Abstract: Quantum circuit complexity is a crucial metric across quantum information science, many-body physics, and high-energy physics, traditionally focused on closed systems. In this talk, we delve into the notion of embedded complexity in quantum circuits, characterizing interactions within larger systems. We introduce and analyze the complexity of projected states within subsystems, demonstrating that it is significantly influenced by the circuit volume—the aggregate of gates affecting both the subsystem and its complement. Our results indicate that ancillary qubits and measurements typically do not diminish the preparation cost of these projected states. We explore the implications of circuit volume for embedded complexity and present a spacetime conversion method that leverages random gate teleportation to optimize circuit volume. Additionally, we propose a streamlined shadow tomography protocol utilizing ancillary random states and Bell state measurements, providing valuable insights for practical implementations in quantum circuit design and analysis. Details are available in [arXiv: 2408.16602].
马雄峰，清华大学交叉信息研究院长聘教授，博士生导师，教育部高层次人才项目特聘教授。2003年北京大学物理学院本科毕业后赴加拿大多伦多大学攻读博士学位，2008年获得博士学位。先后在加拿大量子计算中心、多伦多大学、英国利兹大学等机构从事研究工作，2012年回国进入清华大学交叉信息研究院工作。主要从事量子密码学，量子信息基础和量子计算等方面的研究工作。2023年起担任Physical Review Letters编委会委员，2023年入选APS Fellow。
