Related papers: Quantum complexity and the virial theorem
Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical…
Given a multiparticle quantum state, one may ask whether it can be represented as a thermal state of some Hamiltonian with k-particle interactions only. The distance from the exponential family defined by these thermal states can be…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
Kolmogorov's foundation of probability takes measure spaces, $\sigma$-algebras, and probability measures as basic objects. It is, however, widely recognized that this classical framework is inadequate for random phenomena involving quantum…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
A quantum gravity computer is one for which the particular effects of quantum gravity are relevant. In general relativity, causal structure is non-fixed. In quantum theory non-fixed quantities are subject to quantum uncertainty. It is…
In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the…
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper we build a framework for probabilistic theories with non-fixed causal…
We discuss some of the issues to be addressed in arriving at a definitive noncommutative Riemannian geometry that generalises conventional geometry both to the quantum domain and to the discrete domain. This also provides an introduction to…
In this note, we study the celebrated virial theorem for dissipative systems, both classical and quantum. The classical formulation is discussed and an intriguing effect of the random force (noise) is made explicit in the context of the…
We propose an implementation of quantum logic gates via virtual vibrational excitations in an ion trap quantum computer. Transition paths involving unpopulated, vibrational states interfere destructively to eliminate the dependence of rates…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
In this paper, we investigate the use of variational quantum algorithms for simulating the thermodynamic properties of dinuclear metal complexes. Our study highlights the potential of quantum computing to transform advanced simulations and…
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the…
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…