Approximate Approximation on a Quantum Annealer

Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum mechanical properties of nature. However, they compete with efficient heuristics and probabilistic or randomised algorithms on classical machines that allow for finding approximate solutions to large NP-complete problems. While first implementations of QA have become commercially available, their practical benefits are far from fully explored. To the best of our knowledge, approximation techniques have not yet received substantial attention. In this paper, we explore how problems' approximate versions of varying degree can be systematically constructed for quantum annealer programs, and how this influences result quality or the handling of larger problem instances on given set of qubits. We illustrate various approximation techniques on both, simulations and real QA hardware, on different seminal problems, and interpret the results to contribute towards a better understanding of the real-world power and limitations of current-state and future quantum computing.Comment: Proceedings of the 17th ACM International Conference on Computing Frontiers (CF 2020

Quantum Permutation Synchronization

We present QuantumSync, the first quantum algorithm for solving a synchronization problem in the context of computer vision. In particular, we focus on permutation synchronization which involves solving a non-convex optimization problem in discrete variables. We start by formulating synchronization into a quadratic unconstrained binary optimization problem (QUBO). While such formulation respects the binary nature of the problem, ensuring that the result is a set of permutations requires extra care. Hence, we: (i) show how to insert permutation constraints into a QUBO problem and (ii) solve the constrained QUBO problem on the current generation of the adiabatic quantum computers D-Wave. Thanks to the quantum annealing, we guarantee global optimality with high probability while sampling the energy landscape to yield confidence estimates. Our proof-of-concepts realization on the adiabatic D-Wave computer demonstrates that quantum machines offer a promising way to solve the prevalent yet difficult synchronization problems

A QUBO formulation for the Tree Containment problem

Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze phylogenetic networks, the problem of deciding whether or not a given rooted phylogenetic network embeds a given rooted phylogenetic tree is of recurring interest. This problem, formally know as Tree Containment, is NP-complete in general and polynomial-time solvable for certain classes of phylogenetic networks. In this paper, we connect ideas from quantum computing and phylogenetics to present an efficient Quadratic Unconstrained Binary Optimization formulation for Tree Containment in the general setting. For an instance (N,T) of Tree Containment, where N is a phylogenetic network with n_N vertices and T is a phylogenetic tree with n_T vertices, the number of logical qubits that are required for our formulation is O(n_N n_T).Comment: final version accepted for publication in Theoretical Computer Scienc

Where Quantum Complexity Helps Classical Complexity

Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum computing. Nonetheless, there are defined boundaries to the capabilities of quantum computing. This paper concentrates on aggregating prior research efforts dedicated to solving intricate classical computational problems through quantum computing. The objective is to systematically compile an exhaustive inventory of these solutions and categorize a collection of demanding problems that await further exploration

QuAnt: Quantum Annealing with Learnt Couplings

Modern quantum annealers can find high-quality solutions to combinatorialoptimisation objectives given as quadratic unconstrained binary optimisation(QUBO) problems. Unfortunately, obtaining suitable QUBO forms in computervision remains challenging and currently requires problem-specific analyticalderivations. Moreover, such explicit formulations impose tangible constraintson solution encodings. In stark contrast to prior work, this paper proposes tolearn QUBO forms from data through gradient backpropagation instead of derivingthem. As a result, the solution encodings can be chosen flexibly and compactly.Furthermore, our methodology is general and virtually independent of thespecifics of the target problem type. We demonstrate the advantages of learntQUBOs on the diverse problem types of graph matching, 2D point cloud alignmentand 3D rotation estimation. Our results are competitive with the previousquantum state of the art while requiring much fewer logical and physicalqubits, enabling our method to scale to larger problems. The code and the newdataset will be open-sourced.<br