Related papers: On Multiplicative Linear Logic, Modality and Quant…
We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-elimination corresponds to error correction.
Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people's lives. This leads to explainable AI (XAI) manifesting itself as an…
Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…
The proposed framework represents the first tool to compile a quantum circuit across photonic-connected distributed quantum processors. Its design follows a divide-and-conquer paradigm for circuit partitioning, transpilation, and assembly,…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
In the past few years it has been shown that universal quantum computation can be obtained by projective measurements alone, with no need for unitary gates. This suggests that the underlying logic of quantum computing may be an algebra of…
In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.
Quantum machine learning (QML) is a computational paradigm that seeks to apply quantum-mechanical resources to solve learning problems. As such, the goal of this framework is to leverage quantum processors to tackle optimization,…
In this paper we show that there is a direct correspondence between quantum Boolean operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
Quantized integrable systems can be made to perform universal quantum computation by the application of a global time-varying control. The action-angle variables of the integrable system function as qubits or qudits, which can be coupled…
A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…
Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement,…
Quantum Separation Logic (QSL) has been proposed as an effective tool to improve the scalability of deductive reasoning for quantum programs. In QSL, separation is interpreted as disentanglement, and the frame rule brings a notion of…
Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system…
This paper presents a proof-theoretic analysis of the modal $\mu$-calculus. More precisely, we prove a syntactic cut-elimination for the non-wellfounded modal $\mu$-calculus, using methods from linear logic and its exponential modalities.…