Related papers: Thermodynamic-Complexity Duality: Embedding Comput…
Classical circuit complexity characterizes parallel computation in purely combinatorial terms, ignoring the physical constraints that govern real hardware. The standard classes $\mathbf{NC}$, $\mathbf{AC}$, and $\mathbf{TC}$ treat unlimited…
In this article a definition of reversible processes in terms of differences in intensive Thermodynamics properties (Affinities) is proposed. This definition makes it possible to both define reversible processes before introducing the…
We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing…
Since reversible computing requires preservation of all information throughout the entire computational process, this implies that all errors that appear as a result of the interaction of the information-carrying system with uncontrolled…
The fundamental lower bounds of the thermodynamic energy cost (work) needed for the measurement and the erasure of information are found. The lower bound for the erasure vindicates the "Landauer's principle" for a special case, but…
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…
The process of creating goods and services, measured by their value, is considered a process of creating complexity. This allows us to consider the production system as an open thermodynamic system, and to develop a simple heuristic model…
The new mathematical framework based on the free energy of pure classical fluids presented in [R. D. Rohrmann, Physica A 347, 221 (2005)] is extended to multi-component systems to determine thermodynamic and structural properties of…
Thermodynamic computing exploits fluctuations and dissipation in physical systems to efficiently solve various mathematical problems. For example, it was recently shown that certain linear algebra problems can be solved thermodynamically,…
It is widely anticipated that a large-scale quantum computer will offer an evermore accurate simulation of nature, opening the floodgates for exciting scientific breakthroughs and technological innovations. Here, we show a complete,…
Measuring the complexity of high-dimensional data in physical systems becomes a critical factor in determining the information and quality of the systems. However, traditional metrics, such as Lyapunov exponent, fractal dimension, and…
We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
The paper describes a novel technique that allows to reduce by half the number of delta values that were required to be computed with complexity O(N) in most of the heuristics for the quadratic assignment problem. Using the correlation…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
The vast majority of scientific community believes that P!=NP, with countless supporting arguments. The number of people who believe otherwise probably amounts to as few as those opposing the 2nd Law of Thermodynamics. But isn't nature…
Quantum thermodynamics investigates how robust the second law of thermodynamics serves as the unique fundamental law in the small quantum world. To tackle this problem, the quantum coherence constitutes a major difficulty of investigations,…
A unification of thermodynamics and information theory is proposed. It is argued that similarly to the randomness due to collisions in thermal systems, the quenched randomness that exists in data files in informatics systems contributes to…
The paper reviews two prominent approaches for the measurement of technological complexity: the method of reflection and the assessment of technologies' combinatorial difficulty. It discusses their central underlying assumptions and…
Many important quantities in quantum information science, such as entropy and entanglement, are non-linear functions of the density matrix and cannot be expressed as operator observables. Standard open-system approaches evolve only a single…