental efforts have been made during this thesis to cross the demanding threshold where the correction is faster than the occurrence of all errors, including those induced by the correcting mechanism itself. This has led us to question the current limitations of parametric pumping to better design our superconducting circuits. Mastering the dissipation engineering toolbox also brought us to other applications such as itinerant microwave photon detection for which an experimental proof of principle was realised during this thesis.Les états quantiques peuvent occuper des états particuliers tels que les états de superposition ou intriqués. Ces états sont fragiles et finissent toujours par être détruits par d’inévitables interactions avec l’environnement. La protection d’états quantiques contre la décohérence est un problème fondamental en physique, mais aussi un point crucial pour l’avenir de l’informatique quantique. Dans cette thèse, nous discutons d’expériences conduites sur des circuits supraconducteurs qui cherchent à mettre en évidence un nouveau qubit : le qubit de chat de Schrödinger. Ce qubit appartient à la classe des codes bosoniques qui encodent l’information quantique dans l’espace de Hilbert de dimension infinie d’un résonateur microonde. En modelant avec soin la dissipation de ce résonateur, nous parvenons à stabiliser les états de base du qubit de chat sans affecter leurs superpositions. En terme d’erreurs, cela se traduit en un taux de bit-flip réduit sans augmenter le taux de phase-flip initial. Cette approche vient défier l’intuition selon laquelle un qubit doit être isolé de son environnement. Au lieu de cela, cette dissipation bien choisie agit comme une boucle de rétroaction qui corrige les erreurs de manière continue et autonome. Cette dissipation décisive est connue sous le nom de dissipation à deux photons et est générée grâce à la méthode du pompage paramétrique. Dans notre cas, il est utilisé pour intensifier sélectivement une interaction d’échange de photons deux-pour-un entre le résonateur du qubit de chat et un autre résonateur dissipatif. Pour démontrer la correction d’erreur avec les qubits de chats, des efforts expérimentaux ont été fournis pendant cette thèse pour franchir le seuil au delà duquel la correction est plus rapide que l’apparition de nouvelles erreurs, notamment celles induites par le mécanisme de correction lui-même. Ceci nous a conduit à questionner les limites actuelles du pompage paramétrique afin de mieux concevoir nos circuits supraconducteurs. Maitriser ces dissipations exotiques nous a aussi amené à d’autres applications telles que la détection de photon microondes itinérants pour laquelle une preuve de principe expérimentale a été réalisée au cours de cette thèse

Réalisation d’une dissipation multi-photonique grâce aux circuitssupraconducteurs pour la correction d’erreur quantique

Quantum systems can occupy peculiar states, such as superposition or entangled states. These states are intrinsically fragile and eventually get wiped out by inevitable interactions with the environment. Protecting quantum states against decoherence is a fundamental problem in physics and is pivotal for the future of quantum computing. In this thesis, we discuss experiments on superconducting circuits that investigate a new kind of qubit: the Schrödinger cat qubit. It belongs to the class of bosonic codes that store quantum information in the infinite dimensional Hilbert space of a microwave resonator. By carefully tailoring the dissipation of the resonator, we are able to stabilize the two basis states of the cat-qubit without affecting their superposition. In terms of errors, this translates into a reduced bit-flip rate while keeping a native phase-flip rate. This approach challenges the intuition that a qubit must be isolated from its environment. Instead, the dissipation acts as a feedback loop which continuously and autonomously corrects against errors. This enabling dissipation is known as two-photon dissipation and was engineered by the general method of parametric pumping. In our case, it is used to selectively intensify a two-to-one photon exchange interaction between the cat-qubit resonator and a dissipative resonator. To demonstrate error correction with cat-qubits, experimental efforts have been made during this thesis to cross the demanding threshold where the correction is faster than the occurrence of all errors, including those induced by the correcting mechanism itself. This has led us to question the current limitations of parametric pumping to better design our superconducting circuits. Mastering the dissipation engineering toolbox also brought us to other applications such as itinerant microwave photon detection for which an experimental proof of principle was realised during this thesis.Les états quantiques peuvent occuper des états particuliers tels que les états de superposition ou intriqués. Ces états sont fragiles et finissent toujours par être détruits par d’inévitables interactions avec l’environnement. La protection d’états quantiques contre la décohérence est un problème fondamental en physique, mais aussi un point crucial pour l’avenir de l’informatique quantique. Dans cette thèse, nous discutons d’expériences conduites sur des circuits supraconducteurs qui cherchent à mettre en évidence un nouveau qubit : le qubit de chat de Schrödinger. Ce qubit appartient à la classe des codes bosoniques qui encodent l’information quantique dans l’espace de Hilbert de dimension infinie d’un résonateur microonde. En modelant avec soin la dissipation de ce résonateur, nous parvenons à stabiliser les états de base du qubit de chat sans affecter leurs superpositions. En terme d’erreurs, cela se traduit en un taux de bit-flip réduit sans augmenter le taux de phase-flip initial. Cette approche vient défier l’intuition selon laquelle un qubit doit être isolé de son environnement. Au lieu de cela, cette dissipation bien choisie agit comme une boucle de rétroaction qui corrige les erreurs de manière continue et autonome. Cette dissipation décisive est connue sous le nom de dissipation à deux photons et est générée grâce à la méthode du pompage paramétrique. Dans notre cas, il est utilisé pour intensifier sélectivement une interaction d’échange de photons deux-pour-un entre le résonateur du qubit de chat et un autre résonateur dissipatif. Pour démontrer la correction d’erreur avec les qubits de chats, des efforts expérimentaux ont été fournis pendant cette thèse pour franchir le seuil au delà duquel la correction est plus rapide que l’apparition de nouvelles erreurs, notamment celles induites par le mécanisme de correction lui-même. Ceci nous a conduit à questionner les limites actuelles du pompage paramétrique afin de mieux concevoir nos circuits supraconducteurs. Maitriser ces dissipations exotiques nous a aussi amené à d’autres applications telles que la détection de photon microondes itinérants pour laquelle une preuve de principe expérimentale a été réalisée au cours de cette thèse

Structural Instability of Driven Josephson Circuits Prevented by an Inductive Shunt

International audienceSuperconducting circuits are a versatile platform to implement a multitude of Hamiltonians that perform quantum computation, simulation, and sensing tasks. A key ingredient for realizing a desired Hamiltonian is the irradiation of the circuit by a strong drive. These strong drives provide an in situ control of couplings, which cannot be obtained by near-equilibrium Hamiltonians. However, as shown in this paper, out-of-equilibrium systems are easily plagued by complex dynamics, leading to instabilities. The prediction and prevention of these instabilities is crucial, both from a fundamental and application perspective. We propose an inductively shunted transmon as the elementary circuit optimized for strong parametric drives. Developing a numerical approach that avoids the built-in limitations of perturbative analysis, we demonstrate that adding the inductive shunt significantly extends the range of pump powers over which the circuit behaves in a stable manner

Escape of a Driven Quantum Josephson Circuit into Unconfined States

International audienceJosephson circuits have been ideal systems with which to study complex nonlinear dynamics that can lead to chaotic behavior and instabilities. More recently, Josephson circuits in the quantum regime, particularly in the presence of microwave drives, have demonstrated their ability to emulate a variety of Hamiltonians that are useful for the processing of quantum information. In this paper, we show that these drives lead to an instability that results in the escape of the circuit mode into states that are not confined by the Josephson cosine potential. We observe this escape in a ubiquitous circuit: a transmon embedded in a 3D cavity. When the transmon occupies these free-particle-like states, the circuit behaves as though the junction had been removed and all nonlinearities are lost. This work deepens our understanding of strongly driven Josephson circuits, which is important for fundamental and application perspectives, such as the engineering of Hamiltonians by parametric pumping