Peering into the Anneal Process of a Quantum Annealer

Commercial adiabatic quantum annealers have the potential to solve important NP-hard optimization problems efficiently. The newest generation of those machines additionally allows the user to customize the anneal schedule, that is, the schedule with which the anneal fraction is changed from the start to the end of the annealing. In this work we use the aforementioned feature of the D-Wave 2000Q to attempt to monitor how the anneal solution evolves during the anneal process. This process we call slicing: at each time slice during the anneal, we are able to obtain an approximate distribution of anneal solutions. We use our technique to obtain a variety of insights into the D-Wave 2000Q. For example, we observe when individual bits flip during the anneal process and when they stabilize, which allows us to determine the freeze-out point for each qubit individually. We highlight our results using both random QUBO (quadratic unconstrained binary optimization) instances and, for better visualization, instances which we specifically optimize (using our own genetic algorithm) to exhibit a pronounced evolution of its solution during the anneal

Advanced unembedding techniques for quantum annealers

The D-Wave quantum annealers make it possible to obtain high quality solutions of NP-hard problems by mapping a problem in a QUBO (quadratic unconstrained binary optimization) or Ising form to the physical qubit connectivity structure on the D-Wave chip. However, the latter is restricted in that only a fraction of all pairwise couplers between physical qubits exists. Modeling the connectivity structure of a given problem instance thus necessitates the computation of a minor embedding of the variables in the problem specification onto the logical qubits, which consist of several physical qubits "chained" together to act as a logical one. After annealing, it is however not guaranteed that all chained qubits get the same value (-1 or +1 for an Ising model, and 0 or 1 for a QUBO), and several approaches exist to assign a final value to each logical qubit (a process called "unembedding"). In this work, we present tailored unembedding techniques for four important NP-hard problems: the Maximum Clique, Maximum Cut, Minimum Vertex Cover, and Graph Partitioning problems. Our techniques are simple and yet make use of structural properties of the problem being solved. Using Erd\H{o}s-R\'enyi random graphs as inputs, we compare our unembedding techniques to three popular ones (majority vote, random weighting, and minimize energy). We demonstrate that our proposed algorithms outperform the currently available ones in that they yield solutions of better quality, while being computationally equally efficient

Inferring the Dynamics of the State Evolution During Quantum Annealing

To solve an optimization problem using a commercial quantum annealer, one has to represent the problem of interest as an Ising or a quadratic unconstrained binary optimization (QUBO) problem and submit its coefficients to the annealer, which then returns a user-specified number of low-energy solutions. It would be useful to know what happens in the quantum processor during the anneal process so that one could design better algorithms or suggest improvements to the hardware. However, existing quantum annealers are not able to directly extract such information from the processor. Hence, in this work we propose to use advanced features of D-Wave 2000Q to indirectly infer information about the dynamics of the state evolution during the anneal process. Specifically, D-Wave 2000Q allows the user to customize the anneal schedule, that is, the schedule with which the anneal fraction is changed from the start to the end of the anneal. Using this feature, we design a set of modified anneal schedules whose outputs can be used to generate information about the states of the system at user-defined time points during a standard anneal. With this process, called "slicing", we obtain approximate distributions of lowest-energy anneal solutions as the anneal time evolves. We use our technique to obtain a variety of insights into the annealer, such as the state evolution during annealing, when individual bits in an evolving solution flip during the anneal process and when they stabilize, and we introduce a technique to estimate the freeze-out point of both the system as well as of individual qubits

Solving large Minimum Vertex Cover problems on a quantum annealer

We consider the minimum vertex cover problem having applications in e.g. biochemistry and network security. Quantum annealers can find the optimum solution of such NP-hard problems, given they can be embedded on the hardware. This is often infeasible due to limitations of the hardware connectivity structure. This paper presents a decomposition algorithm for the minimum vertex cover problem: The algorithm recursively divides an arbitrary problem until the generated subproblems can be embedded and solved on the annealer. To speed up the decomposition, we propose several pruning and reduction techniques. The performance of our algorithm is assessed in a simulation study