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Bulletin of the American Physical Society

Optimization and characterization of protected Josephson circuits

Eva Dupont-Ferrier, Sergey P. Gladchenko, L. B. Ioffe, M. E. Gershenson

Published Mar 18, 2009• 0 citations
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We have studied the low-energy excitations in a minimalistic protected Josephson circuit which contains two basic elements (rhombi) characterized by the π periodicity of the Josephson energy. Novel design of these elements, which reduces their sensitivity to the offset charge fluctuations, has been employed. We have observed that the lifetime T1 of the first excited state of this quantum circuit in the protected regime is increased up to 70 μs, a factor of ∼100 longer than that in the unprotected state. The quality factor ω01T1 of this qubit exceeds 106. Our results are in agreement with theoretical expectations; they demonstrate the feasibility of symmetry protection in the rhombus-based qubits fabricated with existing technology.

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Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

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Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

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Josephson circuits for protected quantum bits

Wen-Sen Lu

Over the past two decades the performance of superconducting quantum bits (qubits) has been improved tremendously: the coherence time of individual qubits has been increased by five orders of magnitude, from a few nanoseconds to >100 μs. The much-improved coherence, lithographic scalability, and compatibility with microwave control place superconducting qubits in the leading position in the race amongst several quantum systems being considered for quantum information processing. Despite this very impressive progress, experimental realization of quantum error corrections and demonstration of logical qubits remains a considerable challenge.One of possible solutions to this problem is the development of so-called protected qubits whose errors would be suppressed by special symmetries of the underlying Hamiltonian. The realization of such qubits requires elements not found in the conventional superconducting circuit toolbox, such as Josephson elements with cos(ϕ/2) and cos(2ϕ) dependences of the Josephson energy E_J on the phase difference ϕ, circuits with a very large kinetic inductance, and junctions with unusually low E_J.This thesis focuses on design, fabrication and characterization of circuits based on low-E_J Josephson junctions (JJs) and superinductors (SIs). By analyzing limitations on the junction performance imposed by the thermally activated phase slips, we observed a dramatic reduction of the critical currents in the regime E_J≤T which was accompanied by an increase of the zero-bias resistance R_0. The first part of this work provides practical considerations for the use of such junctions in quantum circuits. With the aim of improving elements with a very high kinetic inductance, in the second part we developed superinductors based on the granular Aluminum (grAl) films, in which Josephson junctions are realized between nanoscale grains. The circuits based on such SIs demonstrate low microwave losses at ultra-low temperatures. Superinductors are an essential element of a novel qubit that we have developed – the so-called bifluxon. The qubit consists of a Cooper-pair box (CPB) with low-E_J Josephson junctions shunted by a superinductor, thus forming a superconducting loop. When the loop is threaded by the magnetic flux Φ=Φ_0⁄2 where Φ_0 is the flux quantum, the qubit offers exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise. In the last part of this work, we observed an increase of the energy relaxation time by two orders of magnitude, up to 100μs, by turning on protection in the bifluxon qubit.

•Jan 1, 2021•1 citation
We have studied the low-energy excitations in a minimalistic protected Josephson circuit which contains two basic elements (rhombi) characterized by the π periodicity of the Josephson energy. Novel design of these elements, which reduces their sensitivity to the offset charge fluctuations, has been employed. We have observed that the lifetime T1 of the first excited state of this quantum circuit in the protected regime is increased up to 70 μs, a factor of ∼100 longer than that in the unprotected state. The quality factor ω01T1 of this qubit exceeds 106. Our results are in agreement with theoretical expectations; they demonstrate the feasibility of symmetry protection in the rhombus-based qubits fabricated with existing technology.
Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.
Over the past two decades the performance of superconducting quantum bits (qubits) has been improved tremendously: the coherence time of individual qubits has been increased by five orders of magnitude, from a few nanoseconds to >100 μs. The much-improved coherence, lithographic scalability, and compatibility with microwave control place superconducting qubits in the leading position in the race amongst several quantum systems being considered for quantum information processing. Despite this very impressive progress, experimental realization of quantum error corrections and demonstration of logical qubits remains a considerable challenge.One of possible solutions to this problem is the development of so-called protected qubits whose errors would be suppressed by special symmetries of the underlying Hamiltonian. The realization of such qubits requires elements not found in the conventional superconducting circuit toolbox, such as Josephson elements with cos(ϕ/2) and cos(2ϕ) dependences of the Josephson energy E_J on the phase difference ϕ, circuits with a very large kinetic inductance, and junctions with unusually low E_J.This thesis focuses on design, fabrication and characterization of circuits based on low-E_J Josephson junctions (JJs) and superinductors (SIs). By analyzing limitations on the junction performance imposed by the thermally activated phase slips, we observed a dramatic reduction of the critical currents in the regime E_J≤T which was accompanied by an increase of the zero-bias resistance R_0. The first part of this work provides practical considerations for the use of such junctions in quantum circuits. With the aim of improving elements with a very high kinetic inductance, in the second part we developed superinductors based on the granular Aluminum (grAl) films, in which Josephson junctions are realized between nanoscale grains. The circuits based on such SIs demonstrate low microwave losses at ultra-low temperatures. Superinductors are an essential element of a novel qubit that we have developed – the so-called bifluxon. The qubit consists of a Cooper-pair box (CPB) with low-E_J Josephson junctions shunted by a superinductor, thus forming a superconducting loop. When the loop is threaded by the magnetic flux Φ=Φ_0⁄2 where Φ_0 is the flux quantum, the qubit offers exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise. In the last part of this work, we observed an increase of the energy relaxation time by two orders of magnitude, up to 100μs, by turning on protection in the bifluxon qubit.