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arXiv:1803.01079 · Physical Review A

Universal stabilization of single-qubit states using a tunable coupler

Ziwen Huang, Yao Lu, Eliot Kapit, David Schuster, Jens Koch

Published Jun 29, 2018• 13 citations
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Abstract

We theoretically analyze a scheme for fast stabilization of arbitrary qubit states with high fidelities, extending a protocol recently demonstrated experimentally [Lu et al., Phys. Rev. Lett. 119, 150502 (2017)]. That experiment utilized red and blue sideband transitions in a system composed of a fluxonium qubit, a low-$Q$ $LC$ oscillator, and a coupler enabling us to tune the interaction between them. Under parametric modulations of the coupling strength, the qubit can be steered into any desired pure or mixed single-qubit state. For realistic circuit parameters, we predict that stabilization can be achieved within $100\phantom{\rule{0.28em}{0ex}}\mathrm{ns}$. By varying the ratio between the oscillator's damping rate and the effective qubit-oscillator coupling strength, we can switch between underdamped, critically damped, and overdamped stabilization and find optimal working points. We further analyze the effect of thermal fluctuations and show that the stabilization scheme remains robust for realistic temperatures.

DOI
10.1103/physreva.97.062345

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We theoretically analyze a scheme for fast stabilization of arbitrary qubit states with high fidelities, extending a protocol recently demonstrated experimentally [Lu et al., Phys. Rev. Lett. 119, 150502 (2017)]. That experiment utilized red and blue sideband transitions in a system composed of a fluxonium qubit, a low-QQQ LCLCLC oscillator, and a coupler enabling us to tune the interaction between them. Under parametric modulations of the coupling strength, the qubit can be steered into any desired pure or mixed single-qubit state. For realistic circuit parameters, we predict that stabilization can be achieved within 100ns100\phantom{\rule{0.28em}{0ex}}\mathrm{ns}100ns. By varying the ratio between the oscillator's damping rate and the effective qubit-oscillator coupling strength, we can switch between underdamped, critically damped, and overdamped stabilization and find optimal working points. We further analyze the effect of thermal fluctuations and show that the stabilization scheme remains robust for realistic temperatures.
We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achieved with a tunable coupling design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasistatic tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single-photon exchange in 6 ns. Qubit coherence times exceeding 20 μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon nonconserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80%.
The fluxonium qubit is a promising candidate for quantum computation due to its long coherence times and large anharmonicity. We present a tunable coupler that realizes strong inductive coupling between two heavy-fluxonium qubits, each with ∼50\sim50∼50MHz frequencies and ∼5\sim5∼5 GHz anharmonicities. The coupler enables the qubits to have a large tuning range of XX\textit{XX}XX coupling strengths (−35-35−35 to 757575 MHz). The ZZ\textit{ZZ}ZZ coupling strength is <3<3<3kHz across the entire coupler bias range, and <100<100<100Hz at the coupler off-position. These qualities lead to fast, high-fidelity single- and two-qubit gates. By driving at the difference frequency of the two qubits, we realize a iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​ gate in 258258258ns with fidelity 99.72%99.72\%99.72%, and by driving at the sum frequency of the two qubits, we achieve a bSWAP\sqrt{b\mathrm{SWAP}}bSWAP​ gate in 102102102ns with fidelity 99.91%99.91\%99.91%. This latter gate is only 5 qubit Larmor periods in length. We run cross-entropy benchmarking for over 202020 consecutive hours and measure stable gate fidelities, with bSWAP\sqrt{b\mathrm{SWAP}}bSWAP​ drift (2σ2 σ2σ) <0.02%< 0.02\%<0.02% and iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​ drift <0.08%< 0.08\%<0.08%.
The fluxonium qubit is a promising candidate for quantum computation due to its long coherence times and large anharmonicity. We present a tunable coupler that realizes strong inductive coupling between two heavy-fluxonium qubits, each with approximately 50 -MHz frequencies and approximately 5 -GHz anharmonicities. The coupler enables the qubits to have a large tuning range of X X coupling strengths ( − 35 to 75 MHz). The Z Z coupling strength is < 3 kHz across the entire coupler bias range and < 100 Hz at the coupler off position. These qualities lead to fast high-fidelity single- and two-qubit gates. By driving at the difference frequency of the two qubits, we realize a i SWAP gate in 258 ns with fidelity 99.72%, and by driving at the sum frequency of the two qubits, we achieve a b SWAP gate in 102 ns with fidelity 99.91%. This latter gate is only five qubit Larmor periods in length. We run cross-entropy benchmarking for over 20 consecutive hours and measure stable gate fidelities, with b SWAP drift ( 2 σ ) < 0.02 % and i SWAP drift < 0.08 % . Published by the American Physical Society 2024
Controllable interaction between superconducting qubits is desirable for large-scale quantum computation and simulation. Here, based on a theoretical proposal by Yan et al. [Phys. Rev. Appl. 10, 054061 (2018)] we experimentally demonstrate a simply designed and flux-controlled tunable coupler with a continuous tunability by adjusting the coupler frequency, which can completely turn off adjacent superconducting qubit coupling. Utilizing the tunable interaction between two qubits via the coupler, we implement a different type of controlled-phase (cz) gate with ``dynamically decoupled regime,'' which allows the qubit-qubit coupling to be only ``on'' at the usual operating point while dynamically ``off'' during the tuning process of one qubit frequency into and out of the operating point. This scheme not only efficiently suppresses the leakage out of the computational subspace, but also allows for the acquired two-qubit phase being geometric at the operating point. We achieve an average cz gate fidelity of $98.3\ifmmode\pm\else\textpm\fi{}0.6\mathrm{%}$, which is dominantly limited by qubit decoherence. The demonstrated tunable coupler provides a desirable tool to suppress adjacent qubit coupling and is suitable for large-scale quantum computation and simulation.
Tunable couplers have recently emerged as an essential component in superconducting quantum processors. These couplers usually do not have readout resonators to save control or hardware overhead; this makes it challenging to characterize and calibrate the coupler, which will undoubtedly limit the performance of a fast two-qubit gate. Here, we theoretically demonstrate that by mapping the coupler's state onto that of its neighboring qubit, the high-contrast readout of the coupler can be realized. We experimentally implement such a readout scheme with a single-shot readout fidelity of 86%, which is mainly limited by the thermal population of our sample. We further demonstrate how to calibrate the flux crosstalk related to the coupler and its flux distortion that are ignored in the previous works. These calibration steps are imperative for realizing robust and accurate quantum operations in frequency-tunable superconducting circuits.
Abstract Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high-fidelity single-qubit and two-qubit gates, single-shot readout, and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element. We experimentally demonstrate fSim-type and controlled-Z-gates with 99.55 and 99.23% fidelities, respectively. The residual ZZ interaction is suppressed down to the few kHz levels. Using a galvanically coupled flux control line, we implement high-fidelity single-qubit gates and ground state initialization with a single arbitrary waveform generator channel per qubit.