This paper discusses techniques for solving discrete optimization problems using quantum annealing. Practical issues likely to affect the computation include precision limitations, finite temperature, bounded energy range, sparse connectivity, and small numbers of qubits. To address these concerns we propose a way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware. We validate the approach by describing experiments with D-Wave quantum hardware for low density parity check decoding with up to 1000 variables.

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.

Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware.The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave's QA hardware using the local mapping technique is significantly better than global embedding.We validate the approach by applying D-Wave's hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware. arXiv:1603.03111v1 [quant-ph]

Surgical tool detection is attracting increasing attention from the medical image analysis community. The goal generally is not to precisely locate tools in images, but rather to indicate which tools are being used by the surgeon at each instant. The main motivation for annotating tool usage is to design efficient solutions for surgical workflow analysis, with potential applications in report generation, surgical training and even real-time decision support. Most existing tool annotation algorithms focus on laparoscopic surgeries. However, with 19 million interventions per year, the most common surgical procedure in the world is cataract surgery. The CATARACTS challenge was organized in 2017 to evaluate tool annotation algorithms in the specific context of cataract surgery. It relies on more than nine hours of videos, from 50 cataract surgeries, in which the presence of 21 surgical tools was manually annotated by two experts. With 14 participating teams, this challenge can be considered a success. As might be expected, the submitted solutions are based on deep learning. This paper thoroughly evaluates these solutions: in particular, the quality of their annotations are compared to that of human interpretations. Next, lessons learnt from the differential analysis of these solutions are discussed. We expect that they will guide the design of efficient surgery monitoring tools in the near future.

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