Related papers: Towards Quantifying Complexity with Quantum Mechan…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We discuss the possibility for such transitions…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for…
We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement…
Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…