Flux-tunable qubits are a useful resource for superconducting quantum processors. They can be used to perform cPhase gates, facilitate fast reset protocols, avoid qubit-frequency collisionsin large processors, and enable certain fast readout schemes. However, flux-tunable qubits suffer from a trade-off between their tunability range and sensitivity to flux noise. Optimizing this trade-off is particularly important for enabling fast, high-fidelity, all-microwave cross-resonance gates in large, high-coherence processors. This is mainly because cross-resonance gates set stringent conditions on the frequency landscape of neighboring qubits, which are difficult to satisfy with non-tunable transmons due to their relatively large fabrication imprecision. To solve this problem, we realize a coherent, flux-tunable, transmon-like qubit, which exhibits a frequency tunability range as small as 43 MHz, and whose frequency, anharmonicity and tunability range are set by a few experimentally achievable design parameters. Such a weakly tunable qubit is useful for avoiding frequency collisions in a large lattice while limiting its susceptibility to flux noise.
Flux-tunable qubits are a useful resource for superconducting quantum processors. They can be used to perform cPhase gates, facilitate fast reset protocols, avoid qubit-frequency collisionsin large processors, and enable certain fast readout schemes. However, flux-tunable qubits suffer from a trade-off between their tunability range and sensitivity to flux noise. Optimizing this trade-off is particularly important for enabling fast, high-fidelity, all-microwave cross-resonance gates in large, high-coherence processors. This is mainly because cross-resonance gates set stringent conditions on the frequency landscape of neighboring qubits, which are difficult to satisfy with non-tunable transmons due to their relatively large fabrication imprecision. To solve this problem, we realize a coherent, flux-tunable, transmon-like qubit, which exhibits a frequency tunability range as small as 43 MHz, and whose frequency, anharmonicity and tunability range are set by a few experimentally achievable design parameters. Such a weakly tunable qubit is useful for avoiding frequency collisions in a large lattice while limiting its susceptibility to flux noise.
Hamiltonians of the superconducting qubits of Transmon type involve non-zero ZZ-interaction terms due to their finite and small anharmonicities. These terms might lead to the unwantedaccumulation of spurious phases during the execution of the two-qubit gates. Exact calculation of the ZZ-interaction rates requires the full diagonalization of the circuit Hamiltonians which very quickly becomes computationally demanding as the number of the modes in the coupler circuit increases. Here we propose a direct analytical method for the accurate estimation of the ZZ-interaction rates between low-anharmonicity qubits in the dispersive limit of the multi-mode circuit-QED. We observe very good agreement between the predictions of our method and the measurement data collected from the multi-qubit devices. Our method being an extension of our previous work in [1] is a new addition to the toolbox of the quantum microwave engineers as it relates the ZZ-interaction rates directly to the entries of the impedance matrix defined between the qubit ports.
For superconducting quantum processors consisting of low anharmonicity qubits such as transmons we give a complete microwave description of the system in the qubit subspace. We assumethat the qubits are dispersively coupled to a distributed microwave structure such that the detunings of the qubits from the internal modes of the microwave structure are stronger than their couplings. We define qubit ports across the terminals of the Josephson junctions and drive ports where transmission lines carrying drive signals reach the chip and we obtain the multiport impedance response of the linear passive part of the system between the ports. We then relate interaction parameters in between qubits and between the qubits and the environment to the entries of this multiport impedance function: in particular we show that the exchange coupling rate J between qubits is related in a simple way to the off-diagonal entry connecting the qubit ports. Similarly we relate couplings of the qubits to voltage drives and lossy environment to the entries connecting the qubits and the drive ports. Our treatment takes into account all the modes (possibly infinite) that might be present in the distributed electromagnetic structure and provides an efficient method for the modeling and analysis of the circuits.
With the increase of complexity and coherence of superconducting systems made using the principles of circuit quantum electrodynamics, more accurate methods are needed for the characterization,analysis and optimization of these quantum processors. Here we introduce a new method of modelling that can be applied to superconducting structures involving multiple Josephson junctions, high-Q superconducting cavities, external ports, and voltage sources. Our technique, an extension of our previous work on single-port structures [1], permits the derivation of system Hamiltonians that are capable of representing every feature of the physical system over a wide frequency band and the computation of T1 times for qubits. We begin with a black box model of the linear and passive part of the system. Its response is given by its multiport impedance function Zsim(w), which can be obtained using a finite-element electormagnetics simulator. The ports of this black box are defined by the terminal pairs of Josephson junctions, voltage sources, and 50 Ohm connectors to high-frequency lines. We fit Zsim(w) to a positive-real (PR) multiport impedance matrix Z(s), a function of the complex Laplace variable s. We then use state-space techniques to synthesize a finite electric circuit admitting exactly the same impedance Z(s) across its ports; the PR property ensures the existence of this finite physical circuit. We compare the performance of state-space algorithms to classical frequency domain methods, justifying their superiority in numerical stability. The Hamiltonian of the multiport model circuit is obtained by using existing lumped element circuit quantization formalisms [2, 3]. Due to the presence of ideal transformers in the model circuit, these quantization methods must be extended, requiring the introduction of an extension of the Kirchhoff voltage and current laws.
We propose a new quantization method for superconducting electronic circuits involving a Josephson junction device coupled to a linear microwave environment. The method is based onan exact impedance synthesis of the microwave environment considered as a blackbox with impedance function Z(s). The synthesized circuit captures dissipative dynamics of the system with resistors coupled to the reactive part of the circuit in a non-trivial way. We quantize the circuit and compute relaxation rates following previous formalisms for lumped element circuit quantization. Up to the errors in the fit our method gives an exact description of the system and its losses.