Can the quantum switch be deterministically simulated?

Presented at:

Seminar: WOST/QISS Virtual Seminar Series – International consortium (2026; online)
Conference: IFQIF Workshop (São Paulo, Brazil, 2025; online)
Conference: HOAQS 2025 – Higher Order Quantum Structures (Stará Lesná, Slovakia, 2025)
Seminar: Université Grenoble Alpes (UGA), group of Dr. Cyril Branciard (Grenoble, France, 2024)
Seminar: IQOQI Vienna, group of Prof. Časlav Brukner (Vienna, Austria, 2024)
Conference: Causalworlds 2024 (Waterloo, Canada, 2024)
Conference: FQC 2024 – Foundations of Quantum Computing (London, UK, 2024)

Slides coming soon.

References

Simulating the quantum switch with quantum circuits is computationally hard

Jessica Bavaresco, Hlér Kristjánsson, Mio Murao, Tatsuki Odake, Marco Túlio Quintino, Philip Taranto, Satoshi Yoshida

Nature Communications 16, 10216 (2025)

arXiv Journal

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 $k<2^n$. This establishes an exponential separation in quantum query complexity between processes with indefinite causal order and quantum circuits. Moreover, even with one extra call to both input channels, such a simulation remains impossible. We further demonstrate the robustness of this separation by extending the result to probabilistic and approximate simulations scenarios.