LAUSR

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 < 2n. 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. The ability to perform operations in an indefinite causal order allows advantages for various quantum information-processing tasks, yet it’s still unclear to what extent such exotic sequences could be simulated using standard quantum circuits. Here, the authors prove that such simulations - even if approximate or probabilistic - would incur an exponential quantum query complexity overhead.