Related papers: State Complexity Approximation
We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
An attempt of a new kind of complexity anthropology is considered.
Although probabilistic inference in a general Bayesian belief network is an NP-hard problem, computation time for inference can be reduced in most practical cases by exploiting domain knowledge and by making approximations in the knowledge…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
In this paper we present the extension of an existing method for abstract graph-based state space exploration, called neighbourhood abstraction, with a reduction technique based on subsumption. Basically, one abstract state subsumes another…
Complex Systems were identified and studied in different fields, such as physics, biology, and economics. These systems exhibit exciting properties such as self-organization, robust order, and emergence. In recent years, software systems…
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…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…
We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen's geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we…
We propose a notion of state distinguishability that does not refer to probabilities, but rather to the ability of a set of states to serve as programs for a desired set of gates. Using this notion, we reconstruct the structural features of…
Previous work (Frank and Satta 1998; Karttunen, 1998) has shown that Optimality Theory with gradient constraints generally is not finite state. A new finite-state treatment of gradient constraints is presented which improves upon the…
Beyond computer science, quantum complexity theory can potentially revolutionize multiple branches of physics, ranging from quantum many-body systems to quantum field theory. In this paper, we investigate the relationship between the sample…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides potential applications in quantum resource theory. Here we find a closed form of the minimal distance in the sense of…
A good process model is expected not only to reflect the behavior of the process, but also to be as easy to read and understand as possible. Because preferences vary across different applications, numerous measures provide ways to reflect…
In the article we made an attempt to reveal the contents and development of the concept of economic clusters, to characterize the specificity of the regional cluster as a project. We have identified features of an estimation of efficiency…
The challenging deployment of compute-intensive applications from domains such as Artificial Intelligence (AI) and Digital Signal Processing (DSP), forces the community of computing systems to explore new design approaches. Approximate…
Measuring the closest distance between two states is an alternative and significant approach in the resource quantification, which is the core task in the resource theory. Quite limited progress has been made for this approach even in…