Unraveling Quantum Annealers using Classical Hardness

Abstract

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip.

Degeneracy, degree, and heavy tails in quantum annealing

“…This indicates that heavy tails in DW2X results are not caused by error sensitivity, but rather that error sensitivity is closely related to hardness of the instance in terms of the quantum potential, rather than some classical measure of hardness derived from Boltzmann sampling, matrix condition number, or mixing time of a thermal process as studied in Ref. [10]. This perspective is further justified by heavy tails in SQA results [12] where the Hamiltonian is not prone to error, and by the fact that error sensitivity as measured by the spread of quantiles does not increase monotonically as energy scale decreases, increasing relative control error (see appendix).…”

“…Previous work has advocated searching for quantum speedup in hard U 6 1 problems [2,10,12,25]. The relationship between degree and degeneracy provides two limitations of this choice, in addition to the fact that the classical potential of U 1 instances presents little challenge to simulated thermal solvers [8].…”

“…Fig. 11 shows analogous data from experiments using noisy SA as the solver rather than DW2X: For each experiment consisting of 1000 simulated annealing samples drawn using 2 10 Monte Carlo sweeps, each entry of h and J corresponding to a physically existing coupler or qubit is perturbed by an independent Gaussian error with standard deviation 0.03. This error is relative to full energy scale, so experiments run at energy scale 0.2 will experience Hamiltonian misspecification errors five times as large as those experienced by experiments run at full energy scale.…”

“…These recent works have proposed various important considerations such as error sensitivity, thermal hardness [10], ground state degeneracy, consistency of energy scale across a random ensemble [6,7], potential barrier shape [4,5], and the existence of classical phase transitions [8]. In parallel to this line of research is the consideration of suitable performance metrics for exact and approximate optimization [9,11,12].…”

Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stoquastic Hamiltonians

“…This implies that the system eventually reaches the ground state of the original Ising model representing the solution to the combinatorial optimization problem. There exists a large body of analytical, numerical, and experimental studies on quantum annealing, and active debates are going on to compare quantum annealing with the corresponding classical heuristic, simulated annealing, recent examples of which include Matsuda et al (2009), Young et al (2010), Hen and Young (2011), Farhi et al (2012), Boixo et al (2014), Katzgraber et al (2014Katzgraber et al ( , 2015, Rønnow et al (2014), Albash et al (2015), Heim et al (2015), Hen et al (2015), Isakov et al (2016), Martin-Mayor and Hen (2015), Steiger et al (2015), Venturelli et al (2015), Crosson and Harrow (2016), Denchev et al (2016), Kechedzhi and Smelyanskiy (2016), Mandrà et al (2016a,b), Marshall et al (2016), and Muthukrishnan et al (2016).…”