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  • Open Access

Constant-depth fan-out with real-time feedforward on a superconducting quantum processor

Yongxin Song1,2,3,*, Liberto Beltrán1,2,3, Ilya Besedin1,2,3, Michael Kerschbaum1,2,3, Marek Pechal1,2,3, François Swiadek1,2, Christoph Hellings1,2, Dante Colao Zanuz1,2, Alexander Flasby1,2,3 et al.

Jean-Claude Besse1,2,3 and Andreas Wallraff1,2,3

  • *Contact author: yongxin.song@phys.ethz.ch
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Phys. Rev. Applied 24, 024068 – Published 28 August, 2025

DOI: https://doi.org/10.1103/q418-pydy

Abstract

When using unitary gate sequences, the growth in depth of many quantum circuits with output size poses significant obstacles to practical quantum computation. The quantum fan-out operation, which reduces the circuit depth of quantum algorithms such as the quantum Fourier transform and Shor’s algorithm, is an example that can be realized in constant depth independent of the output size. Here, we demonstrate a quantum fan-out gate with real-time feedforward on up to four output qubits using a superconducting quantum processor. By performing quantum state tomography on the output states, we benchmark our gate with input states spanning the entire Bloch sphere. We decompose the output-state error into a set of independently characterized error contributions. We extrapolate our constant-depth circuit to offer a scaling advantage compared to the unitary fan-out sequence beyond 25 output qubits with feedforward control, or beyond 17 output qubits if the classical feedforward latency is negligible. Our work highlights the potential of midcircuit measurements combined with real-time conditional operations to improve the efficiency of complex quantum algorithms.

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Outline

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Phys. Rev. Applied 24, 024068– Published 28 August, 2025
  • Received 27 September 2024
  • Revised 30 June 2025
  • Accepted 23 July 2025
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