In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The formal system takes as its starting point an observation of Garrett Birkhoff and John von Neumann, that the structure of experimental tests in classical mechanics forms a Boolean algebra, but the structure of experimental tests in quantum mechanics forms a much more complicated structure.
A number of other logics have also been proposed to analyze quantum-mechanical phenomena, unfortunately also under the name of "quantum logic(s)." They are not the subject of this article. For discussion of the similarities and differences between quantum logic and some of these competitors, see .
Quantum logic has been proposed as the correct logic for propositional inference generally, most notably by the philosopher Hilary Putnam, at least at one point in his career. This thesis was an important ingredient in Putnam's 1968 paper "Is Logic Empirical?" in which he analysed the epistemological status of the rules of propositional logic. Modern philosophers reject quantum logic as a basis for reasoning, because it lacks a material conditional; a common alternative is the system of linear logic, of which quantum logic is a fragment.
Mathematically, quantum logic is formulated by weakening the distributive law for a Boolean algebra, resulting in an orthocomplemented lattice. Quantum-mechanical observables and states can be defined in terms of functions on or to the lattice, giving an alternate formalism for quantum computations.
The most notable difference between quantum logic and classical logic is the failure of the propositional distributive law:
p and (q or r) = (p and q) or (p and r),
where the symbols p, q and r are propositional variables.
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This course will discuss the main methods for the simulation of quantum time dependent properties for molecular systems. Basic notions of density functional theory will be covered. An introduction to
The course explains how to execute scalable algorithms on fault-tolerant quantum computers. It describes error correction used to build reliable logical operations from noisy physical operations, and
Covers the formalism of quantum density matrices and their applications in quantum mechanics.
Explains quantum teleportation, demonstrating the successful transfer of quantum information using classical communication channels and various quantum operations.
Covers quantum computing basics, quantum algorithms, error correction, and quantum bit manipulation.
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We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...
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