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arXiv:2312.17305 · PRX Quantum

Quantum Circuits with Multiterminal Josephson-Andreev Junctions

F. J. Matute-Cañadas, L. Tosi, A. Levy Yeyati

Published May 22, 2024• 18 citations
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Abstract

We explore superconducting quantum circuits where several leads are simultaneously connected beyond the tunneling regime, such that the fermionic structure of Andreev bound states in the resulting multiterminal Josephson junction influences the states of the full circuit. Using a simple model of single-channel contacts and a single level in the middle region, we discuss different circuit configurations where the leads are islands with finite capacitance and/or form loops with finite inductance. We find situations of practical interest where the circuits can be used to define noise-protected qubits, which map to the bifluxon and 0−π qubits in the tunneling regime. We also point out the subtleties of the gauge choice for a proper description of these quantum circuit dynamics. Published by the American Physical Society 2024

DOI
10.1103/prxquantum.5.020340

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We explore superconducting quantum circuits where several leads are simultaneously connected beyond the tunneling regime, such that the fermionic structure of Andreev bound states in the resulting multiterminal Josephson junction influences the states of the full circuit. Using a simple model of single-channel contacts and a single level in the middle region, we discuss different circuit configurations where the leads are islands with finite capacitance and/or form loops with finite inductance. We find situations of practical interest where the circuits can be used to define noise-protected qubits, which map to the bifluxon and 0−π qubits in the tunneling regime. We also point out the subtleties of the gauge choice for a proper description of these quantum circuit dynamics. Published by the American Physical Society 2024
Although Josephson junctions can be viewed as highly nonlinear impedances for superconducting quantum technologies, they also possess internal dynamics that may strongly affect their behavior. Here, we construct a computational framework that includes a microscopic description of the junction (full fledged treatment of both the superconducting condensate and the quasiparticles) in the presence of a surrounding electrical circuit. Our approach generalizes the standard resistor capacitor Josephson model to arbitrary junctions (including, e.g., multiterminal geometries and/or junctions that embed topological or magnetic elements) and arbitrary electric circuits treated at the classical level. By treating the superconducting condensate and quasiparticles on equal footings, we capture nonequilibrium phenomena such as multiple Andreev reflection. We show that the interplay between the quasiparticle dynamics and the electrical environment leads to the emergence of new phenomena. In a RC circuit connected to single channel Josephson junction, we find out-of-equilibrium current-phase relations that are strongly distorted with respect to the (almost sinusoidal) equilibrium one, revealing the presence of the high harmonic ac Josephson effect. In an RLC circuit connected to a junction, we find that the shape of the resonance is strongly modified by the quasiparticle dynamics: close to resonance, the current can be smaller than without the resonator. Our approach provides a route for the quantitative modeling of superconducting-based circuits.
Hybrid devices integrating quantum dots with Josephson junctions are gaining interest because they combine spin-based quantum computing with circuit quantum electrodynamics (circuit QED) methods. In particular, Andreev spin qubits have shown significant experimental progress including strong two-qubit coupling, and are predicted to exhibit all-to-all connectivity. Here we propose superconducting singlet-triplet (SST) qubits that rely on parallel-aligned double quantum dots in Josephson junctions. While Andreev spin qubits require spin-orbit interaction to unlock the spin degree-of-freedom, SST qubits do not require spin-orbit interaction, making the advantages of hybrid devices available to a wider range of materials. Similar to Andreev spin qubits, the qubit states couple to the superconducting phase across the junction, which allows for control and readout using circuit QED, and supports all-to-all connectivity. Only NNN flux lines are required to perform any single- and two-qubit gate among NNN qubits, and thus the overhead of control lines is small. Finally, linear protection from charge or flux noise makes these qubits interesting candidates for a future quantum processor.
We propose a microscopic model of critical current noise in Josephson junctions based on individual trapping centers in the tunnel-barrier hybridized with electrons in the superconducting leads. We calculate the noise exactly in the limit of no on-site Coulomb repulsion. Our result reveals a noise spectrum that is dramatically different from the usual Lorentzian assumed in simple models. We show that the noise is dominated by sharp subgap resonances associated to the formation of pairs of Andreev bound states, thus providing a possible explanation for the spurious two-level systems (microresonators) observed in Josephson-junction qubits [R. W. Simmonds et al., Phys. Rev. Lett. 93, 077003 (2004).]. Another implication of our model is that each trapping center will contribute a sharp dielectric resonance only in the superconducting phase, providing an effective way to validate our results experimentally. We derive an effective Hamiltonian for a qubit interacting with Andreev bound states, establishing a direct connection between phenomenological models and the microscopic parameters of a Fermionic bath.
We consider a Josephson junction formed by a quantum dot connected to two bulk superconductors in the presence of Coulomb interaction and coupling to both an electromagnetic environment and a finite density of electronic quasiparticles. In the limit of a large superconducting gap we obtain a Born-Markov description of the relevant Andreev bound-states dynamics. We calculate the current-phase relation and we find that the experimentally unavoidable presence of quasiparticles can dramatically modify the 0-π standard transition picture. We show that photon-assisted quasiparticle absorption allows the dynamic switching from the 0 to the π state and vice versa, washing out the 0-π transition predicted by purely thermodynamic arguments. Spectroscopic signatures of Andreev bound-states broadening are investigated by considering microwave irradiation.
The quantum mechanics of the Josephson effect is the core ingredient for quantum technologies with superconducting circuits. A new avenue was recently opened in this field by predicting that the Josephson quantum mechanics in the odd parity sector, when a quasiparticle in trapped in an Andreev bound state, is fundamentally different from the conventional one in the even sector. The focus was then on a Josephson junction surrounded by an electromagnetic environment formed of a collection of bosonic modes, including the case of an ohmic environment. Here we consider the distinct case of a superconducting qubit made of a single Josephson junction whose environment reduces to a capacitance. We find a novel structure for the low-lying discrete states in the odd sector, which is altogether different from the one that appears in the even sector. Our study of the bound-state spectrum ranges from the Coulomb-dominated (Cooper pair box) to the Josephson-dominated (transmon) regime. Our prediction could be tested in forthcoming experiments with superconductor/semiconductor/superconductor junctions, which have been studied intensively in recent years, both using nanowires as well as two-dimensional electron gases.
Bound states in quantum dots coupled to superconductors can be in a coherent superposition of states with different electron number but with the same fermion parity. Electrostatic gating can tune this superposition to a sweet spot, where the quantum dot has the same mean electric charge independent of its electron-number parity. Here, we propose to encode quantum information in the local fermion parity of two tunnel-coupled quantum dots embedded in a Josephson junction. At the sweet spot, the qubit states have zero charge dipole moment. This protects the qubit from dephasing due to charge noise acting on the potential of each dot, as well as fluctuations of the (weak) interdot tunneling. At weak interdot tunneling, relaxation is suppressed because of disjoint qubit states. However, for strong interdot tunneling the system is protected against noise affecting each quantum dot separately (energy-level noise, dot-superconductor tunneling fluctuations, and hyperfine interactions). Finally, we describe initialization and readout as well as single-qubit and two-qubit gates by pulsing gate voltages. Published by the American Physical Society 2024