Path Integral Representations on the Complex Sphere

Casimir forces between spheres and loop integrals

A summary of recent calculations of Casimir forces between a collection of $N$-dielectric spheres is presented. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. A loop integral formulation is also discussed where we rewrite the expressions for the force in terms of loop integrals for the effective classical propagation of the electric and magnetic fields.

由 Schmidt 球上路径诱导的 iSWAP 型几何门

iSWAP-type geometric gates induced by paths on Schmidt sphere

本文提出仅依赖 Schmidt 球路径几何相位的 iSWAP 型双量子比特门，通过逆向工程得到可在 transmon 系统实现的哈密顿量，可产生任意纠缠并与 Bloch 球单比特几何门互补。

The universal path integral

Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined me…

Path Integral for Quantum Operations

In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for quantum operation with a simple infinitesimal generator.

Rules for Integrals over Products of Distributions from Coordinate Independence of Path Integrals

In perturbative calculations of quantum mechanical path integrals in curvilinear coordinates, Feynman diagrams involve multiple temporal integrals over products of distributions, which are mathematically undefined. We derive simple rules for their evaluation from the requirement of coordinate independence of path integrals.

量子通道的Hilbert-Schmidt范数与单位球上的矩阵积分

The Hilbert-Schmidt norms of quantum channels and matrix integrals over the unit sphere

本文研究量子通道的Hilbert-Schmidt范数范围及其互补通道的关系，并探讨了无限维系统上保持纯态的完全正映射以及相关矩阵积分的等价性与扩展。