Adiabatic Quantum Computing
On Adiabatic Theorem:
1) An Elementary Proof of the Quantum Adiabatic Theorem (Andris Ambainis, Oded Regev)
2) Andrew Child’s Lecture note:
Chapter 15 talks about Hamiltonian simulation using Product Formula (but only briefly mentions his latest result using quantum walk and fractional query model)
Chapter 25 (Page 126) has the proof of the Adiabatic Theorem that is different from the proof in 1).
3) Page Tyler’s lecture note: http://www.physics.
A short and easy to understand derivation of the phase change in the adiabatic process; It explains why the slow evolution matters (ignoring the term with dH/dt), and contains formula for the dynamic phase and geometric(Berry) phase. When ground state is always 0, the dynamic phase is 0 according to the formula.
4) Griffith’s textbook: Quantum Mechanics: http://www.fisica.
Page 337-338 states that if the eigenvectors of the Hamiltonian are all real (which is true in our case), then the Berry Phase change is also 0.
5) Farhi’s original paper on using quantum adiabatic to solve SAT:
6) How Powerful is Adiabatic Quantum Computation?
Wim van Dam, Michele Mosca, Umesh Vazirani
analysis of Farhi’s paper, with a bound on what the number of discretization step should be, but no tight bound on the total evolution time.
