ABSTRACT. Quantum Computing (QC) is a new computational paradigm that promises significant speedup over classical computing in various domains. However, near-term QC faces numerous challenges, including limited qubit connectivity and noisy quantum operations. To address the qubit connectivity constraint, circuit mapping is required for executing quantum circuits on quantum computers. This process involves performing initial qubit placement and using the quantum SWAP operations to relocate non-adjacent qubits for nearest-neighbor interaction. Reducing the SWAP count in circuit mapping is essential for improving the success rate of quantum circuit execution as SWAPs are costly and error-prone. In this work, we introduce a novel circuit mapping method by combining incremental and parallel solving for Boolean Satisfiability (SAT). We present an innovative SAT encoding for circuit mapping problems, which significantly improves solver-based mapping methods and provides a smooth trade-off between compilation quality and compilation time. Through comprehensive benchmarking of 78 instances covering 3 quantum algorithms on 2 distinct quantum computer topologies, we demonstrate that our method is 26x faster than state-of-the-art solver-based methods, reducing the compilation time from hours to minutes for important quantum applications. Our method also surpasses the existing heuristics algorithm by 26% in SWAP count.

ABSTRACT. Layout synthesis is mapping a quantum circuit to a quantum processor. SWAP gate insertions are needed for scheduling 2-qubit gates only on connected physical qubits. With the ever-increasing number of qubits in NISQ processors, scalable layout synthesis is of utmost importance. With large optimality gaps observed in heuristic approaches, scalable exact methods are needed. While recent exact and near-optimal approaches scale to moderate circuits, large deep circuits are still out of scope.

In this work, we propose a SAT encoding based on parallel plans that apply 1 SWAP and a group of CNOTs at each time step. Using domain-specific information, we maintain optimality in parallel plans while scaling to large and deep circuits. From our results, we show the scalability of our approach which significantly outperforms leading exact and near-optimal approaches (up to 100x). For the first time, we can optimally map several 8, 14, and 16 qubit circuits onto 54, 80, and 127 qubit platforms with up to 17 SWAPs. While adding optimal SWAPs, we also report near-optimal depth in our mapped circuits.

ABSTRACT. Popular redundancy rules for SAT are not immediately sound for MaxSAT. The works of [Bonacina-Bonet-Buss-Lauria'24] and [Ihalainen-Berg-Järvisalo'22] proposed ways to adapt them, but required specific encodings and more sophisticated checks during proof verification. Here, we propose a different way to adapt redundancy rules from SAT to MaxSAT. Our rules do not require specific encodings, their correcteness is simpler to check, but they are slightly less expressive. However, the proposed redundancy rules, when added to MaxSAT-Resolution, are already strong enough to capture Branch-and-bound algorithms, enable short proofs of the optimal cost of notable principles (e.g. the Pigeonhole principle $\mathrm{PHP}^m_n$ and the Parity Principle), and allow to break simple symmetries (e.g. XOR-ification does not make formulas harder).

ABSTRACT. Local search has been widely applied to solve the well-known (weighted) partial MaxSAT problem, significantly influencing many real-world applications. The main difficulty to overcome when designing a local search algorithm is that it can easily fall into local optima. Clause weighting is a beneficial technique that dynamically adjusts the landscape of search space to help the algorithm escape from local optima. Existing works tend to increase the weights of falsified clauses, and such strategies may result in an unpredictable landscape of search space during the optimization process. Therefore, in this paper, we propose a Unified Soft Clause Weighting Scheme called Unified-SW, which increases the weights of all soft clauses in feasible local optima, whether they are satisfied or not, while preserving the hierarchy among them. We implemented Unified-SW in a new local search solver called USW-LS. Experimental results demonstrate that USW-LS, outperforms the state-of-the-art local search solvers across benchmarks from incomplete tracks of recent MaxSAT Evaluations. More promisingly, a hybrid solver combining USW-LS and TT-Open-WBO-Inc won all four categories in the incomplete track of MaxSAT Evaluation 2023.

ABSTRACT. Parallelization of SAT solvers is an important technique for improving solver performance. The selection of the learnt clauses to share among parallel workers is crucial for its efficiency. Literal block distance (LBD) is often used to evaluate the quality of clauses to select. We propose a new method, Parallel Clause sharing based on graph Structure (PaCS), to select good clauses for sharing. First, we conducted three preliminary experiments to assess the performance of LBD in parallel clause sharing: a performance comparison between the LBD and clause size, an analysis of the utilization of shared clauses, and a comparison of the LBD values of shared clauses at originating and receiving workers. These experiments indicate that the LBD may not be optimal for learnt clause sharing. We attribute the results to the LBD's inherent dependency on decision trees. Each parallel worker has a unique decision tree; thus, a sharing clause that is good for its originating worker may not be good for others. Therefore, we propose PaCS, a search-independent method that uses the graph structure derived from the input CNF of SAT problems. PaCS evaluates clauses using their edges' weight in the variable incidence graph. Using the input CNF's graph is effective for parallel clause sharing because it is the common input for all parallel workers. Furthermore, using edge weight can select clauses whose variables' Boolean values are more likely to be determined. Performance evaluation experiments demonstrate that our strategy outperforms LBD by 4% in the number of solved instances and by 12% in PAR-2. This study opens avenues for further improvements in parallel-solving strategies using the structure of SAT problems and reinterpretations of the quality of learnt clauses.