Most quantum states are too entangled to be useful as computational resources

TL;DR

Most quantum states are excessively entangled to serve as effective computational resources, indicating that high entanglement alone does not guarantee computational usefulness in quantum computing.

Contribution

The paper demonstrates that the majority of quantum states are too entangled to be useful for quantum computation, challenging the assumption that more entanglement always enhances computational power.

Findings

Less than exp(-n^2) of n-qubit states are useful for computation.

High entanglement can render states ineffective for quantum computational tasks.

Useful states are rare among all possible quantum states.

Abstract

It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement-based quantum computing (MBQC), the need for a highly entangled initial state is particularly obvious. Defying this intuition, we show that quantum states can be too entangled to be useful for the purpose of computation. We prove that this phenomenon occurs for a dramatic majority of all states: the fraction of useful n-qubit pure states is less than exp(-n^2). Computational universality is hence a rare property in quantum states. This work highlights a new aspect of the question concerning the role entanglement plays for quantum computational speed-ups. The statements remain true if one allows for certain forms of post-selection and also cover the notion of CQ-universality. We identify scale-invariant states resulting from a MERA construction as likely candidates for physically relevant states subject to this effect.