Related papers: Renormalized quantum tomography
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices…
To simulate a quantum system with continuous degrees of freedom on a quantum computer based on quantum digits, it is necessary to reduce continuous observables (primarily coordinates and momenta) to discrete observables. We consider this…
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product…
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
Quantum uncertainty of laser light limits the sensitivity of gravitational-wave observatories. In the past 30 years, techniques for squeezing the quantum uncertainty as well as for enhancing the gravitational-wave signal with optical…
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
We examine the notion of symmetry in quantum field theory from a fundamental representation theoretic point of view. This leads us to a generalization expressed in terms of quantum groups and braided categories. It also unifies the…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of…
Continuous-variables (CV) quantum optics is a natural formalism for neural networks (NNs) due to its ability to reproduce the information processing of such trainable interconnected systems. In quantum optics, Gaussian operators induce…
Quantum tomography, as a tool to probe foundational aspects of quantum mechanics, relies on extracting spin information from angular distributions. This is inherently a leading-order technique, ill-defined when higher-order corrections are…
A large class of quantum field theories on 1+1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local…
The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity (QC), and rigorous mathematical proofs of its basic properties. The definition used here is similar to that by Berthiaume, van Dam, and Laplante. It…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum…
Quantum state tomography (QST), the process of reconstructing some unknown quantum state $\hat\rho$ from repeated measurements on copies of said state, is a foundationally important task in the context of quantum computation and simulation.…
We prove that a wide class of random quantum channels with few Kraus operators, sampled as random matrices with some sparsity and moment assumptions, typically exhibit a large spectral gap, and are therefore optimal quantum expanders. In…
In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger's picture of Quantum Mechanics in which a groupoid is associated with every quantum system. The attention is focused on spin…