Transitions in the quantum computational power

Abstract

We construct two spin models on lattices (both two and three-dimensional) to study the capability of quantum computational power as a function of temperature and the system parameter. There exists a finite region in the phase diagram such that the thermal equilibrium states are capable of providing a universal fault-tolerant resource for measurement-based quantum computation. Moreover, in such a region the thermal resource states on the 3D lattices can enable topological protection for quantum computation. The two models behave similarly in terms of quantum computational power. However, they have different properties in terms of the usual phase transitions. The first model has a first-order phase transition only at zero temperature whereas there is no transition at all in the second model. Interestingly, the transition in the quantum computational power does not coincide with the phase transition in the first model.

10 pages, 6 figures, close to published version

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Cited by in corpus (6)

• Computational Power of Symmetry-Protected Topological Phases
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Measurement-Based Quantum Computation
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Hybrid valence-bond states for universal quantum computation
• Graph states as ground states of two-body frustration-free Hamiltonians