Related papers: Quantum Markov Networks and Commuting Hamiltonians
The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to the problem, by studying the problem of 'quantum state generation'. This approach provides intriguing links…
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with…
In this article, we consider a spin-spin interaction network governed by $XX + YY$ Hamiltonian. The vertices and edges of the network represent the spin objects and their interactions, respectively. We take a privilege to switch on or off…
We propose that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and…
Society relies and depends increasingly on information exchange and communication. In the quantum world, security and privacy is a built-in feature for information processing. The essential ingredient for exploiting these quantum advantages…
We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…
We propose a method for Hamiltonian engineering in quantum information processing architectures that requires no local control, but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation…
We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition.…
The quantum master equation (QME), used to describe the Markov process of interaction between atoms and field, has a number of significant drawbacks. It is extremely memory intensive, and also inapplicable to the case of long-term memory in…
We study the graphs generated when the formula for linking Markov triples is applied to general triples of integers. We find there are a finite number of equivalence classes of graphs, each with particular properties.
Quantum networks providing shared entanglement over a mesh of quantum nodes will revolutionize the field of quantum information science by offering novel applications in quantum computation, enhanced precision in networks of sensors and…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied…
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by…
A characterization of qubit quantum channels is introduced. In analogy to what happens in the context of Bosonic channels we exploit the possibility of representing the states of the system in terms of characteristic function. The latter…
In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…