Algebraic Classical and Quantum Field Theory on Causal Sets

The framework of perturbative algebraic quantum field theory (pAQFT) is used to construct QFT models on causal sets. We discuss various discretised wave operators, including a new proposal based on the idea of a `preferred past', which we also introduce, and show how they may be used to construct classical free and interacting field theory models on a fixed causal set; additionally, we describe how the sensitivity of observables to changes in the background causal set may be encapsulated in a relative Cauchy evolution. These structures are used as the basis of a deformation quantization, using the methods of pAQFT. The SJ state is defined and discussed as a particular quantum state on the free quantum theory. Finally, using the framework of pAQFT, we construct interacting models for arbitrary interactions that are smooth functions of the field configurations. This is the first construction of such a wide class of models achieved in QFT on causal sets.Comment: 42 pages, 3 figure

A Small Serving of Mash: (Quantum) Algorithms for SPDH-Sign with Small Parameters

We find an efficient method to solve the semidirect discrete logarithm problem (SDLP) over finite nonabelian groups of order $p^3$ and exponent $p^2$ for certain exponentially large parameters. This implies an attack on SPDH-Sign, a signature scheme based on the SDLP, for such parameters. We also take a step toward proving the quantum polynomial time equivalence of SDLP and SCDH

Quantum algorithmic solutions to the shortest vector problem on simulated coherent Ising machines

Quantum computing poses a threat to contemporary cryptosystems, with advances to a state in which it will cause problems predicted for the next few decades. Many of the proposed cryptosystems designed to be quantum-secure are based on the Shortest Vector Problem and related problems. In this paper we use the Quadratic Unconstrained Binary Optimisation formulation of the Shortest Vector Problem implemented as a quantum Ising model on a simulated Coherent Ising Machine, showing progress towards solving SVP for three variants of the algorithm.Comment: 15 page