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arXiv:2210.04793 · Physical Review Applied

Transmon-qubit readout using an in situ bifurcation amplification in the mesoscopic regime

Rémy Dassonneville, Tomás Ramos, Vladimir Milchakov, C. Mori, Luca Planat, F. Foroughi, Cécile Naud, Wiebke Guichard, Juan José García‐Ripoll, Nicolas Roch, O. Buisson

Published Oct 19, 2023• 5 citations
arXivHTMLPDF

Abstract

We demonstrate a transmon-qubit readout based on the nonlinear response to a drive of polaritonic meters in situ coupled to the qubit. Inside a three-dimensional readout cavity, we place a transmon molecule consisting of a transmon qubit and an ancilla mode interacting via nonperturbative cross-Kerr-coupling. The cavity couples strongly only to the ancilla mode, leading to hybridized lower and upper polaritonic meters. Both polaritons are anharmonic and dissipative, as they inherit a self-Kerr nonlinearity $U$ from the ancilla and effective decay $\ensuremath{\kappa}$ from the open cavity. Via the ancilla, the polariton meters also inherit the nonperturbative cross-Kerr-coupling to the qubit. This results in a high qubit-dependent displacement $2\ensuremath{\chi}>\ensuremath{\kappa},U$ that can be read out via the cavity without causing Purcell decay. Moreover, the polariton meters, being nonlinear resonators, present bistability, and bifurcation behavior when the probing power increases. In this work, we focus on the bifurcation at low power in the few-photon regime, called the mesoscopic regime, which is accessible when the self-Kerr and decay rates of the polariton meter are similar, $U\ensuremath{\sim}\ensuremath{\kappa}$. Capitalizing on a latching mechanism by bifurcation, the readout is sensitive to transmon-qubit relaxation error only in the first tens of nanoseconds. We thus report a single-shot fidelity of 98.6% while having an integration time of 500 ns and no requirement for an external quantum-limited amplifier.

DOI
10.1103/physrevapplied.20.044050

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We demonstrate a transmon-qubit readout based on the nonlinear response to a drive of polaritonic meters in situ coupled to the qubit. Inside a three-dimensional readout cavity, we place a transmon molecule consisting of a transmon qubit and an ancilla mode interacting via nonperturbative cross-Kerr-coupling. The cavity couples strongly only to the ancilla mode, leading to hybridized lower and upper polaritonic meters. Both polaritons are anharmonic and dissipative, as they inherit a self-Kerr nonlinearity UUU from the ancilla and effective decay \ensuremathκ\ensuremath{\kappa}\ensuremathκ from the open cavity. Via the ancilla, the polariton meters also inherit the nonperturbative cross-Kerr-coupling to the qubit. This results in a high qubit-dependent displacement 2\ensuremathχ>\ensuremathκ,U2\ensuremath{\chi}>\ensuremath{\kappa},U2\ensuremathχ>\ensuremathκ,U that can be read out via the cavity without causing Purcell decay. Moreover, the polariton meters, being nonlinear resonators, present bistability, and bifurcation behavior when the probing power increases. In this work, we focus on the bifurcation at low power in the few-photon regime, called the mesoscopic regime, which is accessible when the self-Kerr and decay rates of the polariton meter are similar, U\ensuremath∼\ensuremathκU\ensuremath{\sim}\ensuremath{\kappa}U\ensuremath∼\ensuremathκ. Capitalizing on a latching mechanism by bifurcation, the readout is sensitive to transmon-qubit relaxation error only in the first tens of nanoseconds. We thus report a single-shot fidelity of 98.6% while having an integration time of 500 ns and no requirement for an external quantum-limited amplifier.
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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.
Bosonic codes in superconducting resonators are a hardware-efficient avenue for quantum error correction and benefit from the inherent bias toward relaxation errors provided by long-lived cavities compared to typical superconducting qubits. The required coupling to an ancillary control qubit, however, can negate these benefits by inducing highly detrimental effects such as excess decoherence and undesired nonlinearities. This is exemplified by the typically employed transmon qubit that imposes limits on cavity operations due to its finite lifetime as well as the inevitably induced self-Kerr nonlinearity. An important question is thus whether a cavity-qubit coupling can be realized that offers readout and control capabilities without spoiling the cavity. Here, motivated by its long lifetime and design flexibility of its Hamiltonian, we experimentally investigate the fluxonium as a control qubit for superconducting cavities. We couple a fluxonium qubit to a superconducting resonator in the strong-dispersive regime and use it to measure the coherence and flux-tunable inherited nonlinearities of the resonator. We then demonstrate quantum control of the oscillator by preparing and characterizing resonator Fock states and their superpositions, with fidelities limited by resonator decay in our planar prototype device. Finally, we show that the fluxonium can realize cavity-couplings that eliminate undesirable cavity nonlinearities and reach regimes of suppressed self-Kerr that are inaccessible to transmon-based devices. Our results thus demonstrate the potential of the fluxonium as a high-performance bosonic control qubit for superconducting cavities that can outperform existing transmon-based architectures.
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.
One of the most studied model systems in quantum optics is a two-level atom strongly coupled to a single mode of the electromagnetic field stored in a cavity, a research field named cavity quantum electrodynamics or CQED. CQED has recently received renewed attention due to its implementation with superconducting artificial atoms and coplanar resonators in the so-called circuit quantum electrodynamics (cQED) architecture. In cQED, the couplings can be much stronger than in CQED due to the design flexibility of superconducting circuits and to the enhanced field confinement in one-dimensional cavities. This enabled the realization of fundamental quantum physics and quantum information processing experiments with a degree of control comparable to that obtained in CQED. The purpose of this chapter is to investigate the situation where the resonator to which the atom is coupled is made nonlinear with a Kerr-type nonlinearity, causing its energy levels to be nonequidistant. The system is then described by a nonlinear Jaynes-Cummings Hamiltonian. This considerably enriches the physics since a pumped nonlinear resonator displays bistability, parametric amplification, and squeezing. The interplay of strong coupling and these nonlinear effects constitutes a novel model system for quantum optics that can be implemented experimentally with superconducting circuits. This chapter is organized as follows. In a first section we present the system consisting of a superconducting Kerr nonlinear resonator strongly coupled to a transmon qubit. In the second section, we describe the response of the sole nonlinear resonator to an external drive. In the third section, we show how the resonator bistability can be used to perform a high-fidelity readout of the transmon qubit. In the last section, we investigate the quantum backaction exerted by the intracavity field on the qubit.
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.