Editors’ Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing

Abstract

We begin by discussing the history of quantum logic, dividing it into three eras or "lives." The first life has to do with Birkhoff and von Neumann's algebraic approach in the 1930's. The second life has to do with attempt to understand quan- tum logic as logic that began in the late 1950's and blossomed in the 1970's. And the third life has to do with recent developments in quantum logic coming from its connections to quantum computation. We discuss our own work connecting quantum logic to quantum computation (viewing quantum logic as the logic of quantum reg- isters storing qubits), make some speculations about mathematics based on quantum principles, and end by quickly describing the papers by the other authors contribut- ing to this special issue on "Quantum Logic Inspired by Quantum Computing." The overall aim of this issue is to show how work on this topic is leading to interesting new areas of logic.