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arXiv:2407.18351 · Physical Review Applied

Cross-resonance control of an oscillator with an auxiliary fluxonium qubit

Guo Zheng, Simon Lieu, Emma Rosenfeld, Kyungjoo Noh, Connor T. Hann

Published Feb 27, 2025• 2 citations
arXivHTMLPDF

Abstract

The conditional displacement (CD) gate between an oscillator and a discrete-variable auxiliary qubit plays a key role in quantum information processing tasks, such as enabling universal control of the oscillator and longitudinal readout of the qubit; however, the gate is unprotected against the propagation of auxiliary qubit decay errors, meaning it is not fault tolerant. Here, we propose a CD gate scheme with fluxonium as the auxiliary qubit, which has been experimentally demonstrated to have a large noise bias and millisecond-level lifetimes. The proposed gate is applied cross-resonantly by modulating the external flux of the fluxonium at the frequency of the target oscillator, which requires minimal hardware overhead and does not increase sensitivity to decoherence mechanisms such as dephasing. We further provide a perturbative description of the gate mechanism and identify the error budget. Additionally, we develop an approximate procedure for choosing device and gate parameters that optimize gate performance. Following the procedure for multiple sets of fluxonium parameters from the literature, we numerically demonstrate CD gates with unitary fidelity exceeding 99.9% and gate times of hundreds of nanoseconds.

DOI
10.1103/physrevapplied.23.024067

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The conditional displacement (CD) gate between an oscillator and a discrete-variable auxiliary qubit plays a key role in quantum information processing tasks, such as enabling universal control of the oscillator and longitudinal readout of the qubit; however, the gate is unprotected against the propagation of auxiliary qubit decay errors, meaning it is not fault tolerant. Here, we propose a CD gate scheme with fluxonium as the auxiliary qubit, which has been experimentally demonstrated to have a large noise bias and millisecond-level lifetimes. The proposed gate is applied cross-resonantly by modulating the external flux of the fluxonium at the frequency of the target oscillator, which requires minimal hardware overhead and does not increase sensitivity to decoherence mechanisms such as dephasing. We further provide a perturbative description of the gate mechanism and identify the error budget. Additionally, we develop an approximate procedure for choosing device and gate parameters that optimize gate performance. Following the procedure for multiple sets of fluxonium parameters from the literature, we numerically demonstrate CD gates with unitary fidelity exceeding 99.9% and gate times of hundreds of nanoseconds.
Echoed Conditional Displacement (ECD) gates constitute a fundamental building block for quantum control of harmonic oscillator modes. However, bit-flips of the auxiliary qubit remain a dominant error mechanism for this kind of bosonic control. In this work, we present a numerical case study of a bit-flip protected fluxonium operating as the control qubit and numerically implement ECD gates in a single-mode resonator-fluxonium device, demonstrating that fidelities exceeding 99.9% are possible. We systematically investigate the resonator dynamics using a combination of semiclassical trajectories and master equation simulations, numerically revealing asymptotic saturation of the dispersive shift in the strongly driven regime of the resonator. We develop an efficient technique to numerically simulate the strongly driven regime of the resonator using a semiclassical formulation that maps the full perturbation series in the dispersive expansion as order-by-order frequency shifts. This provides a compact polynomial description of the resonator which is intuitive and remains valid throughout the dispersive regime. Furthermore, we propose an improved ECD sequence that accounts for the effects of photon loss and spurious nonlinear terms on resonator trajectories.
We study the cross-resonance effect in capacitively-coupled fluxonium qubits and devise a simple formula for their maximum ZX interaction strength. By going beyond the perturbative regime, we find that a CNOT gate can generally be realized in under 200 ns with residual ZZ limited to 50 kHz, for fluxonium qubits with frequencies below 1 GHz. Our analysis relies on a semi-analytical method: we first numerically diagonalize the Floquet Hamiltonian of the strongly-driven control qubit and then perturbatively incorporate the weak qubit-qubit coupling to obtain an effective Hamiltonian. We also derive frequency collision windows around harmful control-target and control-spectator transitions. For large fluxonium devices, we predict a collision-free yield that is considerably less sensitive to junction variability compared to transmons in the same layout. These results support the viability of an all-fluxonium cross-resonance architecture with only capacitive couplings.
The fluxonium qubits have emerged as a promising platform for gate-based quantum information processing. However, their extraordinary protection against charge fluctuations comes at a cost: when coupled capacitively, the qubit-qubit interactions are restricted to XX interactions. Consequently, effective ZZ or XZ interactions are only constructed either by temporarily populating higher-energy states, or by exploiting perturbative effects under microwave driving. Instead, we propose and demonstrate an inductive coupling scheme, which offers a wide selection of native qubit-qubit interactions for fluxonium. In particular, we leverage a built-in, flux-controlled ZZ interaction to perform qubit entanglement. To combat the increased flux-noise-induced dephasing away from the flux-insensitive position, we use a continuous version of the dynamical decoupling scheme to perform noise filtering. Combining these, we demonstrate a 20 ns controlled-z gate with a mean fidelity of 99.53%. More than confirming the efficacy of our gate scheme, this high-fidelity result also reveals a promising but rarely explored parameter space uniquely suitable for gate operations between fluxonium qubits.
We analyze the cross-resonance effect for fluxonium circuits and investigate a two-qubit gate scheme based on selective darkening of a transition. In this approach, two microwave pulses at the frequency of the target qubit are applied simultaneously with a proper ratio between their amplitudes to achieve a controlled-not operation. We study in detail coherent gate dynamics and calculate gate error. With nonunitary effects accounted for, we demonstrate that gate error below ${10}^{\ensuremath{-}4}$ is possible for realistic hardware parameters. This number is facilitated by long coherence times of computational transitions and strong anharmonicity of fluxoniums, which easily prevents excitation to higher excited states during the gate microwave drive.
Quantum computers use the principles of quantum mechanics to store and manipulate information encoded in the quantized levels of physical systems. A goal of quantum computers is to accurately solve problems that are intractable for classical computers, such as simulating molecular dynamics and prime factorization of large integers. However, the failure probability is too high for quantum computers to solve useful problems. Fortunately, quantum error correction (QEC) provides a way to perform robust computations in the presence of errors by distributing information across multiple physical systems. Bosonic quantum error-correcting codes offer a hardware-efficient avenue for QEC where information is encoded in the continuous phase-space of a single harmonic oscillator. The linear harmonic oscillator realised as the microwave modes of a superconducting resonator is controlled via a nonlinear superconducting control qubit. Experiments on bosonic QEC are limited by bit flip errors in the control qubit, leading to low logical lifetimes of the storage resonator. Our idea is to replace the transmon with a heavy fluxonium qubit that has intrinsic protection against bit-flips. With this architecture in mind, we investigate the performance of a universal gateset comprising of Echoed Conditional Displacement gates and single qubit rotations. Wenumerically solve the Schrödinger equation for a closed resonator- fluxonium device and use a combination of quantum and semiclassical approaches to simulate the system exactly. We adopt a pulse-level implementation of quantum gates where we realize target gates by applying tailored drives on the resonator. We develop a resonator frame-tracking technique that allows us to simulate the dynamics of the driven resonator exactly with less than five fock levels while retaining all the physics of the problem. This technique allowed us to accurately simulate the device up to a few 10000s of photons, matching experimental results, that otherwise would not be possible even using high-performance computers due to excessive memory and simulation time required.
We propose a scalable fluxonium-transmon-fluxonium (FTF) system that utilizes a central transmon to mediate high-fidelity gates and parity checks between two fluxonium qubits without the need for strong non-local interactions. This approach suppresses unwanted long-range interactions, which is critical for developing larger quantum processors. First, we analyze the performance of cross-resonance (CR) CNOT gates between a fluxonium and a transmon. We show that even in the presence of a spectator qubit, these gates maintain high fidelity with coherent errors on the order of 10−510^{-5}10−5. We then demonstrate that these gates, when applied sequentially, enable high-fidelity parity checks and logical fluxonium-fluxonium CNOT gates. In addition, the central transmon can facilitate the readout of the neighboring fluxoniums, consolidating multiple critical functions into a single ancilla. Our work establishes the viability of a dual-species architecture as a promising path toward fault-tolerant quantum computation.