The lambda-q calculus can efficiently simulate quantum computers

TL;DR

The paper demonstrates that the lambda-q calculus can efficiently simulate quantum Turing machines and may surpass quantum computers in solving NP-complete problems like satisfiability.

Contribution

It introduces the lambda-q calculus as a powerful framework capable of efficiently simulating quantum computation and potentially solving problems beyond quantum capabilities.

Findings

Lambda-q calculus efficiently simulates quantum Turing machines

Lambda-q calculus can solve NP-complete problems efficiently

Potentially stronger than quantum computers in computational power

Abstract

We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We conclude by noting that the lambda-q calculus may be strictly stronger than quantum computers because NP-complete problems such as satisfiability are efficiently solvable in the lambda-q calculus but there is a widespread doubt that they are efficiently solvable by quantum computers.