The availability of non-linearities provided through the Josephson junction is superconducting circuits is a key ingredient for the realization of quantum information processing devices. However, the non-linearities provided by the Josephson junction are typically accompanied by a Kerr non-linearity, which is detrimental for the performance of quantum error correction protocols.
In the larger scope of this project, my co-authors and I investigate the possibility of achieving universal control of a bosonic mode without the presence of a static Kerr non-linearity. We show that this is possible by balancing the even- and odd-order nonlinearities of the Superconducting Asymmetric Nonlinear Element (SNAIL). This project started with a theory proposal published in Physical Review Letters and has recently been completed with the experimental realization of the proposed scheme. The experimental results are under review in nature communications.
References
2023
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Resolving Fock states near the Kerr-free point of a superconducting resonator
Yong Lu, Marina Kudra, Timo Hillmann, Jiaying Yang, Hang-Xi Li, Fernando Quijandría, and 1 more author
npj Quantum Inf, Nov 2023
We have designed a tunable nonlinear resonator terminated by a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement). Such a device possesses a Kerr-free point in which the external magnetic flux allows to suppress the Kerr interaction. We have excited photons near this Kerr-free point and characterized the device using a transmon qubit. The excitation spectrum of the qubit allows to observe photon-number-dependent frequency shifts about nine times larger than the qubit linewidth. Our study demonstrates a compact integrated platform for continuous-variable quantum processing that combines large couplings, considerable relaxation times and excellent control over the photon mode structure in the microwave domain.
2022
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Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops
Timo Hillmann, and Fernando Quijandría
Phys. Rev. Applied, Jun 2022
Continuous-variable systems realized in high-coherence microwave cavities are a promising platform for quantum information processing. While strong dynamic nonlinear interactions are desired to implement fast and high-fidelity quantum operations, static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Here we study theoretical models of nonlinear oscillators describing superconducting quantum circuits with asymmetric Josephson-junction loops. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. We support our analytical results by numerical experiments and show that the effective Kerr-type couplings can be canceled by an interplay of higher-order nonlinearities. This can be better understood in a simplified model supporting only cubic and quartic nonlinearities. Our results show that a cubic interaction allows an increase in the effective rates of both linear and nonlinear operations without an increase in the undesired anharmonicity of an oscillator which is crucial for many bosonic encodings.
2020
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Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
Timo Hillmann, Fernando Quijandría, Göran Johansson, Alessandro Ferraro, Simone Gasparinetti, and Giulia Ferrini
Phys. Rev. Lett., Oct 2020
We provide an explicit construction of a universal gate set for continuous-variable quantum computation with microwave circuits. Such a universal set has been first proposed in quantum-optical setups, but its experimental implementation has remained elusive in that domain due to the difficulties in engineering strong nonlinearities. Here, we show that a realistic three-wave mixing microwave architecture based on the superconducting nonlinear asymmetric inductive element [Frattini et al., Appl. Phys. Lett. 110, 222603 (2017)] allows us to overcome this difficulty. As an application, we show that this architecture allows for the generation of a cubic phase state with an experimentally feasible procedure. This work highlights a practical advantage of microwave circuits with respect to optical systems for the purpose of engineering non-Gaussian states and opens the quest for continuous-variable algorithms based on few repetitions of elementary gates from the continuous-variable universal set.