Quantifying Quantum Speedups: Improved Classical Simulation From Tighter Magic Monotones

作     者：James R. Seddon Bartosz Regula Hakop Pashayan Yingkai Ouyang Earl T. Campbell 

作者机构：Department of Physics and Astronomy University College London London United Kingdom School of Physical and Mathematical Sciences Nanyang Technological University 637371 Singapore Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada Centre for Engineered Quantum Systems School of Physics The University of Sydney Sydney New South Wales 2006 Australia Department of Physics & Astronomy University of Sheffield Sheffield S3 7RH United Kingdom AWS Center for Quantum Computing Pasadena California 91125 USA 

出 版 物：《PRX Quantum》 (PRX. Quantum.)

年 卷 期：2021年第2卷第1期

页      面：010345-010345页

核心收录：

基　　金：Australian Research Council, ARC, (CE170100009) Australian Research Council, ARC Engineering and Physical Sciences Research Council, EPSRC, (EP/P510270/1) Engineering and Physical Sciences Research Council, EPSRC 

主　　题：Quantum algorithms Quantum computation Quantum simulation Resource theories 

摘      要：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.