Noise in One-Dimensional Measurement-Based Quantum Computing

TL;DR

This paper analyzes how physical noise impacts measurement-based quantum computing on 1D cluster states, using matrix product operators to model and map physical errors to logical errors, enabling simulation of noisy quantum processes.

Contribution

It extends the matrix product state framework to mixed states for modeling noise, allowing for more general error analysis in MBQC.

Findings

Mapped physical noise to logical errors in the correlation space

Extended MPS to MPO for mixed states and noise modeling

Provided a framework for simulating noisy quantum computation

Abstract

Measurement-Based Quantum Computing (MBQC) is an alternative to the quantum circuit model, whereby the computation proceeds via measurements on an entangled resource state. Noise processes are a major experimental challenge to the construction of a quantum computer. Here, we investigate how noise processes affecting physical states affect the performed computation by considering MBQC on a one-dimensional cluster state. This allows us to break down the computation in a sequence of building blocks and map physical errors to logical errors. Next, we extend the Matrix Product State construction to mixed states (which is known as Matrix Product Operators) and once again map the effect of physical noise to logical noise acting within the correlation space. This approach allows us to consider more general errors than the conventional Pauli errors, and could be used in order to simulate noisy quantum computation.