Related papers: Classification on the Computational Complexity of …
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
The concept of statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allows us to understand this driven…
We consider a classical spinning particle in the frame of the relativistic physics by means of a covariant Hamiltonian and of a generalization of Poisson brackets which take into account the gauge fields. We obtain different equations of…
Enormous activity in the Quantum Computing area has resulted in considering them to solve different difficult problems, including those of applied nature, together with classical computers. An attempt is made in this work to nail down a…
Spin models are used in many studies of complex systems---be it condensed matter physics, neural networks, or economics---as they exhibit rich macroscopic behaviour despite their microscopic simplicity. Here we prove that all the physics of…
The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…
Inspired by path integral molecular dynamics, we build a spin model, in terms of spin coherent states, from which we can compute the quantum expectation values of a spin in a constant magnetic field, at finite temperature. This formulation…
We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with…
Some questions concerning the calculation of the number of ``physical'' (metastable) states or complexity of the spherical $p$-spin spin glass model are reviewed and examined further. Particular attention is focused on the general…
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…