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We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
Complex systems typically have many different parts and facets, with different characteristics. In a multi-paradigm approach to modeling, formalisms with different natures are used in combination to describe complementary parts and aspects…
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
We present a formulation of quantum circuits where the focus is set on whether a given circuit (made of unitary operators and projective measurements with definite outcomes) does reflect an actually realizable physical experiment. In order…
We investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in Ref.~\cite{Guo:2023ecc} that relates the…
Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular…
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…
The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making…
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space…