An Unsharp Logic from Quantum Computation

An Unsharp Logic from Quantum Computation

Logical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and the √ NOT (which admit of natural physical models). This leads to a semantic characterization of a logic that we call computational quantum logic (CQL).

Turing machines based on unsharp quantum logic

In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E , we introduce E -valued non-deterministic Turing machines (E NTMs) and E -valued deterministic Turing machines (E DTMs). We discuss different E valued recursively enumerable languages from width-first and depth-first recognition. We find that width-first recog...

Automata theory based on unsharp quantum logic

By studying two unsharp quantum structures, namely extended lattice ordered effect algebras and lattice ordered QMV algebras, we obtain some characteristic theorems of MV algebras. We go on to discuss automata theory based on these two unsharp quantum structures. In particular, we prove that an extended lattice ordered effect algebra (or a lattice ordered QMV algebra) is an MV algebra if and on...

Quantum Logic and Quantum Computation

Logic and Quantum Computation

The goal of these lectures is to describe a “structural” theory of quantum computation. Quantum programs can be reasoned about at many different levels. They can be reasoned about numerically and algebraically, which involves specific calculations with complex numbers and vector space notation. Programs can also be reasoned about symbolically, by expressing them in a formal language and formula...