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arXiv:2206.07216 · Nature Communications

High-fidelity qutrit entangling gates for superconducting circuits

Noah Goss, Alexis Morvan, Brian Marinelli, Bradley Mitchell, Long B. Nguyen, Ravi Naik, Larry Chen, Christian Jünger, John Mark Kreikebaum, David Santiago, Joel J. Wallman, Irfan A. Siddiqi

Published Dec 5, 2022• 131 citations
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Abstract

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.

DOI
10.1038/s41467-022-34851-z

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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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Quantum computing offers the potential to surpass classical computing speeds by leveraging quantum entanglement and superposition. However, progress towards fault-tolerant quantum computers is limited by low qubit counts and considerable gate errors. A promising direction involves transitioning from two-level qubits to d-level qudits, expanding the state space beyond conventional qubit-based quantum computers. The superconducting transmon-tunable coupler-transmon (TTT) system has emerged as a key building block of current quantum processors. Recent demonstration has shown its capability to host three-level qudits (qutrits), including the implementation of qutrit controlled-phase (CPhase) gate via an adiabatic scheme. Despite this progress, further modeling or optimization studies for the qudit-based TTT system are still unexplored. In this work, we propose an integrated simulation framework that predicts the cross-Kerr interactions of the TTT system and the fidelities of two-qutrit CPhase gate with the presence of noise effect. We validate the prediction of the cross-Kerr interactions against data from TTT systems reported in the literature. We also identify the conditions for the maximum target frequency in the adiabatic scheme necessary to achieve higher qutrit CPhase gate fidelity. Furthermore, we demonstrate the control-device co-optimization of the system, showing the potential of achieving the highest gate fidelity allowed by the hardware and noise. This work provides valuable insights which can guide the development towards more reliable and powerful superconducting quantum processors.
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Recently, significant progress has been made in the demonstration of single-qutrit and coupled-qutrit gates with superconducting circuits. Coupled-qutrit gates have significantly lower fidelity than single-qutrit gates, owing to long implementation times. We present a protocol to implement the CZ universal gate for two qutrits based on a decomposition involving two partial-state swaps and local operations. The partial-state swaps can be implemented effectively using parametric coupling, which is fast and has the advantage of frequency selectivity. We perform a detailed analysis of this protocol in a system consisting of two fixed-frequency transmons coupled by a flux-tunable transmon. The application of an AC flux in the tunable transmon controls the parametric gates. This protocol has the potential to lead to fast and scalable two-qutrit gates in superconducting circuit architectures.