Universal resources for approximate and stochastic measurement-based quantum computation

Abstract

We investigate which quantum states can serve as universal resources for approximate and stochastic measurement-based quantum computation, in the sense that any quantum state can be generated from a given resource by means of single-qubit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting e.g. from a restriction to finite measurement settings or from possible imperfections in the resources or local operations. We show that entanglement-based criteria for universality obtained for the exact, deterministic case can be lifted to the much more general approximate, stochastic case, moving from the idealized situation considered in previous works, to the practically relevant context of non-perfect state preparation. We find that any entanglement measure fulfilling some basic requirements needs to reach its maximum value on some element of an approximate, stochastic universal family of resource states, as the resource size grows. This allows us to rule out various families of states as being approximate, stochastic universal. We provide examples of resources that are efficient approximate universal, but not exact deterministic universal. We also study the robustness of universal resources for measurement-based quantum computation under realistic assumptions about the (imperfect) generation and manipulation of entangled states, giving an explicit expression for the impact that errors made in the preparation of the resource have on the possibility to use it for universal approximate and stochastic state preparation. Finally, we discuss the relation between our entanglement-based criteria and recent results regarding the uselessness of states with a high degree of geometric entanglement as universal resources.

17 pages; abstract shortened with respect to the published version to respect the arXiv limit of 1,920 characters

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• Novel schemes for measurement-based quantum computation
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Cited by in corpus (20)

• The maximally entangled symmetric state in terms of the geometric measure
• Limitations of quantum computing with Gaussian cluster states
• Quantum computational renormalization in the Haldane phase
• Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities
• Additivity and non-additivity of multipartite entanglement measures
• Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states
• Classification of Entanglement in Symmetric States
• A comparison of old and new definitions of the geometric measure of entanglement
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
• Epsilon-smooth measure of coherence
• An algorithmic proof for the completeness of two-dimensional Ising model
• Geometric Entanglement of Symmetric States and the Majorana Representation
• Completeness of classical ${\varphi }^4$ theory on 2D lattices
• Compact quantum circuits from one-way quantum computation
• The Hadamard gate cannot be replaced by a resource state in universal quantum computation
• General scheme for preparation of different topological states on the cluster states
• Maximally entangled gapped ground state of lattice fermions
• Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication
• Scheme for measurement-based quantum computation on projected entangled-pair states
• Efficient classical simulation of cluster state quantum circuits with alternative inputs