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arXiv · 1701.05182

Universal Quantum Hamiltonians

Toby Cubitt·Ashley Montanaro·Stephen Piddock
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Abstract

Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We first characterise precisely what it means for one quantum many-body system to replicate the entire physics of another. We then show that certain very simple spin-lattice models are universal in this very strong sense. Examples include the Heisenberg and XY models on a 2D square lattice (with non-uniform coupling strengths). We go on to fully classify all two-qubit interactions, determining which are universal and which can only simulate more restricted classes of models. Our results put the practical field of analogue Hamiltonian simulation on a rigorous footing and take a significant step towards justifying why error correction may not be required for this application of quantum information technology.

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Toby Cubitt, Ashley Montanaro, Stephen Piddock. 2019-05-31. Universal Quantum Hamiltonians. https://doi.org/10.1073/pnas.1804949115

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