Quantum lambda calculus with quantum control

ALEJANDRO DÍAZ CARO

Ciudad Autónoma de Buenos Aires

Workshop; V International Workshop on Quantum Mechanics and Quantum Information; 2019

The lambda-calculus is a formal logical system for expressing the concept of computation. There are two main approaches for quantum extensions to the lambda calculus. The first and more developed one, uses the so-called classical-control. The idea is to provide a classical description of quantum circuits: its wires, what operations to apply and to which qubits. The second one, uses the so-called quantum-control. The idea here is to provide a proper encoding of the quantum operations and linear combinations in order to understand its behaviour. In this talk, I will focus the second approach, by explaining lambda_S, which combines algebraic linearity with logical linearity, to capture the concept of quantum superpositions and no-cloning.