Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 50, Issue 10, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.3236685
Keywords
eigenvalues and eigenfunctions; many-body problems; quantum computing
Categories
Funding
- National Science Foundation [CCF-0726439, PHY-0803304]
- USC Center for Quantum Information Science Technology
- Foundational Questions Institute
- Government of Canada through NSERC
- Province of Ontario through MRI
- Division Of Physics
- Direct For Mathematical & Physical Scien [803304] Funding Source: National Science Foundation
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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 nondegenerate 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.
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