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This paper provides a systematic study of the operational idea that a quantum ``state'' is only defined up to what can be distinguished by a chosen family of observables. Concretely, any von Neumann algebra of observables $\mathscr{M}$…
Unitary operators are essential to quantum mechanics, however for discrete systems larger than a qubit, it is difficult to express them in a self-contained way. This report presents just such a description, providing a compact, useful…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
Within the framework of the algebraic approach the problem of hidden parameters in quantum mechanics is surveyed. It is shown that the algebraic formulation of quantum mechanics permits introduction of a specific hidden parameter, which has…
We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing…
This is the first installment of a paper in three parts, where we use noncommutative geometry to study the space of commensurability classes of Q-lattices and we show that the arithmetic properties of KMS states in the corresponding quantum…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with interval-posets, themselves known to be in bijection with Tamari intervals. We show that in each…
Quantum spin ice represents a paradigmatic example on how the physics of frustrated magnets is related to gauge theories. In the present work we address the problem of approximately realizing quantum spin ice in two dimensions with cold…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice…
We apply the machinery of projection lattices and von Neumann algebras to analyze the question of how modal interpretations can (and do) circumvent von Neumann's infamous 'no-hidden-variables' theorem.
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
We show how it is possible to realize quantum computations on a system in which most of the parameters are practically unknown. We illustrate our results with a novel implementation of a quantum computer by means of bosonic atoms in an…
We propose a regularized lattice model for quantum gravity purely formulated in terms of fermions. The lattice action exhibits local Lorentz symmetry, and the continuum limit is invariant under general coordinate transformations. The metric…
Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience…
Gedanken experiments in quantum gravity motivate generalised uncertainty relations (GURs) implying deviations from the standard quantum statistics close to the Planck scale. These deviations have been extensively investigated for the…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…