Simulating the quantum switch with quantum circuits is computationally hard

Jessica Bavaresco, Hlér Kristjánsson, Mio Murao, Tatsuki Odake, Marco Túlio Quintino (), Philip Taranto and Satoshi Yoshida
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Jessica Bavaresco: University of Geneva, Department of Applied Physics
Hlér Kristjánsson: Perimeter Institute for Theoretical Physics
Mio Murao: The University of Tokyo, Department of Physics, Graduate School of Science
Tatsuki Odake: The University of Tokyo, Department of Physics, Graduate School of Science
Marco Túlio Quintino: Sorbonne Université, CNRS, LIP6
Philip Taranto: The University of Tokyo, Department of Physics, Graduate School of Science
Satoshi Yoshida: The University of Tokyo, Department of Physics, Graduate School of Science

Nature Communications, 2025, vol. 16, issue 1, 1-12

Abstract: Abstract Higher-order transformations acting on input quantum channels in an indefinite causal order—such as the quantum switch—cannot be described by quantum circuits using the same number of calls to the input channels. A natural question is whether they can be simulated, i.e., whether their action can be exactly and deterministically reproduced by a quantum circuit with more calls to the input channels. Here, we prove that the quantum switch acting on two n-qubit channels cannot be simulated by any quantum circuit using k calls to one channel and one to the other, if k

Date: 2025
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DOI: 10.1038/s41467-025-64996-6

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