Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

To solve 3SAT instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3SAT problem with regards to the solution quality on D-Wave's Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality

Attention-Based Recurrence for Multi-Agent Reinforcement Learning under Stochastic Partial Observability

Stochastic partial observability poses a major challenge for decentralized coordination in multi-agent reinforcement learning but is largely neglected in state-of-the-art research due to a strong focus on state-based centralized training for decentralized execution (CTDE) and benchmarks that lack sufficient stochasticity like StarCraft Multi-Agent Challenge (SMAC). In this paper, we propose Attention-based Embeddings of Recurrence In multi-Agent Learning (AERIAL) to approximate value functions under stochastic partial observability. AERIAL replaces the true state with a learned representation of multi-agent recurrence, considering more accurate information about decentralized agent decisions than state-based CTDE. We then introduce MessySMAC, a modified version of SMAC with stochastic observations and higher variance in initial states, to provide a more general and configurable benchmark regarding stochastic partial observability. We evaluate AERIAL in Dec-Tiger as well as in a variety of SMAC and MessySMAC maps, and compare the results with state-based CTDE. Furthermore, we evaluate the robustness of AERIAL and state-based CTDE against various stochasticity configurations in MessySMAC.Comment: Accepted at ICML 202

Algorithmic QUBO formulations for k-SAT and hamiltonian cycles

Quadratic Unconstrained Binary Optimization (QUBO) can be seen as a generic language for optimization problems. QUBOs attract particular attention since they can be solved with quantum hardware, like quantum annealers or quantum gate computers running QAOA. In this paper, we present two novel QUBO formulations for k-SAT and Hamiltonian Cycles that scale significantly better than existing approaches. For k-SAT we reduce the growth of the QUBO matrix from O(k) to O(log(k)). For Hamiltonian Cycles the matrix no longer grows quadratically in the number of nodes, as currently, but linearly in the number of edges and logarithmically in the number of nodes. We present these two formulations not as mathematical expressions, as most QUBO formulations are, but as meta-algorithms that facilitate the design of more complex QUBO formulations and allow easy reuse in larger and more complex QUBO formulations.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Quantum Circuit Architectures and Technolog

Pattern QUBOs: Algorithmic Construction of 3SAT-to-QUBO Transformations

One way of solving 3sat instances on a quantum computer is to transform the 3sat instances into instances of Quadratic Unconstrained Binary Optimizations (QUBOs), which can be used as an input for the QAOA algorithm on quantum gate systems or as an input for quantum annealers. This mapping is performed by a 3sat-to-QUBO transformation. Recently, it has been shown that the choice of the 3sat-to-QUBO transformation can significantly impact the solution quality of quantum annealing. It has been shown that the solution quality can vary up to an order of magnitude difference in the number of correct solutions received, depending solely on the 3sat-to-QUBO transformation. An open question is: what causes these differences in the solution quality when solving 3sat-instances with different 3sat-to-QUBO transformations? To be able to conduct meaningful studies that assess the reasons for the differences in the performance, a larger number of different 3sat-to-QUBO transformations would be needed. However, currently, there are only a few known 3sat-to-QUBO transformations, and all of them were created manually by experts, who used time and clever reasoning to create these transformations. In this paper, we will solve this problem by proposing an algorithmic method that is able to create thousands of new and different 3sat-to-QUBO transformations, and thus enables researchers to systematically study the reasons for the significant difference in the performance of different 3sat-to-QUBO transformations. Our algorithmic method is an exhaustive search procedure that exploits properties of 4×4 dimensional pattern QUBOs, a concept which has been used implicitly in the creation of 3sat-to-QUBO transformations before, but was never described explicitly. We will thus also formally and explicitly introduce the concept of pattern QUBOs in this paper

Consensus statement on the use of rituximab in patients with rheumatoid arthritis

A large number of experts experienced in the treatment of rheumatoid arthritis were involved in formulating a consensus statement on the use of B cell-targeted treatment with rituximab in patients with rheumatoid arthritis. The statement was supported by data from randomised controlled clinical trials and the substantial literature on oncology. The statement underwent three rounds of discussions until its ultimate formulation. It should guide clinicians in the use of this newly approved biological agent in treating patients with rheumatoid arthritis

Impact of elexacaftor/tezacaftor/ivacaftor on lung function, nutritional status, pulmonary exacerbation frequency and sweat chloride in people with cystic fibrosis: real-world evidence from the German CF RegistryResearch in context

Summary: Background: Treatment with elexacaftor/tezacaftor/ivacaftor (ETI) improves multiple clinical outcomes in people with cystic fibrosis (pwCF) with at least one F508del allele. This study evaluated the real-world impact of ETI on lung function, nutritional status, pulmonary exacerbation frequency, and sweat chloride concentrations in a large group of pwCF. Methods: This observational cohort study used data from the German CF Registry for pwCF who received ETI therapy and were followed up for a period of 12 months. Findings: The study included 2645 pwCF from 67 centres in Germany (mean age 28.0 ± 11.5 years). Over the first year after ETI was initiated, percent predicted forced expiratory volume in 1 s (ppFEV1) increased by 11.3% (95% confidence interval [CI] 10.8–11.8, p < 0.0001), body mass index (BMI) z-score increased by 0.3 (95% CI 0.3–0.4, p < 0.0001) in individuals aged 12 to <18 years and BMI in adults increased by 1.4 kg/m2 (95% CI 1.3–1.4, p < 0.0001), pulmonary exacerbations decreased by 75.9% (p < 0.0001) and mean sweat chloride concentration decreased by 50.9 mmol/L (95% CI –52.6, −49.3, p < 0.0001). Improvements in ppFEV1 over the first year of therapy were greater in pwCF who had not previously received cystic fibrosis transmembrane conductance regulator (CFTR) modulator therapy (12.6% [95% CI 11.9–13.4] vs. 9.7% [95% CI 9.0–10.5] in those with prior CFTR modulator treatment. Interpretation: These real-world data are consistent with the findings of randomised clinical trials, and support the use of ETI as a highly effective treatment option for pwCF who have at least one F508del allele. Funding: None