Revisiting the hopes for scalable quantum computation

TL;DR

This paper critically examines the foundational assumptions of the quantum error correction threshold theorem, highlighting that physical imperfections prevent exact assumptions, which questions the feasibility of scalable quantum computing.

Contribution

It emphasizes the need to consider the precision of assumptions in the threshold theorem, revealing a gap in the understanding of practical quantum computing scalability.

Findings

Assumptions in the threshold theorem are idealized and not physically exact.

The required precision of assumptions is crucial for the theorem's applicability.

Scalability prospects depend on the ability to meet these assumptions with sufficient accuracy.

Abstract

The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based on a number of assumptions, which are supposed to be satisfied exactly, like axioms, e.g. zero undesired interactions between qubits, etc. However in the physical world no continuous quantity can be exactly zero, it can only be more or less small. Thus the "error per qubit per gate" threshold must be complemented by the required precision with which each assumption should be fulfilled. This issue was never addressed. In the absence of this crucial information, the prospects of scalable quantum computing remain uncertain.