Bounds on universal quantum computation with perturbed 2d cluster states

TL;DR

This paper analyzes the phase diagram of perturbed 2d cluster states, identifying the boundaries of the cluster phase under noise, which is crucial for measurement-based quantum computation.

Contribution

It provides the first detailed analysis of how small perturbations affect the 2d cluster state's usefulness for quantum computation, combining series expansions and iPEPS methods.

Findings

Identifies a well-defined cluster phase separated by phase transitions.

Determines an upper bound on perturbations for quantum computational utility.

Maps the phase diagram including a tricritical point.

Abstract

Motivated by the possibility of universal quantum computation under noise perturbations, we compute the phase diagram of the 2d cluster state Hamiltonian in the presence of Ising terms and magnetic fields. Unlike in previous analysis of perturbed 2d cluster states, we find strong evidence of a very well defined cluster phase, separated from a polarized phase by a line of 1st and 2nd order transitions compatible with the 3d Ising universality class and a tricritical end point. The phase boundary sets an upper bound for the amount of perturbation in the system so that its ground state is still useful for measurement-based quantum computation purposes. Moreover, we also compute the local fidelity with the unperturbed 2d cluster state. Besides a classical approximation, we determine the phase diagram by combining series expansions and variational infinite Projected entangled-Pair States (iPEPS) methods. Our work constitutes the first analysis of the non-trivial effect of few-body perturbations in the 2d cluster state, which is of relevance for experimental proposals.