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Unanswered Questions

2,291 questions with no upvoted or accepted answers
14 votes
0 answers
583 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 ...
13 votes
0 answers
266 views

Does the Curry-Howard correspondence have a quantum-specific type system?

In Wikipedia we can read that the Curry–Howard correspondence is a correspondence between formal proof calculi and type systems for models of computation. In particular, it splits into two ...
12 votes
0 answers
280 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 votes
0 answers
128 views

Active improving of nanodiamond surfaces for NV centers?

This question is related (and complementary) to "Passive improving of nanodiamond surfaces for NV centers?". Nitrogen-Vacancy centers (NVs) have astonishing quantum properties, which make them ...
11 votes
0 answers
203 views

Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities

For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, ...
10 votes
0 answers
130 views

Are there separable $\rho$ that cannot be decomposed with less than $\operatorname{rank}(\rho)^2$ pure product states?

In What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?, examples were given of separable states $\rho$ with separable decompositions requiring ...
10 votes
0 answers
555 views

Can we use quantum phase estimation to learn anything about the dynamics of puzzles like the Rubik's cube?

Introduction Consider a state $\vert\psi\rangle$ such as below, which is in a superposition of a difference between a Rubik's cube in a solved state and a Rubik's cube in the "superflip" ...
10 votes
0 answers
102 views

Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ...
10 votes
0 answers
116 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 ...
10 votes
0 answers
171 views

Anti-symmetrization on the lattice

Assume, I'm using a system of qubits to simulate a fermionic system. If I'm using the second-quantized formalism (e.g. orbitals in quantum chemistry), the anti-symmetric nature of the fermionic wave ...
10 votes
0 answers
213 views

Entanglement transfer of spin-entangled triplet-pair states between flying qubits and stationary qubits

The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin ...
9 votes
0 answers
189 views

How can time crystals be useful in qRAM design?

A time crystal is a phase of a matter which is ordered in time, similar to classical crystals which are ordered spatially. In other words, the structure of a time crystal is ever-changing but with ...
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 ...
8 votes
0 answers
272 views

Can you programatically check whether a given set of gates is universal?

I am wondering if there is an automated way to determine whether a given set of quantum operations is universal. More precisely given a set of 1 and 2 qubit gates can we write a program to determine ...
8 votes
0 answers
196 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 ...

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