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Universal Quantum Hamiltonians

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In “analogue” quantum simulation, the Hamiltonian of a quantum many body system is directly encoded into the Hamiltonian of another quantum system, without the need for a fully scalable fault tolerant quantum computer. In this talk, I will rigorously justify our definition of analogue simulation, where all the physics of a target Hamiltonian is reproduced in the low energy part of another, up to arbitrarily small accuracy. This definition is very strong and immediately leads to a number of interesting consequences. For example, the locality structure of the original Hamiltonian is preserved, such that local errors/observables on the simulator correspond to local errors/observables on the original system, allowing us to to take a first step in justifying why error correction may not be needed in analogue simulations of this form. A family of Hamiltonians which can simulate all other local spin hamiltonians is called “universal”, and we show that this property easily implies BQP -completeness (up to a depth 1 quantum circuit reduction). Finally we show that very simple spin models such as the qubit Heisenberg or XY interactions are universal in this sense, and we are in fact able to classify all sets of two-qubit interactions into universality classes. (Based on joint work with Toby Cubitt and Ashley Montanaro)

This talk is part of the CQIF Seminar series.

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