Estimating the density of states of frustrated spin systems

Barash, L. Yu.; Marshall, Jeffrey; Weigel, Martin; Hen, Itay

doi:10.1088/1367-2630/ab2e39

Cited by 21 publications

(26 citation statements)

References 67 publications

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“…and from Eq. (6) we see that this transformation is precisely the transformation fromS c toS, thus verifying (15). Formulas for the weighted average of the two entropies are slightly more complicated to derive because the entropy depends on a thermodynamic integration over all of the annealing steps, Eq.…”

Section: Weighted Averagessupporting

confidence: 60%

“…If multiple replicas of the system are simultaneously annealed, resampling can also be done among the set of replicas. The resulting scheme is population annealing [9,10,[12][13][14][15] and is an example of a sequential Monte Carlo [16] algorithm. Population annealing in the canonical ensemble is an effective tool for simulating equilibrium systems with rough free energy landscapes, such as spin glasses [13,14,17].…”

Section: Introductionmentioning

confidence: 99%

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Equilibrium microcanonical annealing for first-order phase transitions

Rose

Machta

2019

Phys. Rev. E

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A framework is presented for carrying out simulations of equilibrium systems in the microcanonical ensemble using annealing in an energy ceiling. The framework encompasses an equilibrium version of simulated annealing, population annealing and hybrid algorithms that interpolate between these extremes. These equilibrium, microcanonical annealing algorithms are applied to the thermal firstorder transition in the 20-state, two-dimensional Potts model. All of these algorithms are observed to perform well at the first-order transition though for the system sizes studied here, equilibrium simulated annealing is most efficient. arXiv:1907.07067v1 [cond-mat.stat-mech]

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Section: Weighted Averagessupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Equilibrium microcanonical annealing for first-order phase transitions

Rose

Machta

2019

Phys. Rev. E

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“…With the advent of a new entropic sampling technique based on population annealing [10], we were able to accurately estimate the degeneracies for 225 planted-solution instances containing 501 qubits (that is the estimated ground and first excited state degeneracies are within 5% of the known values found by planting). For more information on these techniques see Refs.…”

Section: E Classical Boltzmann Distributionmentioning

confidence: 99%

“…The second advance we rely on is new entropic sampling techniques based on population annealing that enable accurate estimates (i.e., with quantifiable error) of the eigenspectum degeneracies for large-scale (e.g. 500 qubits) planted-solution problems [8,10].…”

Section: Introductionmentioning

confidence: 99%

Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers

et al. 2019

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We investigate alternative annealing schedules on the current generation of quantum annealing hardware (the D-Wave 2000Q), which includes the use of forward and reverse annealing with an intermediate pause. This work provides new insights into the inner workings of these devices (and quantum devices in general), particular into how thermal effects govern the system dynamics. We show that a pause mid-way through the anneal can cause a dramatic change in the output distribution, and we provide evidence suggesting thermalization is indeed occurring during such a pause. We demonstrate that upon pausing the system in a narrow region shortly after the minimum gap, the probability of successfully finding the ground state of the problem Hamiltonian can be increased over an order of magnitude. We relate this effect to relaxation (i.e. thermalization) after diabatic and thermal excitations that occur in the region near to the minimum gap. For a set of large-scale problems of up to 500 qubits, we demonstrate that the distribution returned from the annealer very closely matches a (classical) Boltzmann distribution of the problem Hamiltonian, albeit one with a temperature at least 1.5 times higher than the (effective) temperature of the annealer. Moreover, we show that larger problems are more likely to thermalize to a classical Boltzmann distribution. arXiv:1810.05881v2 [quant-ph]

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“…(22) and (23) will not be the same, meaning the Eqs. (19) cannot be simultaneously satisfied. We demonstrate this by example.…”

Section: One Findsmentioning

confidence: 99%

Perils of embedding for sampling problems

Marshall

Gioacchino

Rieffel

2020

Phys. Rev. Research

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Sampling from certain distributions is a prohibitively challenging task. Special-purpose hardware such as quantum annealers may be able to more efficiently sample from such distributions, which could find application in optimization, sampling tasks, and machine learning. Current quantum annealers impose certain constraints on the structure of the cost Hamiltonian due to the connectivity of the individual processing units. This means that in order to solve many problems of interest, one is required to embed the native graph into the hardware graph. The effect of embedding for sampling is more pronounced than for optimization; for optimization one is just concerned with mapping ground states to ground states, whereas for sampling one needs to consider states at all energies. We argue that as the problem size grows, or the embedding size grows, the chance of a sample being in the logical subspace is exponentially suppressed. It is therefore necessary to construct post-processing techniques to evade this exponential sampling overhead, techniques that project from the embedded distribution one is physically sampling from, back to the logical space of the native problem. We show that the most naive (and most common) projection technique, known as majority vote, can fail quite spectacularly at preserving distribution properties. We show that, even with care, one cannot avoid bias in the general case. Specifically we prove through a simple and generic (counter) example that no post-processing technique, under reasonable assumptions, can avoid biasing the statistics in the general case. On the positive side, we demonstrate a new resampling technique for performing this projection which substantially out-performs majority vote and may allow one to much more effectively sample from graphs of interest.

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Estimating the density of states of frustrated spin systems

Cited by 21 publications

References 67 publications

Equilibrium microcanonical annealing for first-order phase transitions

Equilibrium microcanonical annealing for first-order phase transitions

Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers

Perils of embedding for sampling problems

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