Universal quantum computation via superposed orders of single-qubit gates

Superposed orders of quantum channels have already been proved—both theoretically and experimentally—to enable unparalleled opportunities in the quantum communication domain. Superposition of orders can be exploited within the quantum computing domain as well, by relaxing the (traditional) assumption underlying quantum computation about applying gates in a well-defined causal order. In this context, we address a fundamental question arising with quantum computing: Whether superposed orders of single-qubit gates can enable universal quantum computation. As shown in this paper, the answer to this key question is a definitive “yes.” Indeed, we prove that any two-qubit controlled quantum gate can be realized, including the so-called Barenco gate that alone enables universal quantum computation.