D-Wave quantum computing system was used to find solutions to optimization problems in what is known as Ramsey theory, after British mathematician Frank Ramsey. This field deals with situations in which a certain kind of order appears within a disordered system.
A well-known problem called the “party problem” asks what the minimum number of guests you would need to invite to a gathering to ensure that a small subset is made of people who all know each other and another who all don’t. Solutions to this problem are given in what’s known as Ramsey numbers. Calculating the minimum number of guests to ensure groups of three strangers and three friends is fairly easy (the answer is six). But increasing the number of people makes the solution increasingly hard to calculate, with most Ramsey numbers being beyond the capability of our current computers.
While noting that the D-Wave experiment’s calculations were correct, the authors of a commentary piece in the same issue wrote that “many more tests would be needed to conclude that the logical elements are functioning as qubits and that the device is a real quantum computer.”
The algorithms used to calculate these Ramsey numbers “don’t need as much coherence as a full-blown quantum computer,” said physicist Frank Gaitan of the University of Maryland, who worked on the D-Wave experiment.
D-Wave’s machine is not necessarily a universal quantum computer, which could run any algorithm given to it. Instead, it is designed to be particularly good at solving optimization problems, such as those in Ramsey theory, and the evidence from his research shows that the device “uses some kind of quantum effect that solves some kind of problems.”
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 R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) 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.