Magic Resources of the Heisenberg Picture
Neil Dowling, Pavel Kos, Xhek Turkeshi

TL;DR
This paper introduces a resource theory for operators' non-stabilizerness, providing a computable measure that quantifies operator magic, with applications in many-body systems and quantum circuit complexity.
Contribution
It develops an operator stabilizer Rènyi entropy as a new magic monotone, linking it to circuit complexity and local dynamical properties, with analytical results in random and integrable systems.
Findings
Operator magic reaches near-maximal value under random evolution.
Operator stabilizer entropy saturates quickly in integrable XXZ circuits.
The measure provides bounds on non-Clifford gate counts and insights into many-body magic generation.
Abstract
We study a non-stabilizerness resource theory for operators, which is dual to that describing states. We identify that the stabilizer R\'enyi entropy analog in operator space is a good magic monotone satisfying the usual conditions while inheriting efficient computability properties and providing a tight lower bound to the minimum number of non-Clifford gates in a circuit. Operationally, this measure quantifies how well an operator can be approximated by one with only a few Pauli strings -- analogous to how entanglement entropy relates to tensor-network truncation. A notable advantage of operator stabilizer entropies is their inherent locality, as captured by a Lieb-Robinson bound. This feature makes them particularly suited for studying local dynamical magic resource generation in many-body systems. We compute this quantity analytically in two distinct regimes. First, we show that…
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Taxonomy
TopicsColor perception and design
