Putting “Quantumness” to the Test

Abstract

Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers Rðm; nÞ. Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers Rð3; 3Þ and Rðm; 2Þ for 4 m 8. The Rð8; 2Þ computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date. In recent years first steps have been taken towards experimentally realizing the computational advantages promised by well-known quantum algorithms. As with any nascent effort, these initial steps have been limited. To date the largest experimental implementations of scientifically meaningful quantum algorithms have used just a handful of qubits. For circuit-based algorithms [1], seven spin qubits were used to factor 15, while for adiabatic algorithms [2], four spin qubits were used to factor 143. In both cases compiled versions of the algorithms were needed to allow factoring with such small numbers of qubits. Although factoring was the focus of both experiments, other scientifically significant applications exist.In Ref.[3] an algorithm for determining the two-color Ramsey numbers was proposed which could be implemented using adiabatic quantum evolution. Ramsey numbers are part of an active research area in mathematics known as Ramsey theory [4] whose central theme is the emergence of order in large disordered structures. The disordered structures can be represented by an N-vertex graph G, and the ordered substructures by specific graphs H 1 and H 2 that are to appear as subgraphs of G. For two-color Ramsey numbers the subgraphs H 1 and H 2 are m-cliques and n-independent sets, respectively. An m-clique is a set of m vertices that has an edge connecting any two of the m vertices, and an n-independent set is a set of n vertices in which no two of the n vertices are joined by an edge. Using Ramsey theory [4,5], one can prove that a threshold value Rðm; nÞ exists so that for N ! Rðm; nÞ every graph with N vertices will contain either an m-clique or an n-independent set. The threshold value Rðm; nÞ is an example of a two-color Ramsey number. Other types of Ramsey numbers exist, though we focus on two-color Ramsey numbers here. Ramsey numbers Rðm; nÞ grow extremely quickly and are notoriously difficult to calculate. In fact, for m, n ! 3, only nine are presently known [5].In the Ramsey number algorithm (RNA) [3], the calculation of Rðm; nÞ is formulated as an optimization problem which can be solved using adiabatic quantum evolution [6]. Here we present evidence of an experimental implementation of the RNA using a...

Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities

“…The U 5,6,7 and S 28 Sidon instance classes reduce the probability of zero local fields drastically by design, and thus maximize the yield of unique ground states. In fact, while U 1 has an average probability of 23% to have zero local fields, this number is reduced to 6% in the U 4 class.…”

When does a physical system compute?

“…Originally presented as implementing a relatively simple quantum annealing paradigm, the consensus has shifted (not least within D-wave itself) that this physical theory is not a good fit for predicting the computational abilities of the machines. Work is now underway to characterize the devices at a mathematical and phenomenological level, treating them as black boxes [ 49 , 50 ].…”

Lack of a thermodynamic finite-temperature spin-glass phase in the two-dimensional randomly coupled ferromagnet

“…The advent of analog quantum annealing machines [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and, in particular, the D-Wave Inc. [15] D-Wave 2X quantum annealer has sparked a new interest in the study of (quasi-) planar Ising spin glasses [16][17][18][19] with finite-temperature transitions. While there have been multiple attempts to discern if the D-Wave quantum annealers display an advantage over conventional technologies [20][21][22][23][24][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], to date there are only few "success stories" [32,39] where the analog quantum optimizers show an advantage over current conventional silicon-based computers. Recent results [26,32] suggest that problems with a more complex energy landscape are needed to discern if quantum annealers can outperform current digital computers.…”