Propositional satisfiability problem (SAT) is represented in a conjunctive normal form with multiple clauses, which is an important non-deterministic polynomial-time (NP) complete problem that plays a major role in various applications including artificial intelligence, graph colouring, and circuit analysis. Quantum annealing (QA) is a promising methodology for solving complex SAT problems by exploiting the parallelism of quantum entanglement, where the SAT variables are embedded to the qubits. However, the long embedding time fundamentally limits existing QA-based methods, leading to inefficient hardware implementation and poor scalability.In this paper, we propose HyQSAT, a hybrid approach that integrates QA with the classical Conflict-Driven Clause Learning (CDCL) algorithm to enable end-to-end acceleration for solving SAT problems. Instead of embedding all clauses to QA hardware, we quantitatively estimate the conflict frequency of clauses and apply breadth-first traversal to choose their embedding order. We also consider the hardware topology to maximize the utilization of physical qubits in embedding to QA hardware. Besides, we adjust the embedding coefficients to improve the computation accuracy under qubit noise. Finally, we present how to interpret the satisfaction probability based on QA energy distribution and use this information to guide the CDCL search. Our experiments demonstrate that HyQSAT can effectively support larger-scale SAT problems that are beyond the capability of existing QA approaches, achieve up to 12.62X end-to-end speedup using D-Wave 2000Q compared to the classic CDCL algorithm on Intel E5 CPU, and considerably reduce the QA embedding time from 17.2s to 15.7µs compared to the D-Wave Minorminer algorithm [11].

In the current Noisy Intermediate-Scale Quantum era, quantum circuit analysis is an essential technique for designing high-performance quantum programs. Current analysis methods exhibit either accuracy limitations or high computational complexity for obtaining precise results. To reduce this tradeoff, we propose QuCT, a unified framework for extracting, analyzing, and optimizing quantum circuits. The main innovation of QuCT is to vectorize each gate with each element, quantitatively describing the degree of the interaction with neighboring gates. Extending from the vectorization model, we propose two representative downstream models for fidelity prediction and unitary decomposition. The fidelity prediction model performs a linear transformation on all gate vectors and aggregates the results to estimate the overall circuit fidelity. By identifying critical weights in the transformation matrix, we propose two optimizations to improve the circuit fidelity. In the unitary decomposition model, we significantly reduce the search space by bridging the gap between unitary and circuit via gate vectors. Experiments show that QuCT improves the accuracy of fidelity prediction by 4.2 × on 5-qubit and 18-qubit quantum devices and achieves 2.5 × fidelity improvement compared to existing quantum compilers [19, 55]. In unitary decomposition, QuCT achieves 46.3 × speedup for 5-qubit unitary and more than hundreds of speedup for 8-qubit unitary, compared to the state-of-the-art method [87].

In spatial regression models, spatial heterogeneity may be considered with either continuous or discrete specifications. The latter is related to delineation of spatially connected regions with homogeneous relationships between variables (spatial regimes). Although various regionalization algorithms have been proposed and studied in the field of spatial analytics, methods to optimize spatial regimes have been largely unexplored. In this paper, we propose two new algorithms for spatial regime delineation, two-stage K-Models and Regional-K-Models. We also extend the classic Automatic Zoning Procedure to a spatial regression context. The proposed algorithms are applied to a series of synthetic datasets and two real-world datasets. Results indicate that all three algorithms achieve superior or comparable performance to existing approaches, while the two-stage K-Models algorithm largely outperforms existing approaches on model fitting, region reconstruction and coefficient estimation. Our work enriches the spatial analytics toolbox to explore spatial heterogeneous processes.

Instance segmentation is an important method for high-resolution remote sensing images (HRRSIs) analysis. Traditional instance segmentation algorithms are not suitable to analyze complex HRRSIs that exhibit: 1) various shapes and sizes of targets; 2) a large number of small targets; and 3) data with long tail distribution. Here we introduce DB-BlendMask, an efficient and accurate instance segmentation method that can accommodate complex HRRSIs. It is composed of size balance coefficient (SBC), class balance module (CBM), and decomposed attention blender module (DA-Blender module). SBC consists of a fair weight allocation strategy for positive samples in object detection. CBM combines classification obtained in object detection stage to guide the semantic feature extraction. Complementary to a traditional convolutional neural network (CNN) architecture, DA-Blender module has the ability to considerably compress space complexity of attention and merge attention with semantic feature to generate the instance mask. We compare the performance of DB-BlendMask with a benchmark Mask R-CNN on two typical datasets, iSAID, and ISPRS Postdam. We obtain an average detection precision of 39.2% on iSAID and 63.6% on ISPRS Postdam, which corresponds to an improvement of 2.5% and 2.7%, respectively, compared to the benchmark in a real-time scenario.