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Results tagged with complexity-theory
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user 1874
For questions regarding complexity analysis of quantum algorithms and comparisons with complexities of classical algorithms.
2
votes
1
answer
78
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Beyond polynomial speedups in diagonal entries estimation
Consider the task of estimating the diagonal entries of the power of a real sparse matrix A with $N = 2^n$ rows:
Input: $A \in \mathbb{R}^{N \times N}$ with $A = A^\top$ and $s$-sparse and row-effici …
- 817
4
votes
2
answers
164
views
Relation between BQP-Complete and BQP \ PH
Recently, the oracle separation between BQP and PH has been proven. Does this result tell us something about the relation between BQP-complete problems (e.g. approximation Jones polynomial solved by A …
- 817
1
vote
1
answer
93
views
Reference for a proof of QMA-completeness of sparse Hamiltonian
It is well-known that the $k$-local Hamiltonian problem is QMA-complete for $k$ constants over $n$ qubits, $||{H}|| \in \text{poly}(n)$ under a reasonably large promise gap. See e.g. these notes.
Cons …
- 817