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Superposed orders of quantum channels have already been proved - boththeoretically and experimentally - to enable unparalleled opportunities in thequantum communication domain. As a matter of fact, superposition of orders canbe exploited within the quantum computing domain as well, by relaxing the(traditional) assumption underlying quantum computation about applying gates ina well-defined causal order. In this context, we address a fundamental questionarising with quantum computing: whether superposed orders of single-qubit gatescan enable universal quantum computation. As shown in this paper, the answer tothis key question is a definitive "yes". Indeed, we prove that any two-qubitcontrolled quantum gate can be deterministically realized, including theso-called Barenco gate that alone enables universal quantum computation.

Universal Quantum Computation via Superposed Orders of Single-Qubit Gates