Transitions in the computational power of thermal states for measurement-based quantum computation

Abstract

We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct "phases" - one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical or quantum, in the underlying spin-lattice model.

9 pages, 2 figures, v4 published version

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• Symmetry protection of measurement-based quantum computation in ground states
• Measurement-based quantum computation in a 2D phase of matter
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Quantum Computation with Topological Codes: from qubit to topological fault-tolerance
• Universal resources for approximate and stochastic measurement-based quantum computation
• Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
• Optical spin-1 chain and its use as a quantum computational wire
• Holonomic quantum computing in symmetry-protected ground states of spin chains
• Graph states as ground states of two-body frustration-free Hamiltonians
• Transitions in the quantum computational power
• Computational quantum-classical boundary of complex and noisy quantum systems
• Efficient classical simulation of cluster state quantum circuits with alternative inputs