Related papers: Classifying Quantum Phases With The Torus Trick
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase…
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a…
Topological phase transitions in free fermion systems can be characterized by closing of single-particle gap and change in topological invariants. However, in the presence of electronic interactions, topological phase transitions are more…
Many-body quantum games provide a natural perspective on phases of matter in quantum hardware, crisply relating the quantum correlations inherent in phases of matter to the securing of quantum advantage at a device-oriented task. In this…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
Dynamical Lie-algebraic method for the construction of local quantum invariants of motion in non-integrable many-body systems is proposed and applied to a simple but generic toy model, namely an infinite kicked $t-V$ chain of spinless…
We introduce a coherence susceptibility method, based on the fact that it signals quantum fluctuations, for identifying quantum phase transitions, which are induced by quantum fluctuations. This method requires no prior knowledge of order…
We consider periodic quantum Hamiltonians on the torus phase space (Harper-like Hamiltonians). We calculate the topological Chern index which characterizes each spectral band in the generic case. This calculation is made by a semi-classical…
Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of $q=2$ groups. However, analytic…
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…
Research on topological phases of matter is a core field in modern condensed matter physics. Free fermion systems, such as topological insulators and superconductors, have been studied using the "Tenfold Way" and K-theory. Building on…
This article is aimed at a pedagogical introduction to the physics of quantum phase transitions that is unique to metallic systems. It has been recognized for some time that quantum criticality can result in a breakdown of Landau's Fermi…
Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical…
Contextuality in quantum physics provides a key resource for quantum information and computation. The topological approach in [Abramsky and Brandenburger, New J. Phys., 2011, Abramsky et al., CSL 2015, 2015] characterizes contextuality as…
Two classes of time-periodic systems of ordinary differential equations with a small nonnegative parameter, those with fast and slow time, are studied. Right-hand sides of these systems are three times continuously differentiable with…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…