Logical paradoxes in quantum computation

TL;DR

This paper explores how certain quantum states exhibiting strong contextuality and logical paradoxes can deterministically enable universal quantum computation, advancing understanding of quantum advantages over classical systems.

Contribution

It introduces new number-theoretic methods to construct exotic quantum paradoxes and identifies strongly contextual magic states that enable deterministic quantum gates.

Findings

Large classes of strongly contextual magic states constructed.

These states enable deterministic implementation of Clifford hierarchy gates.

Refinement of the resource theory of contextuality emphasizing logical paradoxes.

Abstract

While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical reality--has emerged as a promising hypothesis. Magic states are quantum resources critical for practically achieving universal quantum computation. They exhibit the standard form of contextuality that is known to enable probabilistic advantages in a variety of computational and communicational tasks. Strong contextuality is an extremal form of contextuality describing systems that exhibit logically paradoxical behaviour. Here, we consider special magic states that deterministically enable quantum computation. After introducing number-theoretic techniques for constructing exotic quantum paradoxes, we present large classes of strongly contextual magic states that enable deterministic implementation of gates from the Clifford hierarchy. These surprising discoveries bolster a refinement of the resource theory of contextuality that emphasises the computational power of logical paradoxes.