We study the interactions mediated by a symmetric superconducting quantum interference device (SQUID), their renormalizations, and the applicability of the anharmonic oscillator (bosonic) model for a coupled phase qubit. The latter dwells in its metastable well holding a number of anharmonic energy states. The coupling SQUID can switch between the single- and two-photon interactions in situ. We find that, in the bosonic two-photon regime, the cross-Kerr coupling never vanishes as it dresses due to asymmetry in the qubit potential and nonlinearity of the coupler. Our quantitative results also depend on the bosonic approximation. We approach determining its limits by finding the minimum number of coherent energy states required for a dressing. For that, we lay out diagrams of the dressing virtual processes that climb the qubit ladder as high as possible. Near the two-photon resonance with a coupled resonator, we systematically calculate other relevant renormalizations due to nonresonant interactions. We provide verifiable predictions for the coupling rates. Modified systems can be applied for two-photon detection and for quantum-nondemolition readout of a qubit with an asymmetrical potential.
We study the interactions mediated by a symmetric superconducting quantum interference device (SQUID), their renormalizations, and the applicability of the anharmonic oscillator (bosonic) model for a coupled phase qubit. The latter dwells in its metastable well holding a number of anharmonic energy states. The coupling SQUID can switch between the single- and two-photon interactions in situ. We find that, in the bosonic two-photon regime, the cross-Kerr coupling never vanishes as it dresses due to asymmetry in the qubit potential and nonlinearity of the coupler. Our quantitative results also depend on the bosonic approximation. We approach determining its limits by finding the minimum number of coherent energy states required for a dressing. For that, we lay out diagrams of the dressing virtual processes that climb the qubit ladder as high as possible. Near the two-photon resonance with a coupled resonator, we systematically calculate other relevant renormalizations due to nonresonant interactions. We provide verifiable predictions for the coupling rates. Modified systems can be applied for two-photon detection and for quantum-nondemolition readout of a qubit with an asymmetrical potential.
We consider a coupling element based on a symmetric superconducting quantum interference device (SQUID) and show that it mediates a two-photon interaction. This and other inductive interactions due to the SQUID can be switched off . We derive the system Hamiltonian for a coupled resonator and rf SQUID. The rf SQUID dwells in the vicinity of its metastable well holding a number of energy states and acts as an artificial atom. We discuss how the Josephson symmetry breaks owing to magnetic fields in the superconducting loops—both directly and via a nonzero superconducting phase difference over the rf SQUID. We assess that the two-photon coupling strength reaches 18 MHz which can exceed the single-photon capacitive interaction in the coupler.
Superconducting quantum circuits typically use capacitive charge-based linear coupling schemes to control interactions between elements such as qubits. While simple and effective, this coupling scheme makes it difficult to satisfy competing circuit design requirements such as maintaining large qubit anharmonicity and coherence along with a high degree of qubit connectivity and packing density. Moreover, tunable interactions using linear coupling elements produce dynamical variations in mode hybridization, which can induce non-adiabatic transitions, resulting in leakage errors and limiting gate speeds. In this work we attempt to address these challenges by proposing a junction-based coupling architecture based on SQUID (superconducting quantum interference device) couplers with relatively small Josephson energies. SQUID couplers provide intrinsic cross-Kerr interactions that can be controlled by external fluxes and that do not rely on mode hybridization. The small Josephson energies of the coupler maintain the interaction at a perturbative scale, which limits undesired higher-order mixing between coupled elements while achieving a sufficiently strong cross-Kerr interaction originating from diagonal coupling elements. Based on these properties, we show that a SQUID coupler can be used to implement a fast, adiabatic, and high-fidelity controlled-Z gate without introducing extra modes, and the operation is robust against junction asymmetry for high-frequency qubits. Although unconventional crosstalk may arise due to junction asymmetries and parasitic hybridization with spectator qubits, we show that these effects are sufficiently small for realistic circuit parameters. As an example of the utility of such junction-based coupling schemes, we present a scalable tiling strategy for a miniaturized superconducting quantum processor based on merged-element transmon qubits.
Abstract Analog quantum simulations offer rich opportunities for exploring complex quantum systems and phenomena through the use of specially engineered, well-controlled quantum systems. A critical element, increasing the scope and flexibility of such experimental platforms, is the ability to access and tune in situ different interaction regimes. Here, we present a superconducting circuit building block of two highly coherent transmons featuring in situ tuneable photon hopping and nonlinear cross-Kerr couplings. The interactions are mediated via a nonlinear coupler, consisting of a large capacitor in parallel with a tuneable superconducting quantum interference device (SQUID). We demonstrate the working principle by experimentally characterising the system in the single-excitation and two-excitation manifolds, and derive a full theoretical model that accurately describes our measurements. Both qubits have high coherence properties, with typical relaxation times in the range of 15 to 40 μs at all bias points of the coupler. Our device could be used as a scalable building block in analog quantum simulators of extended Bose-Hubbard and Heisenberg XXZ models, and may also have applications in quantum computing such as realising fast two-qubit gates and perfect state transfer protocols.
Strong nonlinear coupling of superconducting qubits and/or photons is a critical building block for quantum information processing. Because of the perturbative nature of the Josephson nonlinearity, linear coupling is often used in the dispersive regime to approximate nonlinear coupling. However, this dispersive coupling is weak and the underlying linear coupling mixes the local modes, which, for example, distributes unwanted self-Kerr nonlinearity to photon modes. Here, we use the quarton to yield purely nonlinear coupling between two linearly decoupled transmon qubits. The quarton's zero ϕ^{2} potential enables an ultrastrong gigahertz-level cross-Kerr coupling, which is an order of magnitude stronger compared to existing schemes, and the quarton's positive ϕ^{4} potential can cancel the negative self-Kerr nonlinearity of qubits to linearize them into resonators. This ultrastrong cross-Kerr coupling between bare modes of qubit-qubit, qubit-photon, and even photon-photon is ideal for applications such as single microwave photon detection, ultrafast two-qubit gates, and readout.
Abstract We theoretically investigate the photon statistical properties of a weakly-driven circuit quantum electrodynamic system with a cross-Kerr nonlinearity, which is built from two coupled transmon qubits through a superconducting quantum interference device (SQUID). We show that when two resonators are resonant with each other, photon blockade and sub-Poissonian photon statistics in the first superconducting transmission line resonator (TLR), TLR1, can be achieved by modulating the resonator-driving detunings and the cross-Kerr nonlinearity. Moreover, the optimal conditions for obtaining sub-Poissonian statistics are put forward through analytical derivations, which are in good agreement with those obtained by numerical simulations. We also examine the role of the resonator–resonator hopping interaction for photon statistics in TLR1 by numerically analyzing the case where the frequencies of two resonators are far detuned from each other. Due to the cutoff of the indirect transition paths in this case, the output field always acquires super-Poissonian statistics. In addition, a physical model with a SQUID embedded in TLR1 is proposed to tune the detuning between two TLRs, making it possible to demonstrate the importance of the resonator–resonator hopping interaction in obtaining a single-photon blockade. Thereby, our model of two coupled resonators with cross-Kerr nonlinearity has the potential to engineer the photon statistics through operating on the system parameters.
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.