Abstract
We develop a framework and give an example for situations where two distinct Hamiltonians living in the same Hilbert space can be used to simulate the same physics. As an example of an analog simulation, we first discuss how one can simulate an infinite-range-interaction one-axis twisting Hamiltonian using a short-range nearest-neighbor-interaction Heisenberg XXX model with a staggered field. Based on this, we show how one can build an alternative version of a digital quantum simulator. As a by-product, we present a method for creating many-body maximally entangled states using only short-range nearest-neighbor interactions.
Highlights
We develop a framework and give an example for situations where two distinct Hamiltonians living in the same Hilbert space can be used to simulate the same physics
One can either come up with some other physical system that has a Hamiltonian H QS that is identical to H T and possesses the same system properties and leads to the same dynamics
If hhas a degenerate eigenspectrum, it might happen that a state jψi composed of degenerate eigenstates of h 1⁄4 H QS − H T will not be an eigenstate of H QS or H T, but the two Hamiltonians will yield the same quantum dynamics with respect to that state
Summary
The system is either too large to perform numerical and analytical calculations on or is intractable from an experimental point of view In this case, one can either come up with some other physical system that has a Hamiltonian H QS that is identical to H T and possesses the same system properties and leads to the same dynamics. The requirement for H QS to be a suitable Hamiltonian of a quantum simulator can be formulated in the following way (for the sake of brevity, we set ħ 1⁄4 1 throughout the entire manuscript): hψ jeitH QS e−itH T jψ i 1⁄4 eiξðtÞ; ð1Þ. We will call hðtÞ a connector operator or connector Due to their construction, connectors are likely to be rather complicated, time-dependent, or even nonlocal, and most often of no practical help.
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