Quantum Inf Process (2017) 16:102
Is the addition of an assisted driving Hamiltonian
always useful for adiabatic evolution?
· Songfeng Lu
· Li Li
Received: 5 February 2016 / Accepted: 23 February 2017 / Published online: 4 March 2017
© Springer Science+Business Media New York 2017
Abstract It has been known that when an assisted driving item is added to the main
system Hamiltonian, the efﬁciency of the resultant adiabatic evolution can be signif-
icantly improved. In some special cases, it can be seen that only through adding an
assisted driving Hamiltonian can the resulting adiabatic evolution be made not to fail.
Thus the additional driving Hamiltonian plays an important role in adiabatic comput-
ing. In this paper, we show that if the driving Hamiltonian is chosen inappropriately,
the adiabatic computation may still fail. More importantly, we ﬁnd that the adiabatic
computation can only succeed if the assisted driving Hamiltonian has a relatively
ﬁxed form. This may help us understand why in the related literature all of the driving
Hamiltonians used share the same form.
Keywords Assisted driving Hamiltonian · Adiabatic evolution· Quantum computing
Adiabatic quantum computation has been under the focus of the community since
Farhi et. al proposed this model for the ﬁrst time . One breakthrough that has been
made is that adiabatic quantum computation is polynomially equivalent to the quantum
circuit model [2,3].
School of Computer Science and Technology, Huazhong University of Science and Technology,
Wuhan 430074, China
College of Educational Information and Technology, Hubei Normal University, Huangshi
College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China