2 0 obj In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. an extremely small gap that is exponentially sensitive to the Hamiltonian We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. ization) as well as its corresponding perturbative value. Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. We raise the basic question about what the appropriate formulation of adiabatic running time should be. weighted maximum independent set problem instance. gaps due to avoided crossings inside a phase. optimization for an NP-hard Ising spin glass instance class with up to 128 Magnetic ordering transitions of disordered systems 16. parameters. order of the phase transitions is not predictive of the scaling of the gap with We show agreement An adiabatic process is a thermodynamic process, in which there is no heat transfer into or out of the system (Q = 0). For this purpose, we introduce a new parametrization definition of the anti-crossing. Thus, a dynamical detection event may have totally different sensitivity scaling. 5 0 obj Basic concepts 2. transition. an instantonic approach, and discuss the (dire) consequences for quantum annealing. We divide the possible failure 3b, a significant drop of, volved, such a transition is not very sharp, as it would be, cal minima vanishes, allowing more dynamics within the. irrespective of the nature of decay of these interactions along the chain. (arXiv:0908.2782 [quant-ph]) that their adiabatic quantum algorithm failed with high probability for randomly generated instances of Exact Cover does not carry over to this new algorithm. OSTI.GOV Journal Article: Adiabatic quantum algorithms as quantum phase transitions: First versus second order Young Talk at the Conference on Quantum Statistical Mechanics, Computation, and Information, ICTP, Trieste, June 14-18, 2010 Anti-crossing vs perturbative crossing Our definition of anti-crossing is more general than the perturbative crossing in, ... Anti-crossing and min-gap size The min-gap size is expected to be exponentially small in O(b k ) where k = ||FS − GS|| for some 0 < b < 1. ���� JFIF H H �� Photoshop 3.0 8BIM ��8ICC_PROFILE (appl mntrRGB XYZ � acspAPPL appl �� �-appl rXYZ gXYZ 4 bXYZ H wtpt \ chad p ,rTRC � gTRC � bTRC � desc � ?cprt T Hvcgt � 0ndin 8dscm � �XYZ tK > �XYZ Zs �� &XYZ ( W �3XYZ �R �sf32 B ����&. Adiabatic quantum computation (AQC) was first pro-, proved that AQC is polynomially equivalent to conven-, In AQC, the system’s Hamiltonian, usually written as, is assumed to have an easily accessible ground, which the system is initialized, while the ground state, state with high fidelity, the adiabatic theorem requires, most fundamental problem in AQC is therefore how to, unveil the quantum evolution blackbox by relating the. At zeroth order perturbation, levels do not cross (solid lines). All figure content in this area was uploaded by Mohammad Amin, All content in this area was uploaded by Mohammad Amin, arXiv:0904.1387v3 [quant-ph] 15 Dec 2009. quantum phase transitions during an adiabatic quantum computation. %PDF-1.3 For couplings not attracted by the Gaussian fixed point above $d=8$, and for all physical couplings below $d=8$, we find runaway renormalization group flows to strong coupling. For wL<2wG, the 6 central vertices make the WMIS, while every combination of 3 vertices each from one triangle is a smaller independent set, altogether making 27 degenerate local minima. Using the Maximum-weighted Independent Set (MIS) problem in which there are flexible parameters (energy penalties J between pairs of edges) in an Ising formulation as the model problem, we construct examples to show that by changing the value of J, we can change the quantum evolution from one that has an anti-crossing (that results in an exponential small min-gap) to one that does not have, or the other way around, and thus drastically change (increase or decrease) the min-gap. Authors: M. H. S. Amin, V. Choi. © 2008-2020 ResearchGate GmbH. Adiabatic quantum optimization has attracted a lot of attention because small scale simulations gave hope that it would allow to solve NP-complete problems efficiently. Quantum fluctuations driven by non-stoquastic Hamiltonians have been conjectured to be an important and perhaps essential missing ingredient for achieving a quantum advantage with adiabatic optimization. We show that the quantum version of random Satisfiability problem with 3 bits in a clause (3-SAT) has a first-order quantum phase transition. Quantum spin glasses. smaller than the temperature and decoherence-induced level broadening. can not only predict the behavior of the gap, but also provide insight on how