Resource theory of quantum uncomplexity

TL;DR

This paper develops a resource theory framework for quantum uncomplexity, linking quantum complexity with resource theories, and introduces measures and tasks to quantify and manipulate uncomplexity in many-body quantum systems.

Contribution

It formalizes a resource theory of quantum uncomplexity, defining allowed operations, tasks, and monotones, bridging quantum complexity with resource theory concepts.

Findings

Defined fuzzy operations as allowed transformations.

Introduced uncomplexity extraction and expenditure tasks.

Established monotones that decrease under fuzzy operations.

Abstract

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or "uncomplexity," the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.