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Experimental Realization of a Protected Superconducting Circuit Derived from the 0 - π Qubit

András Gyenis, Pranav Mundada, Agustín Di Paolo, Thomas Hazard, Xinyuan You, David Schuster, Jens Koch, Alexandre Blais, Andrew Houck

Published Mar 5, 2021• 0 citations
Publisher

Abstract

Encoding a qubit in logical quantum states with wave functions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. One of the most promising candidates for such a fully protected superconducting qubit is the 0-π circuit [Brooks et al., Phys. Rev. A 87, 052306 (2013)]. Here we realize the proposed circuit topology in an experimentally obtainable parameter regime, where the ground-state degeneracy is lifted but the qubit is still largely noise protected. More precisely, the logical states of this qubit feature disjoint support and are exponentially protected against relaxation and exponentially (first order) protected against dephasing due to charge (flux) noise. We name the resultant device the "soft 0-π qubit."Multitone spectroscopy measurements reveal the energy-level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. Using a Raman-type protocol, we exploit a higher-lying charge-insensitive energy level of the device to realize coherent population transfer and logical operations. The measured relaxation (T1 = 1.6 ms) and dephasing (TR = 9 μs, T2E = 25μs) times demonstrate that the soft 0-π circuit not only broadens the family of superconducting qubits but also constitutes an important step toward quantum computing with intrinsically protected superconducting qubits.

DOI
10.6082/52y9p-aay56

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Encoding a qubit in logical quantum states with wave functions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. One of the most promising candidates for such a fully protected superconducting qubit is the 0-π circuit [Brooks et al., Phys. Rev. A 87, 052306 (2013)]. Here we realize the proposed circuit topology in an experimentally obtainable parameter regime, where the ground-state degeneracy is lifted but the qubit is still largely noise protected. More precisely, the logical states of this qubit feature disjoint support and are exponentially protected against relaxation and exponentially (first order) protected against dephasing due to charge (flux) noise. We name the resultant device the "soft 0-π qubit."Multitone spectroscopy measurements reveal the energy-level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. Using a Raman-type protocol, we exploit a higher-lying charge-insensitive energy level of the device to realize coherent population transfer and logical operations. The measured relaxation (T1 = 1.6 ms) and dephasing (TR = 9 μs, T2E = 25μs) times demonstrate that the soft 0-π circuit not only broadens the family of superconducting qubits but also constitutes an important step toward quantum computing with intrinsically protected superconducting qubits.
Superconducting circuits rank among some of the most interesting architectures for the implementation of quantum information processing devices.The recently proposed 0-π qubit (Brooks et al 2013 Phys.Rev. A 87 52306) promises increased protection from spontaneous relaxation and dephasing.In this paper we present a detailed theoretical study of the coherence properties of the 0-π device, investigate relevant decoherence channels, and show estimates for achievable coherence times in multiple parameter regimes.In our analysis, we include disorder in circuit parameters, which results in the coupling of the qubit to a low-energy, spurious harmonic mode.We analyze the effects of such coupling on decoherence, in particular dephasing due to photon shot noise, and outline how such a noise channel can be mitigated by appropriate parameter choices.In the end we find that the 0-π qubit performs well and may become an attractive candidate for the implementation of the next-generation superconducting devices for uses in quantum computing and information.
Encoding quantum information in quantum states with disjoint wave-function support and noise-insensitive energies is the key behind the idea of qubit protection. While fully protected qubits are expected to offer exponential protection against both energy relaxation and pure dephasing, simpler circuits may grant partial protection with currently achievable parameters. Here, we study a fluxonium circuit in which the wave functions are engineered to minimize their overlap while benefiting from a first-order-insensitive flux sweet spot. Taking advantage of a large superinductance ( L ∼ 1 μ H ), our circuit incorporates a resonant tunneling mechanism at zero external flux that couples states with the same fluxon parity, thus enabling bifluxon tunneling. The states | 0 ⟩ and | 1 ⟩ are encoded in wave functions with parities 0 and 1, respectively, ensuring a minimal form of protection against relaxation. Two-tone spectroscopy reveals the energy-level structure of the circuit and the presence of 4 π quantum-phase slips between different potential wells corresponding to m = ± 1 fluxons, which can be precisely described by a simple fluxonium Hamiltonian or by an effective bifluxon Hamiltonian. Despite suboptimal fabrication, the measured relaxation ( T 1 = 177 ± 3 μ s ) and dephasing ( T 2 E = 75 ± 5 μ s ) times not only demonstrate the relevance of our approach but also open an alternative direction toward quantum computing using partially protected fluxonium qubits. Published by the American Physical Society 2024
Abstract Great interest revolves around the development of new strategies to efficiently store and manipulate quantum information in a robust and decoherence-free fashion. Several proposals have been put forward to encode information into qubits that are simultaneously insensitive to relaxation and to dephasing processes. Among all, given their versatility and high-degree of control, superconducting qubits have been largely investigated in this direction. Here, we present a survey on the basic concepts and ideas behind the implementation of novel superconducting circuits with intrinsic protection against decoherence at a hardware level. In particular, the main focus is on multi-mode superconducting circuits, the paradigmatic example being the so-called 0 − π circuit. We report on their working principle and possible physical implementations based on conventional Josephson elements, presenting recent experimental realizations, discussing both fabrication methods and characterizations.
We develop and characterize a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise.The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, forming a superconducting loop.Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a cos (φ/2) Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference.In this regime, the logical-state wavefunctions reside in disjoint regions of Hilbert space, thereby ensuring protection against energy decay.By switching the protection on, we observe a tenfold increase of the decay time, reaching up to 100 μs.Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds 1 μs.Implementation of full dephasing protection can be achieved in the next-generation devices by combining several cos(φ/2) Josephson elements in a small array.
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.