Abstract
Adiabatic gauge potential is the origin of nonadiabatic transitions. In counterdiabatic driving, which is a method of shortcuts to adiabaticity, adiabatic gauge potential can be used to realize identical dynamics to adiabatic time evolution without requiring slow change of parameters. We introduce an algebraic expression of adiabatic gauge potential. Then, we find that the explicit form of adiabatic gauge potential can be easily determined by some algebraic calculations. We demonstrate this method by using a single-spin system, a two-spin system, and the transverse Ising chain. Moreover, we derive a lower bound for fidelity to adiabatic time evolution based on the quantum speed limit. This bound enables us to know the worst case performance of approximate adiabatic gauge potential. We can also use this bound to find dominant terms in adiabatic gauge potential to suppress nonadiabatic transitions. We apply this bound to magnetization reversal of the two-spin system and to quantum annealing of the transverse Ising chain. Adiabatic gauge potential reflects structure of energy eigenstates, and thus we also discuss detection of quantum phase transitions by using adiabatic gauge potential. We find a signature of a quantum phase transition in the transverse Ising chain.
Highlights
Quantum control is a fundamental element of quantum technologies [1]
We apply this bound to magnetization reversal of a two-spin system to find dominant terms suppressing nonadiabatic transitions and to find the worst case performance when we use these terms as approximate adiabatic gauge potential (AGP)
We introduced the algebraic expression of the AGP
Summary
Quantum control is a fundamental element of quantum technologies [1]. To control a quantum system in a desired way, we change parameters of a Hamiltonian at each time. By using the relation to the variational approach, we can construct approximate AGP in the algebraic way. This bound can be used to evaluate the worst case performance of approximate AGP without simulating real time evolution. III, we derive a lower bound for fidelity to adiabatic time evolution We apply this bound to magnetization reversal of a two-spin system to find dominant terms suppressing nonadiabatic transitions and to find the worst case performance when we use these terms as approximate AGP. We apply it to quantum annealing of the transverse Ising chain.
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