Universal quantum Hamiltonians

Toby Cubitt, Ashley Montanaro, Stephen Piddock

Research output: Contribution to journalArticle (Academic Journal)peer-review

47 Citations (Scopus)
409 Downloads (Pure)


Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. However, we prove that the entire physics of any quantum many-body system can be replicated by certain simple, “universal” spin-lattice models. We first characterize precisely what it means for one quantum system to simulate the entire physics of another. We then fully classify the simulation power of all two-qubit interactions, thereby proving that certain simple models can simulate all others, and hence are universal. Our results put the practical field of analogue Hamiltonian simulation on a rigorous footing and take a step toward justifying why error correction may not be required for this application of quantum information technology.

Original languageEnglish
Pages (from-to)9497-9502
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number38
Early online date30 Aug 2018
Publication statusPublished - 18 Sept 2018

Structured keywords

  • Bristol Quantum Information Institute


  • Hamiltonian complexity
  • Many-body physics
  • Quantum information theory
  • Quantum simulation


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