Related papers: On Efficient Algorithms For Partial Quantifier Eli…
We study the performance of our previously proposed Projective Quantum Eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H$_2$, we find that we are able to obtain…
We formalize a multivariate quantifier elimination (QE) algorithm in the theorem prover Isabelle/HOL. Our algorithm is complete, in that it is able to reduce any quantified formula in the first-order logic of real arithmetic to a logically…
Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the Filtering Variational Quantum…
The Variational Quantum Eigensolver (VQE) is a promising algorithm for quantum computing applications in chemistry and materials science, particularly in addressing the limitations of classical methods for complex systems. This study…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
Second-order quantifier elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similarly to PEC, the proposed method represents ideal…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation.…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
Cylindrical Algebraic Decomposition (CAD) was the first practical means for doing real quantifier elimination (QE), and is still a major method, with many improvements since Collins' original method. Nevertheless, its complexity is…
Query Expansion (QE) improves retrieval performance by enriching queries with related terms. Recently, Large Language Models (LLMs) have been used for QE, but existing methods face a trade-off: generating diverse terms boosts performance…
Generalizing the novel clause elimination procedures developed in [M. Heule, M. J\"arvisalo, and A. Biere. Clause elimination procedures for CNF formulas. In Proc. LPAR-17, volume 6397 of LNCS, pages 357-371. Springer, 2010.], we introduce…
Most existing parametric query optimization (PQO) techniques rely on traditional query optimizer cost models, which are often inaccurate and result in suboptimal query performance. We propose Kepler, an end-to-end learning-based approach to…
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
In the last years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised. On one side, "direct" quantum algorithms that aim at encoding the solution of the PDE by executing one…
We present a general method, called Qade, for solving differential equations using a quantum annealer. The solution is obtained as a linear combination of a set of basis functions. On current devices, Qade can solve systems of coupled…
The electronic structure problem is one of the main problems in modern theoretical chemistry. While there are many already-established methods both for the problem itself and its applications like semi-classical or quantum dynamics, it…