Unanswered Questions
162 questions with no upvoted or accepted answers
15
votes
0
answers
599
views
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
287
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
122
views
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
answers
420
views
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 ...
- 12.9k
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
1
answer
322
views
Enforcing a particular layout mapping in Qiskit
I would like to ask how to set a particular layout during transpiling. I guess that the layout can be set by the initial_layout parameter in the transpiler. However,...
CommunityBot
- 1
8
votes
0
answers
195
views
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♦
- 25.9k
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
7
votes
0
answers
332
views
Solving linear system $Ax=b$ with exponential speed-up via binary optimization?
The main disadvantage of HHL algorithm for solving $A|x\rangle = |b\rangle$ is that exponential speed-up is reached only in case we are interested in value $\langle x|M|x\rangle$, where $M$ is a ...
- 1
6
votes
0
answers
133
views
How to use Warm-Start QAOA in QisKit to solve non-convex QUBO problem?
I have a non-convex QUBO problem that I'd like to solve by warm-starting QAOA with a solution obtained from a continuous relaxation solution obtained by a classical algorithm. The specifics of the ...
- 14.6k
6
votes
0
answers
122
views
Is No Free Lunch Theorem generalizable to Quantum Computation?
The "No Free Lunch Theorem" says: that when averaged across all possible problems, any two strategies have equivalent performance. However it uses Bayesian reasoning to arrive at this ...
- 437
6
votes
0
answers
93
views
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 ...
- 1,373
6
votes
2
answers
203
views
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
views
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♦
- 25.9k
5
votes
0
answers
81
views
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