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Abstract
We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to implementing or mimicking dynamics with the most controllable Hamiltonian. As a promising application, this existence theorem allows for a rapidly evolving realization of adiabatic quantum computation by transforming a Hamiltonian where dynamics is in the adiabatic regime into a rapidly evolving one. We illustrate the theorem with examples.
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1 The Basque Country University (EHU/UPV), Department of Theoretical Physics and History of Science, Bilbao, Spain (GRID:grid.11480.3c) (ISNI:0000000121671098); Ikerbasque, Basque Foundation for Science, Bilbao, Spain (GRID:grid.424810.b) (ISNI:0000 0004 0467 2314)
2 University of Toronto, Chemical Physics Theory Group, Department of Chemistry, and Centre for Quantum Information and Quantum Control, Toronto, Canada (GRID:grid.17063.33) (ISNI:0000 0001 2157 2938); University of Toronto, Department of Physics, Toronto, Canada (GRID:grid.17063.33) (ISNI:0000 0001 2157 2938)