Analytically Exact Quantum Simulation of N-Body Interactions via Untunable Decentralized Hamiltonians for Implementing the Toric Code and Its Modifications

TL;DR

This paper introduces an exact quantum simulation method for N-body interactions using untunable, local two-body Hamiltonians, enabling precise simulation of the toric code model crucial for topological quantum computing.

Contribution

The paper presents a novel, analytically exact quantum simulation technique for N-body interactions with untunable, local two-body Hamiltonians, facilitating the simulation of the toric code and its variants.

Findings

The method achieves error-free simulation theoretically.

Controlled two-body interactions are only slightly weaker than target interactions.

Successfully simulates the toric code model and its modifications.

Abstract

We propose a new quantum simulation method for simulating N-body interactions, which are tensor products of N Pauli operators, in an analytically exact manner. This method iteratively attaches many two-body interactions on one two-body interaction to simulate an N-body interaction. Those controlled two-body interactions can be untunable and act only on neighboring spins. The strength difference between controlled and target Hamiltonians is normally not more than one order of magnitude. This simulation is theoretically error-free, and errors due to experimental imperfections are ignorable. A major obstacle to simulating the toric code model and modified toric codes used in topological quantum computation is to simulate N-body interactions. We employ the new quantum simulation method to solve this issue and thus simulate the toric code model and its modifications.