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Bulletin of the American Physical Society

Towards High-Fidelity Gates in the Soft Zero-Pi Qubit

Anjali Premkumar, András Gyenis, Xanthe Croot, Pranav Mundada, Agustín Di Paolo, Jens Koch, Alexandre Blais, Andrew Houck

Published Mar 19, 2021• 0 citations
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This dissertation explores three types of protected superconducting qubits: the rhombusqubit, the 0-π qubit, and the gyrator qubit. For the rhombus qubit, we analyze both symmetric and asymmetric circuit variants, quantizing the system and comparing their energy spectra. We find that the symmetric rhombus exhibits exponential protection against both depolarization and charge noise-induced dephasing. Importantly, we show that introducing asymmetry yields a firstorder flux noise sweet spot, which can significantly extend qubit coherence and improve gate depth. For the soft 0-π qubit, we study single- and two-qubit gates using microwave drives. We demonstrate that driving nθ achieves higher-fidelity single qubit X gate than driving nφ, with simulated fidelities ∼ 99.9% and gate time ∼ 30 ns for T1 = Tφ = 30µs. We also develop two kinds of two-qubit gates, CZ and CNOT gates. These gates are realized using both direct and Raman-type transitions, with fidelities ∼ 99.9% and gate times around 160 ns for T1 = Tφ = 30µs. We also propose a method to generate GKP states using parametrically induced gyration between coupled oscillators. We describe a circuit implementation using a modulated inductor and derive the corresponding quantum Hamiltonian. Importantly I show that having an imperfect gyration ratio degrades the code space of gyrator qubit. Finally I develop a graph-theoretic approach to enumerate superconducting circuits and identify candidates with favorable coherence properties. Applying this framework, we compare transmon, fluxonium, and rhombus qubits in terms of relaxation time, dephasing, and expected gate count, finding that the asymmetric rhombus offers competitive, and potentially superior, performance.

•Apr 11, 2025•0 citations
The 0-π qubit promises longer lifetimes than the transmon, making it a strong candidate for a next-generation, lower-error qubit. Gyenis et al. experimentally demonstrated an unprotected single-qubit gate in the soft 0-π regime [1], but no corresponding two-qubit gate has yet been proposed. We propose an unprotected CZ gate for capacitively coupled soft 0-π qubits. The gate uses a direct transition between a computational state and a higher non-computational state. Assuming negligible device disorder and a phenomenological noise model, the simulated CZ gate achieves a fidelity of approximately 99.9% at a gate time of approximately 160 ns.
We study the implementation of Grover’s algorithm in an Ising spin chain quantum computer. In our scheme, we removed the application of time delay whenever a qubit operation is performed. Instead, we introduced a set of modified pulses that utilizes the interaction of the neighboring qubit. In principle, the absence of time delay pulses allows the overall rotation pulses to be applied simultaneously to execute a gate. We show that the fidelity remains high after continuous application of π/2 pulses. The error arising from the unitary evolution is minimized by using soft pulses. Finally, the probability of finding the target state remain bounded through the application of fixed-point quantum search scheme.
This dissertation explores three types of protected superconducting qubits: the rhombusqubit, the 0-π qubit, and the gyrator qubit. For the rhombus qubit, we analyze both symmetric and asymmetric circuit variants, quantizing the system and comparing their energy spectra. We find that the symmetric rhombus exhibits exponential protection against both depolarization and charge noise-induced dephasing. Importantly, we show that introducing asymmetry yields a firstorder flux noise sweet spot, which can significantly extend qubit coherence and improve gate depth. For the soft 0-π qubit, we study single- and two-qubit gates using microwave drives. We demonstrate that driving nθ achieves higher-fidelity single qubit X gate than driving nφ, with simulated fidelities ∼ 99.9% and gate time ∼ 30 ns for T1 = Tφ = 30µs. We also develop two kinds of two-qubit gates, CZ and CNOT gates. These gates are realized using both direct and Raman-type transitions, with fidelities ∼ 99.9% and gate times around 160 ns for T1 = Tφ = 30µs. We also propose a method to generate GKP states using parametrically induced gyration between coupled oscillators. We describe a circuit implementation using a modulated inductor and derive the corresponding quantum Hamiltonian. Importantly I show that having an imperfect gyration ratio degrades the code space of gyrator qubit. Finally I develop a graph-theoretic approach to enumerate superconducting circuits and identify candidates with favorable coherence properties. Applying this framework, we compare transmon, fluxonium, and rhombus qubits in terms of relaxation time, dephasing, and expected gate count, finding that the asymmetric rhombus offers competitive, and potentially superior, performance.