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Qubit alive thanks to the anomaly

I. L. Egusquiza, A. Iñiguez, E. Rico, A. Villarino

Published Sep 27, 2021• 0 citations
OpenAlex

Abstract

We present an exact full symmetry analysis of the 0-$\pi$ superconducting circuit. We identify points in control parameter space of enhanced anomalous symmetry, which imposes robust twofold degeneracy of its ground state, that is for all values of the energy parameters of the model. We show, both analytically and numerically, how this anomalous symmetry is maintained in the low-energy sector, thus providing us with a strong candidate for robust qubit engineering.

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We present an exact full symmetry analysis of the 0-π\piπ superconducting circuit. We identify points in control parameter space of enhanced anomalous symmetry, which imposes robust twofold degeneracy of its ground state, that is for all values of the energy parameters of the model. We show, both analytically and numerically, how this anomalous symmetry is maintained in the low-energy sector, thus providing us with a strong candidate for robust qubit engineering.
We present an exact full symmetry analysis of the $0\text{\ensuremath{-}}\ensuremath{\pi}$ superconducting circuit. We identify points in control parameter space of enhanced anomalous symmetry, which imposes robust twofold degeneracy of its ground state, that is for all values of the energy parameters of the model. We show, both analytically and numerically, how this anomalous symmetry is maintained in the low-energy sector, thus providing us with a strong candidate for robust qubit engineering.
We show that topological edge states can be realized in a simple superconducting circuit composed of an inductively shunted flux qubit. The Josephson potential of that qubit forms a honeycomb lattice similar to the case of graphene. The additional shunting element produces a quartic potential along one flux direction, which effectively creates a boundary in flux space. We map analytically the low-energy dynamics of the circuit to an extended Su--Schrieffer--Heeger (SSH) chain, in which a quartic potential is added to the usual SSH Hamiltonian. This mapping is confirmed by numerical simulations of the full superconducting circuit. We argue that chiral symmetry still holds for the edge states of the extended model around a chiral point in parameter space. Close to this point, we numerically find that edge states in our superconducting circuit are topologically protected against perturbations that obey chiral symmetry, as is the case for charge noise. Our results show that topological effects previously thought to occur in multi-qubit systems, such as protection against decoherence, can also be found in much simpler single superconducting qubits.
A recent theoretical proposal suggests that a simple circuit utilizing two superinductors may produce a qubit with ground-state degeneracy [Brooks, Phys. Rev. A 87, 052306 (2013)]. We perform a full circuit analysis along with exact diagonalization of the circuit Hamiltonian to elucidate the nature of the spectrum and low-lying wave functions of this $0\text{\ensuremath{-}}\ensuremath{\pi}$ device. We show that the ground-state degeneracy is robust to disorder in charge, flux, and critical current as well as insensitive to modest variations in the circuit parameters. Our treatment is nonperturbative, provides access to excited states and matrix elements, and is immediately applicable also to intermediate parameter regimes of experimental interest.
Symmetries and model reduction in a cos⁡2φ\cos 2\varphicos2φ transmon qubit
Engineered symmetries in superconducting circuits can protect quantum information; much like selection rules in atomic physics, they forbid transitions between the qubit states. Protected circuits, however, combine several loops and islands and host multiple nonlinearly coupled modes, calling for reduced low-energy models that inherit the circuit symmetries and make the protection manifest. We develop such a reduction for the cos⁡2φ\cos 2\varphicos2φ transmon qubit, recently realized experimentally with a two-Cooper-pair interferometer, whose circuit hosts three coupled modes. Exploiting the separation of energy scales between the heavy transmon mode and the light internal modes of the interferometer, we derive an effective single-band Born-Oppenheimer model, including its geometric correction, and extend it to several bands. We identify the symmetries of the full and reduced Hamiltonians and derive exact selection rules. Finally, we identify a parameter regime beyond the single-band description that suppresses flux-noise dephasing without degrading charge-noise protection.
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.