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arXiv:2008.09980 · New Journal of Physics

Effects of higher levels of qubits on control of qubit protected by a Josephson quantum filter

Shumpei Masuda, Kazuki Koshino

Published Jan 1, 2021• 2 citations
arXivHTMLPDF

Abstract

Abstract A Josephson quantum filter (JQF) protects a data qubit (DQ) from the radiative decay into transmission lines (TLs) in superconducting quantum computing architectures. A transmon, which is a weakly nonlinear harmonic oscillator rather than a pure two-level system, can play a role of a JQF or a DQ. However, in the previous study, a JQF and a DQ were modeled as two-level systems neglecting the effects of higher levels. We theoretically examine the effects of the higher levels of the JQF and the DQ on the control of the DQ. It is shown that the higher levels of the DQ cause the shift of the resonance frequency and the decrease of the maximum population of the first excited state of the DQ in the controls with a continuous wave (cw) field and a pulsed field, while the higher levels of the JQF do not. Moreover, we present optimal parameters of the pulsed field, which maximize the control efficiency.

DOI
10.1088/1367-2630/abd809

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Abstract A Josephson quantum filter (JQF) protects a data qubit (DQ) from the radiative decay into transmission lines (TLs) in superconducting quantum computing architectures. A transmon, which is a weakly nonlinear harmonic oscillator rather than a pure two-level system, can play a role of a JQF or a DQ. However, in the previous study, a JQF and a DQ were modeled as two-level systems neglecting the effects of higher levels. We theoretically examine the effects of the higher levels of the JQF and the DQ on the control of the DQ. It is shown that the higher levels of the DQ cause the shift of the resonance frequency and the decrease of the maximum population of the first excited state of the DQ in the controls with a continuous wave (cw) field and a pulsed field, while the higher levels of the JQF do not. Moreover, we present optimal parameters of the pulsed field, which maximize the control efficiency.
The coupling between a superconducting qubit and a control line inevitably results in radiative decay of the qubit into the line. We propose a Josephson quantum filter (JQF), which protects the data qubit (DQ) from radiative decay through the control line without reducing the gate speed on the DQ. The JQF consists of a qubit strongly coupled to the control line of the DQ and its working principle is a subradiance effect that is characteristic of waveguide quantum electrodynamics setups. The JQF is a passive circuit element and is therefore suitable for integration in a scalable superconducting qubit system.
Abstract The rapid development in designs and fabrication techniques of superconducting qubits has made coherence times of qubits longer. In the future, however, the radiative decay of a qubit into its control line will be a fundamental limitation, imposing a trade-off between fast control and long lifetime of the qubit. Here, we break this trade-off by strongly coupling another superconducting qubit along the control line. This second qubit, which we call “Josephson quantum filter” (JQF), prevents the first qubit from emitting microwave photons and thus suppresses its relaxation, while transmitting large-amplitude control microwave pulses due to the saturation of the quantum filter, enabling fast qubit control. This device functions as an automatic decoupler between a qubit and its control line and could help in the realization of a large-scale superconducting quantum processor by reducing the heating of the qubit environment and the crosstalk between qubits.
The rapid development in designs and fabrication techniques of superconducting qubits has made coherence times of qubits longer. In the future, however, the radiative decay of a qubit into its control line will be a fundamental limitation, imposing a trade-off between fast control and long lifetime of the qubit. Here, we break this trade-off by strongly coupling another superconducting qubit along the control line. This second qubit, which we call "Josephson quantum filter" (JQF), prevents the first qubit from emitting microwave photons and thus suppresses its relaxation, while transmitting large-amplitude control microwave pulses due to the saturation of the quantum filter, enabling fast qubit control. This device functions as an automatic decoupler between a qubit and its control line and could help in the realization of a large-scale superconducting quantum processor by reducing the heating of the qubit environment and the crosstalk between qubits.
We present Rabi oscillation measurements of a Nb/AlOx/Nb\text{Nb}/{\text{AlO}}_{\text{x}}/\text{Nb}Nb/AlOx​/Nb dc superconducting quantum interference device (SQUID) phase qubit with a $100\text{ }\ensuremath{\mu}{\text{m}}^{2}$ area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states.
We present theoretical schemes for performing high-fidelity one- and two-qubit pulsed gates for a superconducting flux qubit. The 'IBM qubit' consists of three Josephson junctions, three loops and a superconducting transmission line. Assuming a fixed inductive qubit–qubit coupling, we show that the effective qubit–qubit interaction is tunable by changing the applied fluxes, and can be made negligible, allowing one to perform high-fidelity single qubit gates. Our schemes are tailored to alleviate errors due to 1/ f noise; we find gates with only 1% loss of fidelity due to this source, for pulse times in the range of 20–30 ns for one-qubit gates ( Z rotations, Hadamard) and 60 ns for a two-qubit gate (controlled- Z ). Our relaxation and dephasing time estimates indicate a comparable loss of fidelity from this source. The control of leakage plays an important role in the design of our shaped pulses, preventing shorter pulse times. However, we have found that imprecision in the control of the quantum phase plays a major role in the limitation of the fidelity of our gates.
We theoretically investigate a readout scheme of the quantum state of a superconducting qubit based on time delay of a single flux quantum (SFQ), also known as a fluxon, propagating in a Josephson transmission line (JTL). We concretely study the time-delay readout based on capacitive coupling between a transmon qubit and a JTL, and we evaluate the time delay depending on the qubit state. We also reveal a feature of the absence of fluxon pinning and exponential suppression of nonadiabatic transitions caused by the propagating fluxon, which is advantageous for the time-delay readout. We extend the analysis to a multi-level transmon as well. Owing to the spectral gap in the JTL, the radiative decay of the qubit mediated by the JTL is exponentially suppressed, and thus the transmission line itself also serves as a filter protecting the qubit. The readout scheme requires neither complicated wiring to low-temperature stages nor bulky microwave components, which are bottlenecks for integration of a large-scale superconducting quantum computer.