Universal quantum Hamiltonians

Abstract

Significance Quantum many-body systems exhibit a bewilderingly diverse range of behavior, which forms the central object of study in many areas of physics and beyond. Our work reveals that, in fact, the entire physics of every other quantum many-body system is replicated in certain simple, universal quantum spin-lattice models. A key application is to the field of analogue simulation of quantum systems, which has long been seen as one of the most promising near-term applications of quantum information technology. We put this field on a rigorous footing, give some rigorous justification for why it may not require error correction, and show that simple families of systems can be used as universal quantum simulators. 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.