2020/02/29 by James R. Seddon, Bartosz Regula, Hakop Pashayan +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computation #Computer science #MAGIC (telescope) #Mathematics #Monotone polygon #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum mechanics #Qubit #Scaling #Theoretical computer science #quant-ph
paper · pdf · doi:10.1103/prxquantum.2.010345
published as PRX Quantum 2, 010345 (2021) · 24+13 pages, 8 figures; final author copy. Since v1: restructured with additional discussion, proof sketches and examples. Since v3: minor revisions to improve clarity, additional acknowledgments
openalex publication_date 2021/03/18 · arxiv created 2021/03/21 · arxiv updated 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by establishing precise connections with a family of magic monotones. Our first simulator introduces a new class of quasiprobability distributions and connects its runtime to a generalized notion of negativity. We prove that this algorithm has significantly improved exponential scaling compared to all prior quasiprobability simulators for qubits. Our second simulator is a new variant of the stabilizer-rank simulation algorithm, extended to work with mixed states and with significantly improved runtime bounds. Our third simulator trades precision for speed by discarding negative quasiprobabilities. We connect each algorithm's performance to a corresponding magic monotone and, by comprehensively characterizing the monotones, we obtain a precise understanding of the simulation runtime and error bounds. Our analysis reveals a deep connection between all three seemingly unrelated simulation techniques and their associated monotones. For tensor products of single-qubit states, we prove that our monotones are all equal to each other, multiplicative and efficiently computable, allowing us to make clear-cut comparisons of the simulators' performance scaling. Furthermore, our monotones establish several asymptotic and nonasymptotic bounds on state interconversion and distillation rates. Beyond the theory of magic states, our classical simulators can be adapted to other resource theories under certain axioms, which we demonstrate through an explicit application to the theory of quantum coherence.