A Note on Hierarchy of Quantum Measurement Incompatibilities

Clifford层级中的受控门

Controlled Gates in the Clifford Hierarchy

该研究针对量子比特Clifford层级中的受控门，推导并证明了其需满足的一组强约束必要条件，将结论扩展至特定酉直和构成的门，还给出了该条件具备充分性的相关证据。

不定因果序逆转实-复层级

Indefinite Causal Order Reverses the Real-Complex Hierarchy

研究在不定因果序下，实量子理论与复量子理论的过程相关性比较，发现实量子理论能实现更多过程相关性，逆转了固定因果序下的层级。

Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids

The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach is the use of the BBGKY hierarchy for the time-dependent reduced density matrices. In contrast, our contribution is motivated by the kinetic theory of the weakly nonlinear Schrodinger equation. The main observation is that the results obtained in the latter context carry over directly to weakly interacting quantum fluids provided one does not insist on norma…

Ruling out higher-order interference from purity principles

As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits, there are no genuinely new features resulting from considering three slits instead of two. Sorkin has introduced a hierarchy of mathematically conceivable higher-order interference behaviours, where classical theory lies at the first level of this hierarchy and quantum theory theory at the second. Informally, the order in this hierarchy corresponds to the number of slits on which the inter…

Field Theory and The Sum-of-Squares for Quantum Systems

This is a collection of various result and notes, addressing the sum-of-squares hierarchy for spin and fermion systems using some ideas from quantum field theory, including higher order perturbation theory, critical phenomena, nonlocal coupling in time, and auxiliary field Monte Carlo. This paper should be seen as a sequel to Refs. 1,2. Additionally in this paper, we consider the difficulty of approximating the ground state energy of the Sachdev-Ye-Kitaev (SYK) model using other methods. We provide limitations on the power of the Lanczos method, starting with a Gausian wavefunction, and on the…

一种用于布尔函数模式分类的量子算法

A Quantum Algorithm for the Classification of Patterns of Boolean Functions

本文提出一种量子算法，通过单次预言机查询以概率1分类不平衡布尔函数的层级类别，并详述了可扩展的设计方法论。