Complexity of quantum processes

量子过程的复杂性

• 批准号: RGPIN-2018-04184
• 负责人: Cleve, Richard
• 金额: $ 3.5万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=689651
• 关键词: Complexity; quantum; processes

The proposal is to investigate complexity-theoretic questions that arise from various quantum information processes. In particular, the investigation concerns: ***(1) Local channels with shared entanglement, where the presence of quantum entanglement (possibly enormous quantities of entanglement) can increase the kinds of operations that can be performed in interesting ways; and***(2) Markovian (a.k.a., Lindbladian or dissipative) evolution, where continuous-time trajectories of quantum states can evolve in interesting ways, beyond what is possible with Hamiltonian evolution.***Both projects are concerned with the model of quantum information in extreme settings. For the project on local channels, the entanglement is taken to extremes, while bounding the sizes of the input and output registers. The project on Markovian evolution is also concerned with extremes in the sense that simulating such evolution on a system of bounded size via Hamiltonian evolution on a larger system requires the size of the larger system and the norm of underlying Hamiltonian to approach infinity.

我们的建议是研究由各种量子信息过程产生的复杂性理论问题。特别地，研究关注：***(1)具有共享纠缠的本地通道，其中量子纠缠（可能是大量纠缠）的存在可以增加可以以有趣的方式执行的操作种类；(2)马尔可夫进化（又名林德布拉迪亚或耗散），其中量子态的连续时间轨迹可以以有趣的方式进化，超越了哈密顿进化的可能性。***两个项目都关注极端环境下的量子信息模型。对于本地通道上的项目，当限制输入和输出寄存器的大小时，纠缠被带到极端。关于马尔可夫进化的项目也与极端有关，在某种意义上，通过在更大系统上的哈密顿进化来模拟有限大小系统上的这种进化，需要更大系统的大小和潜在的哈密顿范数接近无穷大。