Adiabatic quantum computation with a one-dimensional projector Hamiltonian
Abstract
Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyze a particular class of quantum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on the corresponding ground state. The minimum-energy gap, which governs the time required for a successful evolution, is shown to be proportional to the overlap of the ground states of the initial and final Hamiltonians. We show that such evolutions exhibit a rapid crossover as the ground state changes abruptly near the transition point where the energy gap is minimum. Furthermore, a faster evolution can be obtained by performing a partial adiabatic evolution within a narrow interval around the transition point. These results generalize and quantify earlier works.
- Publication:
-
Physical Review A
- Pub Date:
- November 2009
- DOI:
- 10.1103/PhysRevA.80.052328
- arXiv:
- arXiv:0806.0385
- Bibcode:
- 2009PhRvA..80e2328T
- Keywords:
-
- 03.67.Lx;
- Quantum computation;
- Quantum Physics
- E-Print:
- revised version