Efficient Decoupling of a Nonlinear Qubit Mode from Its Environment
Frank Pfeiffer, Max Werninghaus, C. Schweizer, N. Bruckmoser, L. Koch, Niklas J. Glaser, Gerhard B. P. Huber, D. Bunch, Franz X. Haslbeck, Martin Knudsen, Gleb Krylov, Klaus Liegener, Achim Marx, L. Richard, João H. Romeiro, Federico Roy, Johannes Schirk, C. M. F. Schneider, M. Singh, Lasse Södergren, Ivan Tsitsilin, Florian Wallner, Carlos A. Riofrío, Stefan Filipp
To control and measure the state of a quantum system, it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect, photon-induced dephasing from measurement backaction, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multimode element—an artificial molecule—with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential nonlinear modes, one of which is flux insensitive and used as the protected qubit mode. The second mode is flux tunable and serves via a cross-Kerr-type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit, which we refer to as P-mon, with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed. Published by the American Physical Society 2024
To control and measure the state of a quantum system, it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect, photon-induced dephasing from measurement backaction, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multimode element—an artificial molecule—with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential nonlinear modes, one of which is flux insensitive and used as the protected qubit mode. The second mode is flux tunable and serves via a cross-Kerr-type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit, which we refer to as P-mon, with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed. Published by the American Physical Society 2024
To scale superconducting quantum processors, it is essential to achieve long coherence times while engineering interactions that do not introduce additional decoherence channels. In superconducting qubit systems, this can be realized using multimode circuits that feature a protected qubit mode alongside a distinct mediator mode. Building on this concept, our recently developed P-mon qubit provides intrinsic protection against decoherence from the readout environment. We extend this approach to controlled two-qubit interactions, by exploiting the mediator modes of P-mons for on-demand coupling. Because direct interactions between the qubit modes are strongly suppressed, unwanted ZZ-type interactions are significantly reduced to below 3.6(5)kHz in the idle state. When tuning the coupled mediator modes on resonance, the cross-Kerr interaction between the qubit and the hybridized mediator modes leads to a qubit-state dependent frequency shift. By selectively addressing these transitions, we implement a 180ns long CZ gate and determine a fidelity of $99.62(4)~\text{%}$. These results represent a significant step toward a scalable superconducting architecture that maintains high performance at scale.
Rapid reset and readout of qubit states are essential for quantum error correction, yet accelerating these operations through stronger coupling to a dissipative environment inevitably increases qubit decay via the Purcell effect. Here we present a broadband Purcell filter that decouples the reset and readout paths, enabling both operations to be independently optimized without compromising qubit coherence. The filter employs two engineered notches - an intrinsic notch and a bandstop notch - to provide broadband Purcell protection, together with an additional reset stub that creates a reset mode below the protected band. To enable fast reset while suppressing filter-mediated interactions between qubits, we couple each qubit to a dedicated reset resonator. We experimentally demonstrate Purcell-limited relaxation times exceeding 1 ms across a 1.2 GHz bandwidth, simultaneously with 500 ns readout without a Josephson parametric amplifier and 100 ns reset with 99.6% efficiency. The reset resonator is designed with a deliberate kappa-chi mismatch, which suppresses photon-shot-noise-induced dephasing by a factor of 70 compared to the readout resonator. Our work provides a scalable hardware solution that resolves the traditional trade-off between fast qubit operations and qubit protection, advancing the prospects for fault-tolerant quantum computing.
Efficient qubit reset and leakage reduction are essential for scalable superconducting quantum computing, particularly in the context of quantum error correction. However, such operations often require additional on-chip components. Here, we propose and experimentally demonstrate a hardware-efficient approach to qubit reset and readout using a multi-mode Purcell filter in a superconducting quantum circuit. We exploit the inherent multi-mode structure of a coplanar waveguide resonator, using its fundamental and second-order modes for qubit reset and readout, respectively, thereby avoiding additional components. Implemented in a flip-chip architecture, our device achieves unconditional reset with residual excitation below 1\% in 220 ns, and a leakage reduction unit that selectively resets the second excited state within 62 ns with a residual ∣f⟩ population of 6.1\%, accounting for the readout error. Despite the qubits being directly coupled to the filter in our configuration, the measured relaxation times are not degraded owing to intrinsic Purcell protection provided by an auxiliary mode. To our knowledge, this is the first experimental trial that exploits different-order modes of a microwave resonator for distinct qubit operations, representing a new direction toward scalable, hardware-efficient quantum processor design.
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.
Achieving high-fidelity qubit readout and reset while maintaining qubit coherence is crucial for quantum error correction and advanced quantum algorithms. Here, we design and experimentally demonstrate a scalable architecture based on frequency-tunable nonlinear Purcell filters, which enables flexible readout and rapid unconditional reset of multiple superconducting qubits. Our readout protocol dynamically adjusts the effective linewidth of the readout resonator through a tunable Purcell filter, optimizing the signal-to-noise ratio during measurement while suppressing photon noise during idle periods. Combined with a multilevel readout protocol, we achieve the highest readout fidelity of 99.3% without any quantum-limited amplifier, even with a small dispersive shift. Moreover, by leveraging a reset channel formed via the adjacent coupling between the filter and the coupler, we realize unconditional qubit reset of both leakage-induced |2⟩ and |1⟩ states within 200 ns and reset of the |1⟩ state alone within 75 ns, with error rates ≤1%. The filter also mitigates both photon-induced dephasing and the Purcell effect, thereby preserving qubit coherence. This scalable Purcell filter architecture shows exceptional performance in qubit readout, reset, and protection, marking it as a promising hardware component for advancing fault-tolerant quantum computing systems.
We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable qubit-resonator coupling strength g. This coupling can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0, the qubit is in a decoherence-free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore, we show that in this decoherence-free subspace, the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement.