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Optimized transmon molecule for high fidelity quantum non demolition readout using cross-Kerr coupling

Vladimir Milchakov

Published Mar 28, 2022• 0 citations
Publisher

Abstract

To carry out quantum computations, it is necessary to construct a circuit containing several interconnected qubits and be able to readout its states with high fidelity. The transverse dispersive coupling between a qubit and a microwave cavity is the most common technique of qubit readout in cQED. However, despite important progresses, implementing a fast high fidelity readout remains a major challenge. Indeed, inferring the qubit state is limited by the trade-off between speed and accuracy due to Purcell effect and unwanted transitions induced by readout photons in the cavity.This work focuses on an experimental investigation of cross-Kerr coupling and its benefits for qubit state readout, providing high fidelity and maximizing QNDness. To build a new readout scheme based on direct cross-Kerr coupling we employed a qubit architecture called "transmon molecule".The direct cross-Kerr coupling is a key point to our readout scheme since it prevents the qubit from Purcell effect.In order to realise the full potential of this system, thorough measurements were taken of an existing system, and then an improved version was designed and fabricated using a new nano fabrication recipe.To improve the qubit and readout performance, we have optimized different parameters: the circuit geometry has been adjusted to reduce the amplitude of the microwave electrical field at the interfaces; the electric circuit parameters were optimized to reach large detuning between the readout and the transmon frequencies; unwanted dipolar coupling between the transmon qubit and the cavity was reduced to avoid the Purcell effect.The fabrication recipe was also investigated and improved to get rid of residuals of resist on the surface of the substrate so-called "Veil of Death", improve the quality of aluminum and reproducibility of Josephson junctions.The measurements demonstrating the quantum non-demolition readout with fidelity as high as 99.4% and relaxation time 5 times higher than before - 20 microseconds.

DOI
10.70675/5977f52bzfe81z48b6zac1czb920eb3e800d

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To carry out quantum computations, it is necessary to construct a circuit containing several interconnected qubits and be able to readout its states with high fidelity. The transverse dispersive coupling between a qubit and a microwave cavity is the most common technique of qubit readout in cQED. However, despite important progresses, implementing a fast high fidelity readout remains a major challenge. Indeed, inferring the qubit state is limited by the trade-off between speed and accuracy due to Purcell effect and unwanted transitions induced by readout photons in the cavity.This work focuses on an experimental investigation of cross-Kerr coupling and its benefits for qubit state readout, providing high fidelity and maximizing QNDness. To build a new readout scheme based on direct cross-Kerr coupling we employed a qubit architecture called "transmon molecule".The direct cross-Kerr coupling is a key point to our readout scheme since it prevents the qubit from Purcell effect.In order to realise the full potential of this system, thorough measurements were taken of an existing system, and then an improved version was designed and fabricated using a new nano fabrication recipe.To improve the qubit and readout performance, we have optimized different parameters: the circuit geometry has been adjusted to reduce the amplitude of the microwave electrical field at the interfaces; the electric circuit parameters were optimized to reach large detuning between the readout and the transmon frequencies; unwanted dipolar coupling between the transmon qubit and the cavity was reduced to avoid the Purcell effect.The fabrication recipe was also investigated and improved to get rid of residuals of resist on the surface of the substrate so-called "Veil of Death", improve the quality of aluminum and reproducibility of Josephson junctions.The measurements demonstrating the quantum non-demolition readout with fidelity as high as 99.4% and relaxation time 5 times higher than before - 20 microseconds.
The field of superconducting qubits is constantly evolving with new circuit designs. However, when it comes to qubit readout, the use of simple transverse linear coupling remains overwhelmingly prevalent. This standard readout scheme has significant drawbacks: in addition to the Purcell effect, it suffers from a limitation on the maximal number of photons in the readout mode, which restricts the signal-to-noise ratio (SNR) and the Quantum Non-Demolition (QND) nature of the readout. Here, we explore the high-power regime by engineering a nonlinear coupling between a transmon qubit and its readout mode. Our approach builds upon previous work by Dassonneville et al. [Physical Review X 10, 011045 (2020)], on qubit readout with a non-perturbative cross-Kerr coupling in a transmon molecule. We demonstrate a readout fidelity of 99.21% with 89 photons utilizing a parametric amplifier. At this elevated photon number, the QND nature remains high at 96.7%. Even with up to 300 photons, the QNDness is only reduced by a few percent. This is qualitatively explained by deriving a critical number of photons associated with the nonlinear coupling, yielding a theoretical value of nˉrcrit=377\bar{n}_r^\text{crit} = 377nˉrcrit​=377 photons for our sample's parameters. These results highlight the promising performance of the transmon molecule in the high-power regime, establishing it as a compelling platform for high-fidelity qubit readout.
Dispersive readout of superconducting qubits relies on a transverse capacitive coupling that hybridizes the qubit with the readout resonator, subjecting the qubit to Purcell decay and measurement-induced state transitions (MIST). Despite the widespread use of Purcell filters to suppress qubit decay and near-quantum-limited amplifiers, dispersive readout often lags behind single- and two-qubit gates in both speed and fidelity. Here, we experimentally demonstrate junction readout, a simple readout architecture that realizes a strong qubit-resonator cross-Kerr interaction without relying on a transverse coupling. This interaction is achieved by coupling a transmon qubit to its readout resonator through both a capacitance and a Josephson junction. By varying the qubit frequency, we show that this hybrid coupling provides intrinsic Purcell protection and enhanced resilience to MIST, enabling readout at high photon numbers. While junction readout is compatible with conventional linear measurement, in this work we exploit the nonlinear coupling to intentionally engineer a large Kerr nonlinearity in the resonator, enabling bifurcation-based readout. Using this approach, we achieve a 99.4 % assignment fidelity with a 68 ns integration time and a 98.4 % QND fidelity without an external Purcell filter or a near-quantum-limited amplifier. These results establish the junction readout architecture with bifurcation-based readout as a scalable and practical alternative to dispersive readout, enabling fast, high-fidelity qubit measurement with reduced hardware overhead.
Molécule transmon optimisée pour une mesure quantique non destructrice en utilisant un couplage cross-Kerr Pour effectuer des calculs quantiques, il est nécessaire de construire un circuit contenant plusieurs qubits interconnectés et d'être capable de lire ses états avec une grande fidélité. Le couplage dispersif transverse entre un qubit et une cavité micro-ondes est la technique la plus courante de lecture de qubits en cQED. Cependant, malgré des progrès importants, la mise en œuvre d'une lecture rapide et de haute fidélité reste un défi majeur. En effet, l'inférence de l'état du qubit est limitée par le compromis entre vitesse et précision dû à l'effet Purcell et aux transitions indésirables induites par les photons de lecture dans la cavité.Ce travail se concentre sur une étude expérimentale du couplage cross-Kerr et de ses avantages pour la lecture de l'état du qubit, en fournissant une haute fidélité et en maximisant la QNDness. Pour construire un nouveau schéma de lecture basé sur le couplage direct cross-Kerr, nous avons utilisé une architecture de qubit appelée "molécule transmon".Le couplage direct de Kerr croisé est un point clé de notre système de lecture, car il empêche le qubit de subir l'effet Purcell.Afin de réaliser le plein potentiel de ce système, des mesures approfondies ont été effectuées sur un système existant, puis une version améliorée a été conçue et fabriquée à l'aide d'une nouvelle recette de nanofabrication.Pour améliorer les performances du qubit et de la lecture, nous avons optimisé différents paramètres : la géométrie du circuit a été ajustée pour réduire l'amplitude du champ électrique micro-ondes aux interfaces ; les paramètres du circuit électrique ont été optimisés pour obtenir un désaccord important entre la lecture et les fréquences du transmon ; le couplage dipolaire indésirable entre le qubit transmon et la cavité a été réduit pour éviter l'effet Purcell.La recette de fabrication a également été étudiée et améliorée afin de se débarrasser des résidus de résine à la surface du substrat, appelés "voile de la mort", d'améliorer la qualité de l'aluminium et la reproductibilité des jonctions Josephson.Les mesures démontrent la lecture sans démolition quantique avec une fidélité aussi élevée que 99,4 % et un temps de relaxation 5 fois plus élevé qu'auparavant - 20 microsecondes.
Fast, high-fidelity, and quantum nondemolition (QND) qubit readout is an essential element of quantum information processing. For superconducting qubits, state-of-the-art readout is based on a dispersive cross-Kerr coupling between a qubit and its readout resonator. The resulting readout can be high fidelity and QND, but readout times are currently limited to the order of 50 nanoseconds due to the dispersive cross-Kerr of magnitude 10 megahertz. Here, we present a readout scheme that uses the quarton coupler to facilitate a large (greater than 200 megahertz) cross-Kerr between a transmon qubit and its readout resonator. Full master equation simulations of the coupled system show a 5-nanosecond readout time with greater than 99% readout fidelity and greater than 99.9% QND fidelity. The quartonic readout circuit is experimentally feasible and preserves the coherence properties of the qubit. Our work reveals a path for order of magnitude improvements of superconducting qubit readout by engineering nonlinear light-matter couplings in parameter regimes unreachable by existing designs.
Superconducting transmon qubits form the backbone of today's leading quantum processors, where high field dispersive readout relies fundamentally on the shape and temporal structure of microwave control pulses. While transmon qubits offer improved robustness against charge noise, their performance is still strongly influenced by environmental coupling, particularly the Purcell effect and by the spectral characteristics of the readout pulses used for state preparation and logic operations. In this study, we present a rigorous comparative analysis of qubit coherence dynamics using measurement under four relevant configurations: a single-step rectangular pulse without Purcell decay, a single-step pulse subject to Purcell-induced relaxation, a two-step shaped pulse without Purcell effects, and a two-step shaped pulse incorporating Purcell decay. By solving the time-dependent Lindblad master equation for a three-level transmon system, we illustrate how readout pulse shaping and Purcell filtering independently and jointly influence qubit population dynamics, excited-state lifetime, and the final-state fidelity. The results demonstrate that two-step readout pulse shaping significantly improves coherence by suppressing overshoot and reducing higher-level population transfer, while the inclusion of Purcell mitigation further stabilizes the dynamics and enhances fidelity. The most notable observation is that the combined application of pulse shaping and Purcell filtering produces the most stable and highest fidelity qubit state discrimination. This unified perspective constitutes the central novelty of our work. Such a comparative framework, integrating pulse engineering with environmental decay modeling, has received limited explicit treatment in prior literature. The findings provide critical insights for optimizing both readout protocols and quantum hardware design in large scale superconducting quantum systems.
Superconducting qubits are a promising technology for building a scalable quantum computer. An important architecture employed in the field is called Circuit Quantum Electrodynamics (circuit QED), where such qubits are combined with high quality microwave cavities to study the interaction between artificial atoms and single microwave photons. The ultra-strong coupling achieved in these systems allows for control and readout of the quantum state of qubits to perform quantum information processing. The work on circuit QED performed in this thesis consisted of realizing an experimental setup for qubit experiments in a new laboratory, investigating the coherence and decay of higher energy levels of superconducting transmon qubits and finally demonstrating a novel coaxial form of circuit QED. Designing and building a 3D circuit QED setup involved the following main accomplishments: producing high quality 3D cavities; designing and installing the cryogenic microwave setup as well as the room temperature amplification and data acquisition circuitry; successfully developing a recipe for the fabrication of Josephson junctions; controlling and measuring superconducting 3D transmon qubits at 10mK. Several qubits were fully characterised and have shown coherence times of several microseconds and relaxation times up to 25μs. Superconducting qubits in fact possess higher energy levels that can provide significant computational advantages in quantum information applications. In experiments performed at MIT, preparation and control of the five lowest states of a transmon qubit was demonstrated, followed by an investigation of the phase coherence and decay dynamics of these higher energy levels. The decay was found to proceed mainly sequentially with relaxation times in excess of 20μs for all transitions. A direct measurement of the charge dispersion of these levels was performed to explore their characteristics of dephasing. This experiment was also reproduced on a 3D transmon fabricated and measured in Oxford, where due to a higher effective qubit temperature a multi-level decay model including thermal excitations was developed to explain the observed relaxation dynamics. Finally, a coaxial transmon, which we name the coaxmon, is presented and measured with a coaxial LC readout resonator and input/output coupling ports placed inline along the third dimension. This novel coaxial circuit QED architecture holds great promise for developing a scalable planar grid of qubits to build a quantum computer.