Unanswered Questions
298 questions with no upvoted or accepted answers
15
votes
0
answers
679
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 ...
- 1,502
13
votes
0
answers
308
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 ...
- 12.4k
11
votes
1
answer
195
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 ...
- 1,993
10
votes
0
answers
146
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
430
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 ...
- 14.4k
8
votes
0
answers
212
views
Optimal estimation of quantum state overlap - Circuit implementation?
I've been reading this paper, but don't understand what their optimal method really is, and how it can be realized as a quantum circuit.
The paper mentions the "Schur transform" which has a ...
- 433
8
votes
0
answers
202
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♦
- 26.9k
7
votes
0
answers
194
views
Sequential circuit using quantum gates
Without feedback/loop how can we build a sequential circuit? The basic feature of sequential circuit is that is depends not only on the current inputs but also on the previous inputs/outputs. I've ...
- 17.8k
6
votes
0
answers
109
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}
...
- 715
6
votes
0
answers
116
views
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 ...
- 2,438
6
votes
0
answers
278
views
Quantum State Tomography Implementation in IBMQ
I am working to understand quantum state tomography, specifically using the algorithm presented in PRL 108, 070502. This paper is referenced in IBMQ implementations of QST, both in old deprecated ...
6
votes
0
answers
297
views
Could the Hamiltonian of a 2x2 Rubik's Cube be simulated with a NISQ device?
Consider the four cells on each of the six faces of the 2x2x2 Rubik's cube (the pocket cube). We can construct and simulate a quarter-turn Hamiltonian as below. $^*$
Let $\langle F_1,U_1,R_1\rangle$ ...
- 14.4k
6
votes
0
answers
98
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 ...
- 1,515
6
votes
2
answers
215
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
6
votes
0
answers
141
views
Bell State 11 not working for parity curve
I am currently writing a script to automate the creation of parity curves for a 2 qubit bell state and then calculate fidelity and proving entanglement from that (inspired by this paper). It was going ...
glS♦
- 26.9k