Observation of Two-Vertex Four-Dimensional Spin Foam Amplitudes with a 10-qubit Superconducting Quantum Processor

Spin Foam Vertex Amplitudes on Quantum Computer -- Preliminary Results

Vertex amplitudes are elementary contributions to the transition amplitudes in the spin foam models of quantum gravity. The purpose of this article is make the first step towards computing vertex amplitudes with the use of quantum algorithms. In our studies we are focused on a vertex amplitude of 3+1 D gravity, associated with a pentagram spin-network. Furthermore, all spin labels of the spin network are assumed to be equal $j=1/2$, which is crucial for the introduction of the \emph{intertwiner qubits}. A procedure of determining modulus squares of vertex amplitudes on universal quantum comput…

Lorentz Spin-Foam with Non Unitary Representations by use of Holomorphic Peter-Weyl Theorem

In quantum gravity the unitary evolution does not follow from the Wheeler-DeWitt dynamics equation as it follows from the Schrödinger equation in non-relativistic quantum mechanics. Therefore we can define a spin-foam model based on SL(2,C) spinor finite non-unitary representations. The recently discovered holomorphic Peter-Weyl theorem \cite{Huebschmann} made it possible to decompose the delta function of a non-compact Lorentz group into the convergent sum of the matrix coefficients. We calculate the vertex amplitude with the help of that theorem and obtain a simple expression for our model. …

Path integral polymer propagator of relativistic and non-relativistic particles

A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The mechanical models we consider are deparametrized and thus the group averaging technique is used to deal with the corresponding constraints. The transition amplitudes are written in a vertex expansion form used in the spin foam models, where here a vertex is actually a jump in position. Polymer propagators previously obtained by spectral methods for a nonrelativisti…

Coarse graining of spin net models: dynamics of intertwiners

Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full four--dimensional models. We consider here simplified analogue models, so called spin nets, that retain the main dynamical ingredient of spin foams, the simplicity constraints. For a certain class of these spin net models we determine the phase diagram and therefore the continuum phases via a coarse graining procedure based on tensor network renormalization. This proced…

非本地游戏作为跨平台量子基准：在囚禁离子处理器上超越无条件经典界限

Nonlocal Games as Cross-Platform Quantum Benchmarks: Exceeding unconditional classical bounds on trapped-ion processors

研究通过在四个囚禁离子量子处理器上实现14顶点图着色游戏，首次在非本地游戏中超越经典界限，展示了非本地游戏作为跨架构量子基准的潜力。

图上的量子辅助会合：显式算法与量子计算机模拟

Quantum-assisted Rendezvous on Graphs: Explicit Algorithms and Quantum Computer Simulations

本研究通过解析、数值模拟及NISQ处理器，分析了简单图上单步会合博弈的量子优势，提出了实现最优界的协议并在环图上推广至任意尺寸，实验表明在完全图K3上实现高精度量子优势，但在图2K4上因电路深度及退相干等因素性能低于经典水平。