Resource theory of quantum uncomplexity
Abstract: Quantum complexity is emerging as a key feature of many-body systems, including black holes, topological materials, and early quantum computers. A state’s complexity quantifies the difficulty of preparing the state from a simple tensor product, or the difficulty of uncomputing the state to 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. I will unite the two domains, proposing a resolution to Brown and Susskind’s long-standing challenge to construct a resource theory of uncomplexity. I will present the resource theory’s definition, operational tasks analyzable in the theory, and monotones (resource-theory measures of a state’s usefulness). This work brings to many-body complexity a powerful mathematical and conceptual toolkit from quantum information theory.
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