Unanswered Questions
76 questions with no upvoted or accepted answers
15
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0
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592
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Relation between quantum entanglement and quantum state complexity
Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds ...
- 1,482
13
votes
0
answers
283
views
Is HHL still BQP-complete when the matrix entries are only in {0,1}?
I'm studying BQP-completeness proofs of a number of interesting problems of Janzing and Wocjan, and Wocjan and Zhang. Janzing and Wocjan show that estimating entries of matrix powers $(A^m)_{ij}$ with ...
- 12.2k
10
votes
0
answers
121
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Strong vs weak simulations and the polynomial hierarchy collapse
(Edited to make the argument and the question more precise)
An argument for quantum computational "supremacy" (specifically in Bremner et al. and the Google paper) assumes that there exists a ...
- 201
9
votes
0
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420
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Is there a BQP algorithm for each level of the polynomial hierarchy PH?
This question is inspired by thinking about quantum computing power with respect to games, such as chess/checkers/other toy games. Games fit naturally into the polynomial hierarchy $\mathrm{PH}$; I'm ...
- 12.8k
9
votes
0
answers
141
views
Empirical Algorithmics for Near-Term Quantum Computing
In Empirical Algorithmics, researchers aim to understand the performance of algorithms through analyzing their empirical performance. This is quite common in machine learning and optimization. Right ...
8
votes
0
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194
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Better "In-Place" Amplification of QMA
$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$
In MW05 the authors demonstrate so-called "in-place" amplitude amplification for QMA, exhibiting a method for Arthur ...
glS♦
- 25.7k
7
votes
0
answers
73
views
Is there a practical architecture-independent benchmark suitable for adversarial proof of quantum supremacy?
Recent quantum supremacy claims rely, among other things, on extrapolation, which motivates the question in the title, where the word "adversarial" is added to exclude such extrapolation-...
- 326
6
votes
0
answers
93
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Postselection and hardness of estimating amplitudes
Let $A$ be a class of quantum circuits such that
\begin{equation}
\text{Post}A = \text{Post}BQP,
\end{equation}
where $\text{Post}$ indicates post-selection. Is only this amount of information ...
- 1,363
6
votes
2
answers
202
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Equivalence checking of quantum circuits up to error
Suppose you are given two circuit descriptions $A$ and $B$ where by a circuit description I mean a sequence of gates (in the order they are applied) and the qubits they are applied on. (For the sake ...
CommunityBot
- 1
5
votes
0
answers
114
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What is the classical cost of simulating an arbitrary quantum state?
The past couple of years has seen various groups claim quantum advantage/utility only to have their experiments efficiently simulated with classical methods, notably using tensor networks.
My question ...
glS♦
- 25.7k
5
votes
0
answers
81
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What is the computational complexity of decomposing operators in terms of quantum gates?
I have recently worked on a problem involving a rather large Hamiltonian, which I wrote some Python code for its generation following the method in this paper.
No when I used qiskits ...
- 51
5
votes
0
answers
107
views
Lowest energy problem with additional constraints
Consider the following minimization problem:
\begin{align}
&\min_{\rho} \mathrm{Tr}[\rho H] \\
\text{such that:}& \\
&Tr[\rho A_i] \leq 0 \ \ \forall A_i, \ i \in \{1,2,3,...\}
\end{align}
...
- 695
5
votes
0
answers
104
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Consequences of MIP*=RE regarding quantum universality
Provided that $\mathsf{MIP}^*=\mathsf{RE}$ there can be Bell inequalities that have violations achievable only for infinite dimensional quantum systems (vide discussions in Post1 and Post2). Does this ...
- 2,357
5
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123
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Complexity of controlled operations in a two-level unitary operation
In Neilsen and Chuang, chapter 4.5.2 (~p.193), why did the authors come to the conclusion that complexity of operations $C^n(X)$ and $C^n(\tilde{U})$ is $O(n)$?
Did they assume using work qubits? If ...
glS♦
- 25.7k
5
votes
0
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119
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complexity of classical counting algorithm
Does anyone know the solution of Exercise 6.14 of Nielsen and Cheung:
Prove that any classical counting algorithm with a probability at least
3/4 for estimating $M$ correctly to within an ...
- 103