Abstract Ternary quantum information processing in superconducting devices poses a promising alternative to its more popular binary counterpart through larger, more connected computational spaces and proposed advantages in quantum simulation and error correction. Although generally operated as qubits, transmons have readily addressable higher levels, making them natural candidates for operation as quantum three-level systems (qutrits). Recent works in transmon devices have realized high fidelity single qutrit operation. Nonetheless, effectively engineering a high-fidelity two-qutrit entanglement remains a central challenge for realizing qutrit processing in a transmon device. In this work, we apply the differential AC Stark shift to implement a flexible, microwave-activated, and dynamic cross-Kerr entanglement between two fixed-frequency transmon qutrits, expanding on work performed for the Z Z interaction with transmon qubits. We then use this interaction to engineer efficient, high-fidelity qutrit CZ † and CZ gates, with estimated process fidelities of 97.3(1)% and 95.2(3)% respectively, a significant step forward for operating qutrits on a multi-transmon device. 

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High-fidelity qutrit entangling gates for superconducting circuits

Transforming stand-alone qubits into a functional, general-purpose quantum processing unit requires an architecture where many-body quantum entanglement can be generated and controlled in a coherent, modular, and measurable fashion. Electronic circuits promise a well-developed pathway for large-scale integration once a mature library of quantum-compatible elements have been developed. In the domain of superconducting circuits, fluxonium has recently emerged as a promising qubit due to its high-coherence and large anharmonicity, yet its scalability has not been systematically explored. In this work, we present a blueprint for a high-performance fluxonium-based quantum processor that addresses the challenges of frequency crowding, and both quantum and classical crosstalk. The main ingredients of this architecture include high-anharmonicity circuits, multipath couplers to entangle qubits where spurious longitudinal coupling can be nulled, circuit designs that are compatible with multiplexed microwave circuitry, and strongly coupled readout channels that do not require complex, frequency-sculpted elements to maintain coherence. In addition, we explore robust and resource-efficient protocols for quantum logical operations, then perform numerical simulations to validate the expected performance of this proposed processor with respect to gate fidelity, fabrication yield, and logical error suppression. Lastly, we discuss practical considerations to implement the architecture and achieve the anticipated performance.11 MoreReceived 27 January 2022Revised 29 June 2022Accepted 5 July 2022DOI:https://doi.org/10.1103/PRXQuantum.3.037001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum controlQuantum engineeringQuantum error correctionQuantum gatesQuantum information architectures & platformsQuantum information processingTechniquesQuantum master equationQuantum InformationCondensed Matter, Materials & Applied Physics 

Blueprint for a High-Performance Fluxonium Quantum Processor

Flux-tunable qubits are a useful resource for superconducting quantum processors. They can be used to perform cPhase gates, facilitate fast reset protocols, avoid qubit-frequency collisions in large processors, and enable certain fast readout schemes. However, flux-tunable qubits suffer from a trade-off between their tunability range and sensitivity to flux noise. Optimizing this trade-off is particularly important for enabling fast, high-fidelity, all-microwave cross-resonance gates in large, high-coherence processors. This is mainly because cross-resonance gates set stringent conditions on the frequency landscape of neighboring qubits, which are difficult to satisfy with non-tunable transmons due to their relatively large fabrication imprecision. To solve this problem, we realize a coherent, flux-tunable, transmon-like qubit, which exhibits a frequency tunability range as small as 43 MHz, and whose frequency, anharmonicity and tunability range are set by a few experimentally achievable design parameters. Such a weakly tunable qubit is useful for avoiding frequency collisions in a large lattice while limiting its susceptibility to flux noise. 

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Weakly Flux-Tunable Superconducting Qubit

As superconducting quantum processors increase in complexity, techniques to overcome constraints on frequency crowding are needed. The recently developed method of laser-annealing provides an effective post-fabrication method to adjust the frequency of superconducting qubits. Here, we present an automated laser-annealing apparatus based on conventional microscopy components and demonstrate preservation of highly coherent transmons. In addition, we perform noise spectroscopy to investigate the change in defect features, in particular, two-level system defects, after laser-annealing. Finally, we present a local heating model as well as demonstrate aging stability for laser-annealing on the wafer scale. Our work constitutes an important step toward both understanding the underlying physical mechanism and scaling up laser-annealing of superconducting qubits.

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Effects of laser-annealing on fixed-frequency superconducting 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. 

/pdf/cnot-gates-for-fluxonium-qubits-via-selective-darkening-of-k9dqln5e.pdf

cnot Gates for Fluxonium Qubits via Selective Darkening of Transitions

Fixed-frequency superconducting quantum processors are one of the most mature quantum computing architectures with high-coherence qubits and simple controls. However, high-fidelity multi-qubit gates pose tight requirements on individual qubit frequencies in these processors , and these constraints are difficult to satisfy when constructing larger processors due to the large dispersion in the fabrication of Josephson junctions. In this article, we propose a mixed-integer-programming-based optimization approach that determines qubit frequencies to maximize the fabrication yield of quantum processors. We study traditional qubit and qutrit (three-level) architectures with cross-resonance interaction processors. We compare these architectures to a differential AC-Stark shift based on entanglement gates and show that our approach greatly improves the fabrication yield and also increases the scalability of these devices. Our approach is general and can be adapted to problems where one must avoid specific frequency collisions. 

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Sharmiladevi Palani

Papers

Optimizing frequency allocation for fixed-frequency superconducting quantum processors