Universal Quantum Computation via Superposed Orders of Single-Qubit Gates

TL;DR

This paper demonstrates that superposed orders of single-qubit gates can enable universal quantum computation, including the realization of any two-qubit controlled gate, challenging traditional causal order assumptions.

Contribution

It proves that superpositions of quantum gate orders can deterministically implement any two-qubit controlled gate, establishing a new paradigm for quantum computation.

Findings

Superposed orders enable deterministic realization of two-qubit controlled gates.

Any two-qubit controlled gate, including the Barenco gate, can be implemented.

Superposition of gate orders relaxes traditional causal constraints in quantum computing.

Abstract

Superposed orders of quantum channels have already been proved - both theoretically and experimentally - to enable unparalleled opportunities in the quantum communication domain. As a matter of fact, 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 deterministically realized, including the so-called Barenco gate that alone enables universal quantum computation.