Bounds on universal quantum computation with perturbed 2d cluster states

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.

7 pages, 4 figures, revised version, to appear in PRA

References in corpus (12)

• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Novel schemes for measurement-based quantum computation
• Robustness of a perturbed topological phase
• Ground state fidelity from tensor network representations
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• First order phase transition in the anisotropic quantum orbital compass model
• A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
• Breakdown of a perturbed Z_N topological phase
• Symmetry protection of measurement-based quantum computation in ground states
• Fate of the cluster state on the square lattice in a magnetic field
• Spin lattices with two-body Hamiltonians for which the ground state encodes a cluster state

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• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Topological Phase Transition in the Extended Cluster Compass Ladder
• Linked Cluster Expansions via Hypergraph Decompositions
• Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet