241 reputation
114
bio website umbc.edu/~shehab1
location Baltimore
age 30
visits member for 1 year, 10 months
seen Sep 16 at 19:58

A PhD student studying quantum computation.


Jul
8
comment Ising formulation of the graph isomorphism problem
I was able to identify my mistake with the first question.
Oct
28
comment Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)
The author replied as follows: To be frank, both of the two interpretations are inaccurate. The proofs are exactly for the cases listed only, and do not work for any other situation. Besides, I think the complexity to make a statement for a case as general as your first interpretation is probably NP-hard.
Oct
28
comment Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)
Can I simply interpret the Theorem 1 as follows? "If the eigenstate of the initial Hamiltonian are superposition of all possible states we cannot perform the adiabatic evolution with a diagonal Hamiltonian as the problem Hamiltonian. " Can I simply interpret the Theorem 2 as follows? "Having diagonal Hamiltonians as both initial and problem Hamiltonians will not work."
Oct
28
comment Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)
The author echoed your answer. Thanks. I just asked them the following though.
Aug
3
comment Adiabatic quantum evolution of single photon or biphoton system
@Ali, is it possible to trap a photon or biphoton in a potential well?
Aug
1
comment Adiabatic quantum evolution of single photon or biphoton system
Any help from anyone?
Jul
31
comment Adiabatic theorem in the regime of quantum optics
@PeterShor, Is that even possible? I think a prerequisite is to have single photon or biphoton system with ground and higher energy level. I am not sure how one can make such state. So I asked a separate question here (physics.stackexchange.com/questions/72863/…)
Jul
31
comment Adiabatic theorem in the regime of quantum optics
@PeterShor, what about correlated photons? Can we change the state of a pair of correlated photons (say, generated by SPDC) adiabatically?
Jul
25
comment Adiabatic theorem in the regime of quantum optics
@PeterShor, thanks! I didn't know that. Just found this (arxiv.org/abs/quant-ph/0507268).
Jul
24
comment Intuition behind Hamiltonian
Thanks for the detailed answer. So, the standard way to create a Hamiltonian, $H$, which has a state, $|\Psi\rangle$, as the lowest eigenstate is as follows: $$H = I - |\Psi\rangle \langle \Psi | $$. Am I right?
Jul
17
comment What is the energy scale of a Hamiltonian?
@Trimok, so in QFT you do the calculation for $c = \hbar = 1$ and rescale the final result, right?
Jul
16
comment What is the energy scale of a Hamiltonian?
@Trimok, your comment partially answers my question. Is this kind of dimensionless Hamiltonian show up often in quantum mechanics or quantum information?
May
29
comment Ising spin vs Pauli spin matrices
@TysonWilliams, I wanted see if any extra insight is available on that forum.
May
28
comment Ising spin vs Pauli spin matrices
understood. So, why did the authors in the first two links of my question use Ising model?
May
16
comment NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
This paper (DOI: 10.5488/CMP.15.43002) describes a hybrid system of both Ising and Heisenberg spins. In Equation 1, $\sigma_z$ is used for Ising spin and $S_z$ is used for Heisenberg spin.
May
16
comment NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
@Siva, it should be $d \ge 3$.
May
16
comment NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
@Lagerbaer, I think I know what went wrong with my understanding. I was trained as a computer scientist and doing my PhD in quantum computation. I learnt about Ising models from papers on adiabatic quantum computation (not by studying condensed matter physics). Papers like this (www-users.math.umd.edu/~mohara/mainthesis.pdf.gz), obviously not wrong but too simplified for me, generally express the Ising Hamiltonians in terms of Pauli spin matrices. So, I was brain washed with a limited understanding.
May
16
comment NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
@Lagerbaer, as $S_i$ and $S_j$ are Pauli matrices, shouldn't be H always in matrix form? If so, for any Ising Hamiltonian, finding the ground state is always the problem of finding the eigenvalues, right? Say, for some reasons, which I don't understand, H is not always in matrix form. Can we then say that the ground states of at least those Ising models, which have Hamiltonians in matrix form, can be calculated in polynomial time? BTW, what are those Ising models which don't have a Hamiltonian in matrix form?
May
16
comment NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
@Lagerbaer, Now I am even more confused. What is exactly NP-complete here?
May
16
comment NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
@Lagerbaer, the Hilbert space is relevant when we try to write the Hamiltonian. So, should I assume that writing the Hamiltonian matrix, not solving it, is NP-complete?