Related papers: Computation in generalised probabilistic theories
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the…
Simulation of quantum systems that provide intrinsically fault-tolerant quantum computation is shown to preserve fault tolerance. Errors committed in the course of simulation are eliminated by the natural error-correcting features of the…
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
We show within the framework of relativistic quantum tasks that the doability of any task is fully determined by a small subset of its parameters that we call its "coarse causal structure", as well as the distributed computation it aims to…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
Continuous-variable bosonic systems stand as prominent candidates for implementing quantum computational tasks. While various necessary criteria have been established to assess their resourcefulness, sufficient conditions have remained…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…
We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…
The computational efficiency of quantum mechanics can be defined in terms of the qubit circuit model, which is characterized by a few simple properties: each computational gate is a reversible transformation in a connected matrix group;…