Abstract
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on explicit constructions, tailored to each specific family of universal Hamiltonians. In this work we go beyond this approach, and completely classify the simulation ability of quantum Hamiltonians by their complexity classes. We do this by deriving necessary and sufficient complexity theoretic conditions characterising universal quantum Hamiltonians. Although the result concerns the theory of analogue Hamiltonian simulation - a promising application of near-term quantum technology - the proof relies on abstract complexity theoretic concepts and the theory of quantum computation. As well as providing simplified proofs of previous Hamiltonian universality results, and offering a route to new universal constructions, the results in this paper give insight into the origins of universality. For example, finally explaining the previously noted coincidences between families of universal Hamiltonian and classes of Hamiltonians appearing in complexity theory.
Highlights
Recent work has precisely defined what it means for one quantum system to simulate the full physics of another [1] and has demonstrated that—within very demanding definitions of what it means for one system to simulate another—there exist families of local Hamiltonians that are universal, in the sense that they can simulate all other Hamiltonians to any accuracy desired
As well as providing simplified proofs of previous Hamiltonian universality results and offering a route to new universal constructions, the results in this paper give insight into the origins of universality; for example, explaining the previously noted coincidences between families of universal Hamiltonian and classes of Hamiltonians appearing in complexity theory
This rigorous mathematical framework of Hamiltonian simulation gives a theoretical foundation for describing analog Hamiltonian simulation—one of the most promising applications of quantum computing in the noisy intermediate-scale quantum (NISQ) era
Summary
Recent work has precisely defined what it means for one quantum system to simulate the full physics of another [1] and has demonstrated that—within very demanding definitions of what it means for one system to simulate another—there exist families of local Hamiltonians that are universal, in the sense that they can simulate all other Hamiltonians to any accuracy desired. This rigorous mathematical framework of Hamiltonian simulation gives a theoretical foundation for describing analog Hamiltonian simulation—one of the most promising applications of quantum computing in the noisy intermediate-scale quantum (NISQ) era. We derive necessary and sufficient complexity-theoretic conditions for a family of Hamiltonians to be an efficient universal model, relating this directly to complexity-theoretic properties of the ground state
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
