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.
Questions tagged [stoquatic-matrices]
7 questions
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Can we get access to the second-lowest 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 $|\lambda_1\rangle$ of a given Hamiltonian, or in any other way learn what this energy…
Mark Spinelli
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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 Hamiltonian obeys an area law, are independent of the…
Mark Spinelli
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3
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2 answers
The support of the ground state of stoquastic Hamiltonian is connected
A Hamiltonian $H$ is stoquastic in the standard basis if all the off-diagonal terms of the Hamiltonian are non-positive. If we choose $\beta$ small enough, all entries of $I-\beta H$ are non-negative. By the Perron-Frobenius Theorem, the eigenvector…
qmww987
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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 balanced, while $\tau=(()))(()()$ is not.
[0002]…
Mark Spinelli
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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 Hamiltonian.
To illustrate: if we constrain ourselves…
devoted4gainz
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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 $\delta (I-\Pi_a) \leq H_a$? (I think the $\leq$ sign here…
Angelo_M
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Is it possible to find a 2x2 Hermitian matrix whose eigenvalues have 1:2 ratio?
Is it possible to find 2x2 Hermitian matrix whose eigenvalues have 1:2 ratio and if it is how is it done?
Mark234
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