# The computational landscape of general physical theories

## TL;DR

This paper explores the computational power of physical theories beyond quantum mechanics, demonstrating that certain theories can efficiently solve problems in the class AWPP while respecting fundamental physical principles.

## Contribution

It constructs a physical theory satisfying key principles that can efficiently perform any computation in the class AWPP, matching previous upper bounds.

## Key findings

- A theory satisfying tomographic locality and causality can decide all problems in AWPP.
- The bound on computational power in such theories is tight.
- The theory can simulate quantum computation efficiently.

## Abstract

There is good evidence that quantum computers are more powerful than classical computers, and that various simple modifications of quantum theory yield computational power that is dramatically greater still. However, these modifications also violate fundamental physical principles. This raises the question of whether there exists a physical theory, allowing computation more powerful than quantum, but which still respects those fundamental physical principles. Prior work by two of us introduced this question within a suitable framework for theories that make good operational sense, and showed that in any theory satisfying tomographic locality, the class of problems that can be solved efficiently is contained in the complexity class AWPP. Here, we show that this bound is tight, in the sense that there exists a theory, satisfying tomographic locality, as well as a basic principle of causality, which can efficiently decide everything in AWPP. Hence this theory can efficiently simulate any computation in this framework, including quantum computation.