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arXiv:0908.3937 · Physical Review B

Superconducting phase qubit based on the Josephson oscillator with strong anharmonicity

Alexander B Zorin, F. Chiarello

Published Dec 30, 2009• 14 citations
arXivHTMLPDF

Abstract

We propose a superconducting phase qubit on the basis of the radio-frequency superconducting quantum interference device with the screening parameter value ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}(2\ensuremath{\pi}/{\ensuremath{\Phi}}_{0})L{I}_{c}\ensuremath{\approx}1$, biased by a half-flux quantum ${\ensuremath{\Phi}}_{e}={\ensuremath{\Phi}}_{0}/2$. Significant anharmonicity $(>30%)$ can be achieved in this system due to the interplay of the cosine Josephson potential and the parabolic magnetic energy potential that ultimately leads to the quartic polynomial shape of the well. The two lowest eigenstates in this global minimum perfectly suit for the qubit which is insensitive to the charge variable, biased in the optimal point and allows an efficient dispersive readout. Moreover, the transition frequency in this qubit can be tuned within an appreciable range allowing variable qubit-qubit coupling.

DOI
10.1103/physrevb.80.214535

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We propose a superconducting phase qubit on the basis of the radio-frequency superconducting quantum interference device with the screening parameter value \ensuremathβL\ensuremath≡(2\ensuremathπ/\ensuremathΦ0)LIc\ensuremath≈1{\ensuremath{\beta}}_{L}\ensuremath{\equiv}(2\ensuremath{\pi}/{\ensuremath{\Phi}}_{0})L{I}_{c}\ensuremath{\approx}1\ensuremathβL​\ensuremath≡(2\ensuremathπ/\ensuremathΦ0​)LIc​\ensuremath≈1, biased by a half-flux quantum \ensuremathΦe=\ensuremathΦ0/2{\ensuremath{\Phi}}_{e}={\ensuremath{\Phi}}_{0}/2\ensuremathΦe​=\ensuremathΦ0​/2. Significant anharmonicity (>30(>30%)(>30 can be achieved in this system due to the interplay of the cosine Josephson potential and the parabolic magnetic energy potential that ultimately leads to the quartic polynomial shape of the well. The two lowest eigenstates in this global minimum perfectly suit for the qubit which is insensitive to the charge variable, biased in the optimal point and allows an efficient dispersive readout. Moreover, the transition frequency in this qubit can be tuned within an appreciable range allowing variable qubit-qubit coupling.
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Quantum computers utilize qubits to store and process quantum information. In superconducting quantum computers, qubits are implemented as quantum superconducting resonant circuits. The circuits are operated only at the two energy states, which form the computational basis for the qubit. To suppress leakage to uncomputational states, superconducting qubits are designed to be anharmonic oscillators, which is achieved using one or more Josephson junctions, a nonlinear superconducting element. One of the main challenges in developing quantum computers is minimizing the decoherence caused by environmental noise. Decoherence is characterized by two coherence times, T1 for depolarization processes and T2 for dephasing. This thesis reviews and investigates the decoherence properties of superconducting qubits. The main goal of the thesis is to analyze the tradeoff between anharmonicity and dephasing in a qubit unimon. Recently developed unimon incorporates a single Josephson junction shunted by a linear inductor and a capacitor. Unimon is tunable by external magnetic flux, and at the half flux quantum bias, the Josephson energy is partially canceled by the inductive energy, allowing unimon to have relatively high anharmonicity while remaining fully protected against low-frequency charge noise. In addition, at the sweet spot with respect to the magnetic flux, unimon becomes immune to first-order perturbations in the flux. The sweet spot, however, is relatively narrow, making unimon susceptible to dephasing through the quadratic coupling to the flux noise. In the first chapter of this thesis, we present a comprehensive look into the basic theory of superconducting qubits, starting with two-state quantum systems, followed by superconductivity and superconducting circuit elements, and finally combining these two by introducing circuit quantum electrodynamics (cQED), a framework for building superconducting qubits. We follow with a theoretical discussion of decoherence in two-state quantum systems, described by the Bloch-Redfield formalism. We continue the discussion by estimating decoherence using perturbation theory, with special care put into the dephasing due to the low-frequency 1/f noise. Finally, we review the theoretical model of unimon, which is used in the numerical analysis. As a main result of this thesis, we suggest a design parameter regime for unimon, which gives the best ratio between anharmonicity and T2.
The Josephson qubit based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-frequency driven tank circuit enabling the readout of the qubit states by measuring the effective Josephson inductance of the transistor. The effect of qubit dephasing and relaxation due to electric and magnetic control lines, as well as the measuring system, is evaluated. Recommendations for qubit operation with minimum decoherence are given.
A superconducting fluxonium circuit is an RF-superconducting quantum interference device-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and couplers are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices with the additional advantage of lower qubit frequency facilitating high-precision gating.
Altermagnets, characterized by vanishing net magnetization and momentum-dependent spin splitting, provide a promising platform for next-generation Josephson devices. Here, we exploit the Josephson effect in superconductor-altermagnet-superconductor junctions and show how to engineer prescribed current-phase relations by device design. Based on these programmable Josephson potentials utilizing altermagnetism, we propose a new class of superconducting qubits that combine large anharmonicity with enhanced robustness against decoherence via coherent two-Cooper-pair tunneling. We show that in the 2φ2φ2φ-junction regime, this kind of qubit is intrinsically protected against both charge and flux noise due to parity protection. Magnetic flux can be used to precisely control the qubit and, under appropriate bias, this architecture further suppresses charge and flux noise. Our results establish altermagnets as a versatile platform for Josephson-potential engineering and open a new route toward high-performance superconducting qubits combining high coherence, large anharmonicity, and broad tunability.
We present a systematic study of the phase coherent dynamics of a superconducting three-Josephson-junction flux qubit. The qubit state is detected with the integrated-pulse method, which is a variant of the pulsed switching-dc-superconducting quantum interference device (SQUID) method. In this scheme, the dc SQUID bias current pulse is applied via a capacitor instead of a resistor, giving rise to a narrow bandpass instead of a pure low-pass filter configuration of the electromagnetic environment. Measuring one and the same qubit with both setups allows a direct comparison. With the capacitive method about four times faster switching pulses and an increased visibility are achieved. Furthermore, the deliberate engineering of the electromagnetic environment, which minimizes the noise due to the bias circuit, is facilitated. Right at the degeneracy point, the qubit coherence is limited by energy relaxation. We find two main noise contributions. White noise limits the energy relaxation and contributes to the dephasing far from the degeneracy point. 1∕f1∕f1∕f noise is the dominant source of dephasing in the direct vicinity of the optimal point. The influence of 1∕f1∕f1∕f noise is also supported by nonrandom beatings in the Ramsey and spin echo decay traces. Numeric simulations of a coupled qubit-oscillator system indicate that these beatings are due to the resonant interaction of the qubit with at least one pointlike fluctuator, coupled especially strongly to the qubit.