We propose a physical realization of the unstructured database search that works via classical, dissipative model of spherical spins. The database is implemented via spin-spin couplings, where the selected coupling refers to a larger ferromagnetic interaction between two selected spins. The low-temperature equilibrium of this model leads to magnetization strongly concentrated on the selected spins, which means that the search is complete. The search time refers to the relaxation time to equilibrium from a homogeneous initial state, and is described via Langevin equations. This time scales as ${\cal O}(M^a)$ with $a<1/2$ , where $M$ is the database volume. This is faster than Grover's search, showing how a dissipative, classical analog computer can overcome the quantum unitary computer.We propose a physical realization of the unstructured database search that works via classical, dissipative model of spherical spins. The database is implemented via spin-spin couplings, where the selected coupling refers to a larger ferromagnetic interaction between two selected spins. The low-temperature equilibrium of this model leads to magnetization strongly concentrated on the selected spins, which means that the search is complete. The search time refers to the relaxation time to equilibrium from a homogeneous initial state, and is described via Langevin equations. This time scales as ${\cal O}(M^a)$ with $a<1/2$, where $M$ is the database volume. This is faster than Grover's search, showing how a dissipative, classical analog computer can overcome the quantum unitary computer.

cond-mat.stat-mechCross-listedarXiv:2606.18835Jun 18, 20260 citations

On classical models of Spin

Marek Czachor

arXiv:quant-ph/0205010Foundations of Physics LettersJun 1, 199221 citations

Classical Spin Models: An Introduction

Andreas Wipf

Lecture notes in physicsOct 26, 20121 citation

Comparison between the Iterative Local Search and Exhaustive Search methods applied to QAOA in Max-Cut and Ising Spin Model problems

Brian García Sarmina

A comparison is made between Exhaustive Search (ES) and Iterative Local Search (ILS). Such comparison was made using the Quantum Approximation Optimization Algorithm (QAOA). QAOA has been extensively researched due to its this potential to be implemented in actual quantum hardware, and its promising future in optimization problems and quantum machine learning. ES and ILS approaches were simulated to determine the pros and cons of these techniques for QAOA in local (classic computer) and real simulations (IBM quantum computer). These classic approaches were used in QAOA to approximate the optimal expected value in Max-Cut and Ising Spin Model (ISM) problems, both of these flavors have three simulated configurations called: linear, cyclic and complete (or full).A comparison is made between Exhaustive Search (ES) and Iterative Local Search (ILS). Such comparison was made using the Quantum Approximation Optimization Algorithm (QAOA). QAOA has been extensively researched due to its this potential to be implemented in actual quantum hardware, and its promising future in optimization problems and quantum machine learning. ES and ILS approaches were simulated to determine the pros and cons of these techniques for QAOA in local (classic computer) and real simulations (IBM quantum computer). These classic approaches were used in QAOA to approximate the optimal expected value in Max-Cut and Ising Spin Model (ISM) problems, both of these flavors have three simulated configurations called: linear, cyclic and complete (or full).

arXiv:2205.03441May 6, 20221 citation

Classical and Quantum Theories of Spin

Fabián H. Gaioli, Edgardo T. Garcia Alvarez

arXiv:hep-th/9807131Foundations of PhysicsOct 1, 199813 citations

Fractionalized Z 2 Classical Heisenberg Spin Liquids

J. Rehn, Arnab Sen, Roderich Moessner

Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalized spin liquid phase, the so-called Coulomb or U(1) spin liquid, has until recently been identified: This exhibits algebraic spin correlations and impurity moments, "orphan spins," whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalization in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z_{2} spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavor.Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalized spin liquid phase, the so-called Coulomb or U(1) spin liquid, has until recently been identified: This exhibits algebraic spin correlations and impurity moments, "orphan spins," whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalization in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z_{2} spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavor.

arXiv:1608.00705Physical Review LettersJan 27, 201736 citations

{\cal O}(M^a)

with

a<1/2

, where

M

is the database volume. This is faster than Grover's search, showing how a dissipative, classical analog computer can overcome the quantum unitary computer.