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Realizing a Continuous Set of Two-Qubit Gates Parameterized by an Idle Time

Colin Scarato1,2,*, Kilian Hanke1,2, Ants Remm1,2,†, Stefania Lazăr1,2,‡, Nathan Lacroix1,2, Dante Colao Zanuz1,2, Alexander Flasby1,2,3, Andreas Wallraff1,2,3, and Christoph Hellings1,2

  • *Contact author: colin.scarato@phys.ethz.ch
  • †Present address: Atlantic Quantum, Cambridge, MA.
  • ‡Present address: Zurich Instruments AG, Zurich, Switzerland.
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PRX Quantum 6, 040317 – Published 24 October, 2025

DOI: https://doi.org/10.1103/h7cv-xgw2

Abstract

Continuous gate sets are a key ingredient for near-term quantum algorithms. Here, we demonstrate a hardware-efficient, continuous set of controlled arbitrary-phase (CZθ) gates acting on flux-tunable transmon qubits. This implementation is robust to control pulse distortions on time scales longer than the duration of the gate, making it suitable for deep quantum circuits. Our calibration procedure makes it possible to parameterize the continuous gate set with a single control parameter, the idle time between the two rectangular halves of the net-zero control pulse. For calibration and characterization, we develop a leakage measurement based on coherent amplification, and a new cycle design for cross-entropy benchmarking. We demonstrate gate errors of 0.7% and leakage of 4×10−4 across the entire gate set. This native gate set has the potential to reduce the depth and improve the performance of near-term quantum algorithms compared to decompositions into CZπ gates and single-qubit gates. Moreover, we expect the calibration and benchmarking methods to find further possible applications.

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Popular Summary

By performing logical operations (quantum logic gates) on quantum bits (qubits), quantum computers hold promise to perform calculations that are outside the reach of traditional computers. As each gate can introduce errors in the computation, a strategy to improve the performance of near-term quantum computers is to implement algorithms as shorter sequences of more versatile gates rather than as long sequences built from a small selection of standard gates. In this work, we present a new kind of versatile set of gates operating on a pair of qubits, and we demonstrate low errors across the whole gate set.

A quantum processor consisting of a superconducting electrical circuit can be controlled with electrical pulses lasting tens of nanoseconds. In our approach, each gate consists of two such pulses with a short idle time between them. We show how carefully calibrating the shape of these pulses makes it possible to achieve all desired logical operations simply by adjusting the idle time separating these two pulses.

Our study contributes to a better understanding of this type of quantum operation, and the presented gate set can be used to increase the performance of near-term quantum algorithms. In addition, we present novel measurement protocols, which will find further applications beyond the presented gate set: a method to characterize small errors by accumulating them over many repetitions of a gate, and an improved benchmarking protocol for two-qubit gates.

Article Text

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PRX Quantum 6, 040317– Published 24 October, 2025
  • Received 4 April 2025
  • Revised 21 July 2025
  • Accepted 4 August 2025
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