A local model of quantum Turing machines

TL;DR

This paper introduces a local model for quantum Turing machines within the matrix-product states framework, establishing their equivalence to circuit and standard models, and highlighting the link between tensor networks and information processing.

Contribution

It presents a novel local model for quantum Turing machines using tensor-network states, demonstrating their equivalence to existing computational models.

Findings

Local quantum Turing machines are equivalent to circuit models.

The model reveals a fundamental connection between tensor networks and information processing.

The framework unifies classical and quantum Turing machine models.

Abstract

The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have definite locations. The local Turing machines are shown to be equivalent to the corresponding circuit models and standard models of Turing machines by simulation methods. This work reveals the fundamental connection between tensor-network states and information processing.