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  • Letter
  • Open Access

Global variational quantum circuits for arbitrary symmetric state preparation

Liam J. Bond1,2,3,*, Matthew J. Davis3, Jiří Minář1,2,4, Rene Gerritsma1,2, Gavin K. Brennen5, and Arghavan Safavi-Naini1,2,3

  • *Contact author: L.J.Bond@uva.nl
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Phys. Rev. Research 7, L022072 – Published 20 June, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022072

Abstract

Quantum states that are symmetric under particle exchange play a crucial role in fields such as quantum metrology and quantum error correction. We use a variational circuit composed of global one-axis twisting and global rotations to efficiently prepare arbitrary symmetric states, i.e., any superposition of Dicke states. The circuit does not require local addressability or ancilla qubits and thus can be readily implemented in a variety of experimental platforms including trapped-ion quantum simulators and cavity QED systems. We provide analytic and numerical evidence that any N-qubit symmetric state can be prepared in 2N/3 steps. We demonstrate the utility of our protocol by preparing (i) metrologically useful N-qubit Dicke states of up to N=300 qubits in O(1) gate steps with theoretical infidelities 1−F<10−3, (ii) the N=9 Ruskai codewords in P=4 gate steps with 1−F<10−4, and (iii) the N=13 Gross codewords in P=7 gate steps with 1−F<10−4. Focusing on trapped-ion platforms, for the N=9 Ruskai and N=13 Gross codewords we estimate that the protocol achieves fidelities ≳95% in the presence of typical experimental noise levels, thus providing a pathway to the preparation of a wide range of useful highly entangled quantum states.

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Phys. Rev. Research 7, L022072– Published 20 June, 2025
  • Received 21 December 2023
  • Revised 7 November 2024
  • Accepted 4 April 2025
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