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Unformatted text preview:  1 MIT 6.443J / 8.371J / 18.409 / MAS.865 Quantum Information Science March 14, 2006 Adiabatic Quantum Computation Adiabatic quantum computation is a HamiltonianBased model of quantum computation. In quantum odinger equation gives the timeevolution of a state in terms of the Hamiltonian mechanics, the Schr  operator H , H = i .  t  Furthermore, if is an energy eigenstate with energy E , then   ( t ) = e iEt/ (0) .  The idea behind Hamiltonianbased QC is that finding the ground state of a Hamiltonian solves inter esting computational problems, including NP complete problems. Adiabatic Theorem The adiabatic theorem says that if we begin in the ground state and change the Hamiltonian slowly, be end in the ground state of the new Hamiltonian. Consider the Hamiltonian H ( t ) for 0 t 1 . Where do we end up if we are in the ground state at s = 0 ? t H T ( t ) = H T H T  = i t  t =0 = ground state   Theorem. As T , ground state .  t =  How Slow Must the Hamiltonian Change? The time depends on the energy gap between the ground state and the lowest excited state. Theorem. If T 1 / 2 , we stay in the ground state (no rigorous proof known). Theorem. If T 1 / 3 , we stay in the ground state....
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This note was uploaded on 02/07/2012 for the course MAS 6.443J taught by Professor Petershor during the Spring '06 term at MIT.
 Spring '06
 PeterShor

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