Adiabatic approximation with exponential accuracy for many-body systems and quantum computation

By Daniel A. Lidar, Ali T. Rezakhani, A. Hamma. 2008

153 citations recorded by the source corpus.

We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real time axis, that some number of its time-derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is non-degenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time-derivative of the Hamiltonian, divided by the cube of the minimal gap.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/8b27a6cf5e249be183cc2c79b569a11b98c84b5c

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Ising machines as hardware solvers of combinatorial optimization problems (2022, background): “The sweep time for which the adiabaticity can be achieved is proportional to a negative power of the minimum energy gap between two lowest energy levels during the sweep 149–152 .”
Adiabatic Quantum Computing (2016, methodology): “The proof of the lower bound is 11 This corrects an omission in (Lidar et al., 2009), where the dependence of ∥∥H(1)∥∥ on V was ignored since the supremum of∥∥H(1)(s)∥∥ was taken over s ∈ [0, 1] instead of over the region of analyticity of H(s), as noted in (Ge et al., 2015).”
Elucidating reaction mechanisms on quantum computers (2016, methodology): “However, since we are primarily interested in high–accuracy state preparation much better strategies exist [52, 53].”
Decoherence in adiabatic quantum computation (2015, background): “[33] showed that in the closed system case, the deviation from the final ground state can be made arbitrarily small at a fixed tf (large enough to satisfy the adiabatic condition with respect to the minimum energy gap) by choosing a family of analytic interpolation functions with an increasing numbe”