The Fisher-Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is probed then than calculating it only in the configuration and momentum spaces will not give a complete description for certain systems. Then a more general measure for the complexity of a quantum system by the integration of the usual Fisher-Shannon measure over all the parameter space is proposed. Finally, these measures are applied to the concrete case of a free particle in a box.
Statistical phase-space complexity of continuous-variable quantum channels
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；Dipartimento di Fisica, Università di Milano（米兰大学物理系）；Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche（帕尔马大学数学、物理与信息科学系）
Harvard University（哈佛大学）；Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局（A*STAR）高性能计算研究所）；Zhejiang Sci-Tech University（浙江理工大学）；Zhejiang University（浙江大学）
In theoretical machine learning, the statistical complexity is a notion that measures the richness of a hypothesis space. In this work, we apply a particular measure of statistical complexity, namely the Rademacher complexity, to the quantum circuit model in quantum computation and study how the statistical complexity depends on various quantum circuit parameters. In particular, we investigate the dependence of the statistical complexity on the resources, depth, width, and the number of input and output registers of a quantum circuit. To study how the statistical complexity scales with resourc…
Harvard University（哈佛大学）；Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局高性能计算研究院）；Zhejiang Sci-Tech University（浙江理工大学）；Zhejiang University（浙江大学）
We investigate how the addition of quantum resources changes the statistical complexity of quantum circuits by utilizing the framework of quantum resource theories. Measures of statistical complexity that we consider include the Rademacher complexity and the Gaussian complexity, which are well-known measures in computational learning theory that quantify the richness of classes of real-valued functions. We derive bounds for the statistical complexities of quantum circuits that have limited access to certain resources and apply our results to two special cases: (1) stabilizer circuits that are …
Error-tolerant witnessing of divergences in classical and quantum statistical complexity
Griffith University（格里菲斯大学）；Nanyang Technological University（南洋理工大学）；National University of Singapore（新加坡国立大学）；Horizon Quantum Computing（Horizon量子计算公司）
Quantum computers will be able solve important problems with significant polynomial and exponential speedups over their classical counterparts, for instance in option pricing in finance, and in real-space molecular chemistry simulations. However, key applications can only achieve their potential speedup if their inputs are prepared efficiently. We effectively solve the important problem of efficiently preparing quantum states following arbitrary continuous (as well as more general) functions with complexity logarithmic in the desired resolution, and with rigorous error bounds. This is enabled …
