Questions tagged [stoquatic-matrices]

For questions related to stoquastic matrices, also known as matrices having no sign problem. These are Hermitian matrices having real, non-positive off-diagonal entries. When viewed as Hamiltonians such matrices may be more efficiently computable than arbitrary Hamiltonians.

Filter by
Sorted by
Tagged with
3 votes
0 answers
77 views

What properties of a local Hamiltonian are basis-(in)dependent?

Some properties of a Hamiltonian are unique to its spectrum and are basis-independent. For example, I think whether the Hamiltonian's gap remains constant as $n$ goes to infinity, or whether the ...
Mark Spinelli's user avatar
0 votes
0 answers
36 views

How could I get this lemma about stoquastic hamiltonian in the paper "Complexity of stoquastic frustration-free Hamiltonians"

In the paper Complexity of stoquastic frustration-free Hamiltonians, I was confused about the derivation of Lemma 4.5: How could we get $\delta Tr(O(I-\Pi_a)) \leq Tr(OH_a)$ given that $\delta (I-\...
Angelo_M's user avatar
2 votes
1 answer
164 views

How best to prepare a uniform superposition over all strings of balanced parentheses?

[0001] Consider the set $D_n\subset \{(,)\}^{2n}$ of all Dyck words of strings of balanced brackets or balanced parentheses of length $2n$. For example, for $n=5$, we have $\sigma=()()()()()$ is ...
Mark Spinelli's user avatar
2 votes
0 answers
20 views

AQC definition modifications costs and pay-offs

I was wondering if one can think of a more general relation between alleviating conditions for the state in which the evolution takes palce in AQC paradigm and constraining the structure of the ...
devoted4gainz's user avatar
0 votes
1 answer
88 views

Is it possible to find a 2x2 Hermitian matrix whose eigenvalues have 1:2 ratio? [closed]

Is it possible to find 2x2 Hermitian matrix whose eigenvalues have 1:2 ratio and if it is how is it done?
Mark234's user avatar
  • 51
4 votes
0 answers
156 views

If we can prepare a ground state efficiently, when can we prepare the second-lowest energy eigenstate?

I'd like to know if there's anything that can be said about whether and when we can efficiently prepare a state corresponding to the second-lowest eigenvalue of a given Hamiltonian, or in any other ...
Mark Spinelli's user avatar