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Quantifying the magic resources for quantum computation

Banff International Research Station for Mathematical Innovation and Discovery

In this work, we develop resource-theoretic approaches to study the non-stabilizer resources in fault-tolerant quantum computation. First, we introduce a family of magic measures to quantify the amount of magic in a quantum state, several of which can be efficiently computed via convex optimization. Second, we show that two classes of states with maximal mana, a previously established magic measure, cannot be interconverted asymptotically at a rate equal to one. This reveals the fundamental difference between the resource theory of magic states and other resource theories such as entanglement and coherence. Third, we establish efficiently computable benchmarks for the rate and efficiency of magic state distillation via our magic measures. Fourth, we introduce efficiently computable magic measures to quantify the magic of quantum channels, which can be applied to evaluate the magic generating capability and gate synthesis. Finally, we propose a classical algorithm for simulating noisy quantum circuits whose sample complexity is quantified by our channel measure. We further show by concrete examples that our algorithm can outperform previous approaches in simulating noisy quantum circuits.

Mathematics; Quantum theory; Operator theory; Mathematical physics

video/mp4

Author affiliation: University of Maryland

2020-01-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73342

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/