Related papers: A local model of quantum Turing machines
Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational…
A polynomial depth quantum circuit effects, by definition a poly-local unitary transformation of tensor product state space. It is a physically reasonable belief [Fy][L][FKW] that these are precisely the transformations which will be…
Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time…
Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are…
Recurrent neural networks (RNNs) and transformers have been shown to be Turing-complete, but this result assumes infinite precision in their hidden representations, positional encodings for transformers, and unbounded computation time in…
Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum…
In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated…
We develop a physics-based model for classical computation based on autonomous quantum thermal machines. These machines consist of few interacting quantum bits (qubits) connected to several environments at different temperatures. Heat flows…
We develop a general framework for self-testing, in which bipartite correlations are described by states on the commuting tensor product of a pair of operator systems. We propose a definition of a local isometry between bipartite quantum…
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here we propose exploring the opposite direction: to take agents as the basic…
This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…
Neural networks are a promising tool for characterizing intermediate-scale quantum devices from limited amounts of measurement data. A challenging problem in this area is to learn the action of an unknown quantum process on an ensemble of…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
We consider a typical realization of a qubit as a single particle in two-path interferometric circuits built from phase shifters, beam splitters and detectors. This framework is often taken as a standard example illustrating various…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
We study the localization properties of bipartite channels, whose action on a subsystem yields a unitary channel. In particular we show that, under such channel, the subsystem must evolve independent of its environment. This point of view…
A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not…
Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes a subset C_i of the qubits. We say that the rho_i are ``consistent'' if there exists some global state…