Related papers: Hard QBFs for Merge Resolution
Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent…
A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and…
We consider the incremental computation of minimal unsatisfiable cores (MUCs) of QBFs. To this end, we equipped our incremental QBF solver DepQBF with a novel API to allow for incremental solving based on clause groups. A clause group is a…
The prediction of spectral properties via linear response (LR) theory is an important tool in quantum chemistry for understanding photo-induced processes in molecular systems. With the advances of quantum computing, we recently adapted this…
Robust matrix factorization (RMF), which uses the $\ell_1$-loss, often outperforms standard matrix factorization using the $\ell_2$-loss, particularly when outliers are present. The state-of-the-art RMF solver is the RMF-MM algorithm,…
Quantum computing faces a key challenge: balancing the need for low circuit depth (crucial for fault tolerance) with the high accuracy required for complex computations like quantum chemistry and error correction, which typically require…
Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model…
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving $\min_{E,r}…
Advanced super-resolution imaging techniques require specific approaches for accurate and consistent estimation of the achievable spatial resolution. Fisher information supplied to Cramer-Rao bound (CRB) has proved to be a powerful and…
The Bit-Flipping (BF) decoder, thanks to its very low computational complexity, is widely employed in post-quantum cryptographic schemes based on Moderate Density Parity Check codes in which, ultimately, decryption boils down to syndrome…
We prove super-polynomial lower bounds on the size of propositional proof systems operating with constant-depth algebraic circuits over fields of zero characteristic. Specifically, we show that the subset-sum variant…
At the intersection of quantum computing and machine learning, quantum machine learning (QML) is poised to revolutionize artificial intelligence. However, the vulnerability of the current generation of quantum computers to noise and…
Multi-model fitting (MMF) presents a significant challenge in Computer Vision, particularly due to its combinatorial nature. While recent advancements in quantum computing offer promise for addressing NP-hard problems, existing…
We present a general framework for good CNF-representations of boolean constraints, to be used for translating decision problems into SAT problems (i.e., deciding satisfiability for conjunctive normal forms). We apply it to the…
We introduce two types of message passing algorithms for quantified Boolean formulas (QBF). The first type is a message passing based heuristics that can prove unsatisfiability of the QBF by assigning the universal variables in such a way…
The QSAT problem, which asks to evaluate a quantified Boolean formula (QBF), is of fundamental interest in approximation, counting, decision, and probabilistic complexity and is also considered the prototypical PSPACEcomplete problem. As…
QEM is widely regarded as a plausible bridge from NISQ devices to FTQC. Yet the empirical studies used to assess the effectiveness of QEM techniques on concrete problems have received comparatively little scrutiny with respect to the…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…