HIGHLIGHTS
SUMMARY
The task in simulation is to generate, for a given Hermitian matrix H, evolution time t, and error tolerance a sequence of quantum gates U (t) such that kU (t) - e-iHt k ≤, for an appropriate norm k · k, and the cost of the sequence of gate operations that comprise U (t) is minimal. The method of qubitization involves the implementation of a walk operator whose eigenvalues are an efficiently computable function of those of H and achieves linear scaling in the simulation time t, logarithmic scaling in the inverse error tolerance, and scaling . . .
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