ترغب بنشر مسار تعليمي؟ اضغط هنا

Equation Planting: A Tool for Benchmarking Ising Machines

83   0   0.0 ( 0 )
 نشر من قبل Itay Hen
 تاريخ النشر 2019
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Itay Hen




اسأل ChatGPT حول البحث

We introduce a methodology for generating benchmark problem sets for Ising machines---devices designed to solve discrete optimization problems cast as Ising models. In our approach, linear systems of equations are cast as Ising cost functions. While linear systems are easily solvable, the corresponding optimization problems are known to exhibit some of the salient features of NP-hardness, such as strong exponential scaling of heuristic solvers runtimes and extensive distances between ground and low-lying excited states. We show how the proposed technique, which we refer to as `equation planting, can serve as a useful tool for evaluating the utility of Ising solvers functioning either as optimizers or as ground-state samplers. We further argue that equation-planted problems can be used to probe the mechanisms underlying the operation of Ising machines.



قيم البحث

اقرأ أيضاً

Thermal machines perform useful tasks--such as producing work, cooling, or heating--by exchanging energy, and possibly additional conserved quantities such as particles, with reservoirs. Here we consider thermal machines that perform more than one us eful task simultaneously, terming these hybrid thermal machines. We outline their restrictions imposed by the laws of thermodynamics and we quantify their performance in terms of efficiencies. To illustrate their full potential, reservoirs that feature multiple conserved quantities, described by generalized Gibbs ensembles, are considered. A minimal model for a hybrid thermal machine is introduced, featuring three reservoirs and two conserved quantities, e.g., energy and particle number. This model can be readily implemented in a thermoelectric setup based on quantum dots, and hybrid regimes are accessible considering realistic parameters.
Quantum annealing (QA) is a hardware-based heuristic optimization and sampling method applicable to discrete undirected graphical models. While similar to simulated annealing, QA relies on quantum, rather than thermal, effects to explore complex sear ch spaces. For many classes of problems, QA is known to offer computational advantages over simulated annealing. Here we report on the ability of recent QA hardware to accelerate training of fully visible Boltzmann machines. We characterize the sampling distribution of QA hardware, and show that in many cases, the quantum distributions differ significantly from classical Boltzmann distributions. In spite of this difference, training (which seeks to match data and model statistics) using standard classical gradient updates is still effective. We investigate the use of QA for seeding Markov chains as an alternative to contrastive divergence (CD) and persistent contrastive divergence (PCD). Using $k=50$ Gibbs steps, we show that for problems with high-energy barriers between modes, QA-based seeds can improve upon chains with CD and PCD initializations. For these hard problems, QA gradient estimates are more accurate, and allow for faster learning. Furthermore, and interestingly, even the case of raw QA samples (that is, $k=0$) achieved similar improvements. We argue that this relates to the fact that we are training a quantum rather than classical Boltzmann distribution in this case. The learned parameters give rise to hardware QA distributions closely approximating classical Boltzmann distributions that are hard to train with CD/PCD.
The seminal work by Sadi Carnot in the early nineteenth century provided the blueprint of a reversible heat engine and the celebrated second law of thermodynamics eventually followed. Almost two centuries later, the quest to formulate a quantum theor y of the thermodynamic laws has thus unsurprisingly motivated physicists to visualise what are known as `quantum thermal machines (QTMs). In this article, we review the prominent developments achieved in the theoretical construction as well as understanding of QTMs, beginning from the formulation of their earliest prototypes to recent models. We also present a detailed introduction and highlight recent progress in the rapidly developing field of `quantum batteries.
We show that Gibbs states of non-homogeneous transverse Ising chains satisfy a emph{shielding} property. Namely, whatever the fields on each spin and exchange couplings between neighboring spins are, if the field in one particular site is null, the r educed states of the subchains to the right and to the left of this site are emph{exactly} the Gibbs states of each subchain alone. Therefore, even if there is a strong exchange coupling between the extremal sites of each subchain, the Gibbs states of the each subchain behave as if there is no interaction between them. In general, if a lattice can be divided into two disconnected regions separated by an interface of sites with zero applied field, we can guarantee a similar result only if the surface contains a single site. Already for an interface with two sites we show an example where the property does not hold. When it holds, however, we show that if a perturbation of the Hamiltonian parameters is done in one side of the lattice, the other side is completely unchanged, with regard to both its equilibrium state and dynamics.
We consider thermal machines powered by locally equilibrium reservoirs that share classical or quantum correlations. The reservoirs are modelled by the so-called collisional model or repeated interactions model. In our framework, two reservoir partic les, initially prepared in a thermal state, are correlated through a unitary transformation and afterwards interact locally with the two quantum subsystems which form the working fluid. For a particular class of unitaries, we show how the transformation applied to the reservoir particles affects the amount of heat transferred and the work produced. We then compute the distribution of heat and work when the unitary is chosen randomly, proving that the total swap transformation is the optimal one. Finally, we analyse the performance of the machines in terms of classical and quantum correlations established among the microscopic constituents of the machine.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا