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Finds and Results from the Swedish Cyprus Expedition: A Gender Perspective at the Medelhavsmuseet

The Place of Quantum Logic in the Landscape of Non-Classical Logics

Sonja Smets

Published Jan 1, 2003• 0 citations
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Related papers

The Relevance of Quantum Logic in the Domain of Non-Classical Logics

María Luisa Dalla Chiara

Studies in logic and the foundations of mathematics•Jan 1, 1986•2 citations

Classical and Non Classical Limiting Cases of Quantum Logic

Ernst-Walter Stachow

Springer eBooks•Jan 1, 1984•2 citations

Computing with qLDPC Codes by Climbing the Chain Map Hierarchy

Rahul Sahay, David M. Long, Vedika Khemani

We develop a framework for logical computation with qLDPC codes that places logical Pauli, Clifford, and non-Clifford operations on the same footing. This brings the simple homological description of Pauli logicals to the patchwork landscape of logical Clifford and non-Clifford operations, providing a tool for the discovery of new logical gates. In particular, we define the chain map hierarchy: a family of chain complexes whose homology classes encode logical unitary and code surgery operations at any level of the Clifford hierarchy, precisely analogous to the chain complex description of Pauli logicals. Consequently, intuition for Pauli logicals can be leveraged to discover new logical operations on qLDPC codes. For instance, the familiar ability to deform Pauli logicals with stabilizers---i.e. boundaries of the chain complex---becomes a way to search for constant-depth unitary implementations of (non-)Clifford logical gates. Using this strategy, we discover constant-depth unitary implementations of the full logical Clifford group on any number of blocks of the 2D toric code, including within a single block, and addressable logical CCZ gates on any triple of logical qubits on any number of blocks of the 3D toric code. Beyond manifold codes, we find addressable non-Clifford gates on codes with many encoded qubits. The chain map hierarchy naturally encompasses and extends other constructions of logical gadgets, for instance providing a universal parameterization of cup products. As such, our work provides a unified, useful, and intuitive language for computing with qLDPC codes.

quant-pharXiv:2609.02999•Sep 4, 2026•0 citations

Human Conceptual Thought and Quantum Structure.

Diederik Aerts, Bart D’Hooghe, Emmanuel E. Haven

In a earlier work [1, 2, 3, 4] we have put forward the hypothesis that two layers of thought can be identified in the human thought process, which we have called the ‘classical logical ’ layer and the ‘quantum conceptual ’ layer. In the classical logical layer thought processes are given form by an underlying Boolean logical conceptual process, its non deterministic ‘lack of knowledge ’ version modeled by Kolmogorovian probability and in an idealized form by a stochastic process. In the quantum conceptual layer, the thought process gets form under the influence of the totality of the surrounding conceptual landscape. The key event within this layer is that different concepts figure as individual entities, even when they are combinations of other concepts. A phenomenon of conceptual emergence is taking place in the quantum conceptual layer mathematically described by superposition within the quantum formalism used to model this layer. The quantum conceptual thought process is indeterministic in essence; i.e. there is not necessarily an underlying deterministic process. It is however an equally well structured layer than the classical logical one, and we belief that it is mainly the lack of insight about the structure of this quantum conceptual layer that often leads to the idea that the thought processes described in it are mainly unstructured and correspond to intuitive or irrational thought. In the present paper we analyze more in detail the cognitive and mathematical structures of these two layers of thought. More specifically we put forward a concrete

Finds and Results from the Swedish Cyprus Expedition: A Gender Perspective at the Medelhavsmuseet•Jan 1, 2009•0 citations

Quantum Logic as an Extension of Classical Logic

Sergio Bernini

Springer eBooks•Jan 1, 1981•3 citations

Some Remarks on the Requirements for Scientific Theory in the Context of Many-worlds Models

Карпенко Иван Александрович

The article discusses the problem of a correct description of reality in science and philosophy, taking into account the acceptance of the many-world hypothe­sis. Many-worlds are understood as modern physical hypotheses that allow the existence of other universes (many-world interpretation, chaotic inflation, string landscape, and others). It is shown that these models are likely to chal­lenge the traditional intellectual intuition on which classical science is built: they require new methodological approaches, and perhaps a new epistemology in general. Some requirements of classical logic, based on principles such as the laws of non-contradiction or the excluded middle, may turn out to be incor­rect and even counterintuitive under many-world hypotheses. It is suggested that some logical systems (paraconsistent logic, quantum logic) may in the future be­come an ontological and epistemological foundation for the concepts of many-world physical reality. It is concluded that the considered multi-world models in conjunction with the indicated logics are more intuitively acceptable, since they allow getting rid of not only a number of cosmological problems (for exam­ple, fine tuning), but also problems of a logical and mathematical nature arising from the considered traditional requirements for formal systems.

Voprosy filosofii•Jul 1, 2024•0 citations
We develop a framework for logical computation with qLDPC codes that places logical Pauli, Clifford, and non-Clifford operations on the same footing. This brings the simple homological description of Pauli logicals to the patchwork landscape of logical Clifford and non-Clifford operations, providing a tool for the discovery of new logical gates. In particular, we define the chain map hierarchy: a family of chain complexes whose homology classes encode logical unitary and code surgery operations at any level of the Clifford hierarchy, precisely analogous to the chain complex description of Pauli logicals. Consequently, intuition for Pauli logicals can be leveraged to discover new logical operations on qLDPC codes. For instance, the familiar ability to deform Pauli logicals with stabilizers---i.e. boundaries of the chain complex---becomes a way to search for constant-depth unitary implementations of (non-)Clifford logical gates. Using this strategy, we discover constant-depth unitary implementations of the full logical Clifford group on any number of blocks of the 2D toric code, including within a single block, and addressable logical CCZ gates on any triple of logical qubits on any number of blocks of the 3D toric code. Beyond manifold codes, we find addressable non-Clifford gates on codes with many encoded qubits. The chain map hierarchy naturally encompasses and extends other constructions of logical gadgets, for instance providing a universal parameterization of cup products. As such, our work provides a unified, useful, and intuitive language for computing with qLDPC codes.
In a earlier work [1, 2, 3, 4] we have put forward the hypothesis that two layers of thought can be identified in the human thought process, which we have called the ‘classical logical ’ layer and the ‘quantum conceptual ’ layer. In the classical logical layer thought processes are given form by an underlying Boolean logical conceptual process, its non deterministic ‘lack of knowledge ’ version modeled by Kolmogorovian probability and in an idealized form by a stochastic process. In the quantum conceptual layer, the thought process gets form under the influence of the totality of the surrounding conceptual landscape. The key event within this layer is that different concepts figure as individual entities, even when they are combinations of other concepts. A phenomenon of conceptual emergence is taking place in the quantum conceptual layer mathematically described by superposition within the quantum formalism used to model this layer. The quantum conceptual thought process is indeterministic in essence; i.e. there is not necessarily an underlying deterministic process. It is however an equally well structured layer than the classical logical one, and we belief that it is mainly the lack of insight about the structure of this quantum conceptual layer that often leads to the idea that the thought processes described in it are mainly unstructured and correspond to intuitive or irrational thought. In the present paper we analyze more in detail the cognitive and mathematical structures of these two layers of thought. More specifically we put forward a concrete
The article discusses the problem of a correct description of reality in science and philosophy, taking into account the acceptance of the many-world hypothe­sis. Many-worlds are understood as modern physical hypotheses that allow the existence of other universes (many-world interpretation, chaotic inflation, string landscape, and others). It is shown that these models are likely to chal­lenge the traditional intellectual intuition on which classical science is built: they require new methodological approaches, and perhaps a new epistemology in general. Some requirements of classical logic, based on principles such as the laws of non-contradiction or the excluded middle, may turn out to be incor­rect and even counterintuitive under many-world hypotheses. It is suggested that some logical systems (paraconsistent logic, quantum logic) may in the future be­come an ontological and epistemological foundation for the concepts of many-world physical reality. It is concluded that the considered multi-world models in conjunction with the indicated logics are more intuitively acceptable, since they allow getting rid of not only a number of cosmological problems (for exam­ple, fine tuning), but also problems of a logical and mathematical nature arising from the considered traditional requirements for formal systems.