Related papers: The Operator Tensor Formulation of Quantum Theory
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
The underlying probabilistic theory for quantum mechanics is non-Kolmogorovian. The order in which physical observables will be important if they are incompatible (non-commuting). In particular, the notion of conditioning needs to be…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
Quantum Mechanics (QM) is a very special probabilistic theory, yet we don't know which operational principles make it so. All axiomatization attempts suffer at least one postulate of a mathematical nature. Here I will analyze the…
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
For a machine to be useful in practice, it preferably has to meet two requirements: namely, (i) to be able to perform work under a load and (ii) its operational regime should ideally not depend on the time at which the machine is…
As increasingly impressive quantum information processors are realized in laboratories around the world, robust and reliable characterization of these devices is now more urgent than ever. These diagnostics can take many forms, but one of…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
We extend the quantum geometric tensor from the state space to the operator level,and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference…
We prove that a single photon with quantum data encoded in its orbital angular momentum can be manipulated with simple optical elements to provide any desired quantum computation. We will show how to build any quantum unitary operator using…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
We propose a technique for optimizing parameterized circuits in variational quantum algorithms based on the probabilistic tensor sampling optimization. This method allows one to relax random initialization issues or heuristics for…
The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
A programmable gate array is a circuit whose action is controlled by input data. In this letter we describe a special--purpose quantum circuit that can be programmed to evaluate the expectation value of any operator $O$ acting on a space of…
A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we…