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The Gn,m Phase Transition is Not Hard for the Hamiltonian Cycle Problem

B. Vandegriend, J. Culberson
1998 The Journal of Artificial Intelligence Research  
Using an improved backtrack algorithm with sophisticated pruning techniques, we revise previous observations correlating a high frequency of hard to solve Hamiltonian Cycle instances with the Gn,m phase  ...  We have so far found no class of graphs correlated with the Gn,m phase transition which asymptotically produces a high frequency of hard instances.  ...  The empirical evidence we collect suggests that in contrast to the graph coloring situation, the Hamiltonian cycle G n;m class is not minimally quadratically hard, even for m at or near the phase transition  ... 
doi:10.1613/jair.512 fatcat:mpvofqezyvbovd25tswy55slbm

Flat Histogram Methods for Quantum Systems: Algorithms to Overcome Tunneling Problems and Calculate the Free Energy

Matthias Troyer, Stefan Wessel, Fabien Alet
2003 Physical Review Letters  
Similar to their classical counterpart, the algorithms are efficient at thermal and quantum phase transitions, greatly reducing the tunneling problem at first order phase transitions, and allow the direct  ...  calculation of the free energy and entropy.  ...  The problem of critical slowing down has been overcome for second order phase transitions by cluster update schemes for classical [3] and quantum systems [4 -7] .  ... 
doi:10.1103/physrevlett.90.120201 pmid:12688855 fatcat:cpkw3hs23fa4pmrrh2npehlbci

Statistical Analysis for Quantum Adiabatic Computations: Quantum Monte Carlo Annealing

T. Neuhaus
2011 Physics Procedia  
In 3SAT we present numerical data for the behavior of quantum Monte Carlo annealing cycles in search for the ground state.  ...  We mention a recent determination of the quantum complexity, i.e. the mass-gap Δm GAP for a specific ensemble of three-satisfiability (3SAT) problems with a unique satisfiability assignment, which shows  ...  Under the assumption P NP, the computational effort for any classical algorithm to solve NP-hard problems is believed to be O(e gN ), where g denotes the growth-rate constant.  ... 
doi:10.1016/j.phpro.2011.06.002 fatcat:oslmrwvcfje4lfgqb2hbdikctu

On the complexity of unfrozen problems

Adam Beacham, Joseph Culberson
2005 Discrete Applied Mathematics  
This study was motivated by results from statistical mechanics being applied to phase transitions of NP-complete problems, which show a correlation of hard instances with a sudden increase in frozen variables  ...  We consider questions such as what is the complexity of recognizing instances of (monotonic) NP-complete problems in which no variable is fixed (or frozen) by the set of solutions.  ...  Hamiltonian cycle and more recently 1-in-k SAT [1] , are NP-complete and are known to have second order phase transitions. 2-SAT which is polynomial, also has a second order transition and thus there  ... 
doi:10.1016/j.dam.2005.05.003 fatcat:g6mkqaznqjh4ho5y4sbfibz3ni

Efficient tensor network simulation of quantum many-body physics on sparse graphs [article]

Subhayan Sahu, Brian Swingle
2022 arXiv   pre-print
Using the variational method we study the phase diagram of the transverse field quantum Ising model defined on sparse expander graphs.  ...  We study tensor network states defined on an underlying graph which is sparsely connected.  ...  The results indicate there is a phase transition at 2 ≤ h x ≤ 3.  ... 
arXiv:2206.04701v1 fatcat:nlo2eualszgz5jo6skkaopetxy

Non-equilibrium dynamics of a nonlinear Jaynes–Cummings model in cavity arrays

Jiří Minář, Şebnem Güneş Söyler, Igor Lesanovsky
2016 New Journal of Physics  
In the limit of large non-linearity, the system exhibits an Ising like phase transition as the coupling between light and matter is varied.  ...  Such system is highly tunable and can be described by a Jaynes-Cummings like Hamiltonian with additional non-linear terms.  ...  We have found a rich behavior including bistable regions, Ising like phase transition or occurrence of limit cycles through Hopf bifurcations.  ... 
doi:10.1088/1367-2630/18/5/053035 fatcat:ds6u2peikfe4zgoeuvco42aft4

Obstacles to State Preparation and Variational Optimization from Symmetry Protection [article]

Sergey Bravyi, Alexander Kliesch, Robert Koenig, Eugene Tang
2019 arXiv   pre-print
This proves a version of the No Low-Energy Trivial States (NLTS) conjecture for a family of local Hamiltonians with symmetry protected topological order.  ...  A surprising consequence of this result is that the Goemans-Williamson algorithm outperforms the Quantum Approximate Optimization Algorithm (QAOA) for certain instances of MaxCut, at any constant level  ...  The authors are grateful to Giacomo Nannicini and Kristan Temme for helpful discussions. SB acknowledges the support of the IBM Research Frontiers Institute and funding from the MIT-IBM Watson AI Lab  ... 
arXiv:1910.08980v1 fatcat:lccra5fk5nh2pkt3cpejfjqkke

Structure of Lefschetz thimbles in simple fermionic systems

Takuya Kanazawa, Yuya Tanizaki
2015 Journal of High Energy Physics  
In zero-dimensional versions of the Gross-Neveu model and the Nambu-Jona-Lasinio model, we study the structure of Lefschetz thimbles and its variation across the chiral phase transition.  ...  We also consider a Chern-Simons theory with fermions in 0+1-dimension and show how Lefschetz thimbles solve the complex phase problem caused by a topological term.  ...  This is not a phase transition, but corresponds to the disappearance (or emergence) of a metastable state.  ... 
doi:10.1007/jhep03(2015)044 fatcat:j3l5umydkfckfluydfyyqfu6xe

Communities, clustering phase transitions, and hysteresis: Pitfalls in constructing network ensembles

David Foster, Jacob Foster, Maya Paczuski, Peter Grassberger
2010 Physical Review E  
We find that our model exhibits phase transitions as the fugacity is changed. For regular graphs (identical degrees for all nodes) with degree k > 2 we find a single first order transition.  ...  In this paper, we study a model where clustering is enhanced by means of a fugacity term as in the Strauss (or "triangle") model, but where the degree sequence is strictly preserved -- thus maintaining  ...  Thus it is not surprising that a simpler scenario holds for regular graphs ͑same degree k for all nodes͒where only a single phase transition occurs for all k Ͼ 2. For k = 2 no transition occurs.  ... 
doi:10.1103/physreve.81.046115 pmid:20481794 fatcat:yyu2oy5q7feurchzbjruxr7ahm

Collapse transition of randomly branched polymers: Renormalized field theory

Hans-Karl Janssen, Olaf Stenull
2011 Physical Review E  
For the collapse θ^'-transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition.  ...  Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related  ...  However, the current understanding of RBPs is still not quite satisfactory. For example, the topology of their phase diagram is not entirely clear.  ... 
doi:10.1103/physreve.83.051126 pmid:21728509 fatcat:xippozp4srgstktsmqyzxtmx4i

Perturbing general uncorrelated networks

Z. Burda, J. Jurkiewicz, A. Krzywicki
2004 Physical Review E  
It is shown that the results obtained for Erd\"os-R\'enyi graphs are generic, at the qualitative level.  ...  This paper is a direct continuation of an earlier work, where we studied Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring the formation of short cycles.  ...  However the stability of this phase is an open problem. In ref.  ... 
doi:10.1103/physreve.70.026106 pmid:15447544 fatcat:uezhxeclyrg5vmrh4qu4ki4r2q

An SU(2) geometric phase induced by periodically driven Raman process in an ultracold dilute Bose gas [article]

Zekai Chen, Joseph D. Murphree, Nicholas P. Bigelow
2019 arXiv   pre-print
We propose a practical protocol to generate and observe a non-Abelian geometric phase using a periodically driven Raman process in the hyperfne ground state manifold of atoms in a dilute ultracold gas.  ...  Our analysis is based upon recent developments and application of Floquet theory to periodically driven quantum systems.  ...  ACKNOWLEDGEMENT We thank Maitreyi Jayaseelan and Elisha Haber for discussions. We also thank Gediminas Juzeliūnas for the useful comments on the manuscript.  ... 
arXiv:1907.10721v2 fatcat:mi7e66l5wzdd5oodk4du5xxsxi

On Gibbs Measures of Models with Competing Ternary and Binary Interactions and Corresponding Von Neumann Algebras II

Farruh Mukhamedov, Utkir Rozikov
2005 Journal of statistical physics  
The structure of Gibbs measures for the model considered is studied.  ...  Keywords: Cayley tree, Ising model, competing interactions, Gibbs measure, GNS-construction, Hamiltonian, von Neumann algebra.  ...  The work is also partially supported by Grant Φ-1.1.2 Rep. Uzb.  ... 
doi:10.1007/s10955-004-2056-3 fatcat:2em44cpgwjfspl6vcsnhtq3pny

The GHS and other correlation inequalities for the two-star model [article]

Alessandra Bianchi, Francesca Collet, Elena Magnanini
2021 arXiv   pre-print
Borrowing tools from statistical mechanics, we study different classes of correlation inequalities for edges, that naturally emerge while taking the partial derivatives of the (finite size) free energy  ...  As a consequence, under the above conditions on the parameters, the average edge density turns out to be an increasing and concave function of the parameter h, at any fixed size of the graph.  ...  In particular, the system undergoes a first order phase transition across the curve and a second order phase transition at the critical point (see [23], Thms. 2.1 & 2.2).  ... 
arXiv:2107.08889v2 fatcat:urppsg5qofcohnolegvbivsxsi

Zero-temperature quantum annealing bottlenecks in the spin-glass phase

Sergey Knysh
2016 Nature Communications  
For smaller N, only the gap at the critical point is relevant, where it scales polynomially, as long as the phase transition is second order.  ...  Regions where the energy gap to excited states is small (for instance at the phase transition) are the algorithm's bottlenecks.  ...  The U.S. Government is authorized to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright annotation thereon.  ... 
doi:10.1038/ncomms12370 pmid:27491338 pmcid:PMC4980455 fatcat:h72cjl3iiferxnemhmszzsxhsm
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