Unanswered Questions

639 questions with no upvoted or accepted answers
20
votes
0answers
773 views

Quantum machine learning after Ewin Tang

Recently, a series of research papers have been released (this, this and this, also this) that provide classical algorithms with the same runtime as quantum machine learning algorithms for the same ...
14
votes
0answers
300 views

Quantum simulation of environment-assisted quantum walks in photosynthetic energy transfer

This question is related to Can the theory of quantum computation assist in the miniaturization of transistors? and Is Quantum Biocomputing ahead of us? About 10 years ago, several papers discussed ...
12
votes
0answers
682 views

Is there a list of accessible open problems in quantum computing from a theoretical computer science perspective?

(Classical) theoretical computer science (TCS) has a number of outstanding open problems that can easily be instantiated in a manner that is accessible to a wider general public. For example, ...
10
votes
0answers
158 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 ...
9
votes
0answers
132 views

Does higher channel fidelity imply higher entanglement fidelity?

Consider two noisy quantum channels (CPTP maps), $\Phi_1^A$ and $\Phi_2^A$, acting on a system $A$. Suppose that for any pure state $\left|\psi\right>\in \mathcal H_A$, $$ F\big(\psi, \Phi_1^A(\psi)...
9
votes
0answers
183 views

Quantum Walk: Why the need of adding “tail” nodes to the root?

As stated in the question, I have found in several papers (e.g. 1, 2) that in order to perform a quantum walk on a given tree it is necessary to add some nodes to the root $r$, say $r^{'}$ and $r^{"}$....
9
votes
0answers
75 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 ...
8
votes
0answers
160 views

What are examples of non-oracular versions of famous oracular problems?

Most quantum algorithms proposed, including Deutsch-Jozsa, Simon's, Bernstein-Vazirani etc, involve querying an oracle. If I understand correctly, the speedups depend on the oracle being efficiently ...
8
votes
0answers
125 views

Reference that explains how to read 3d topological diagrams for surface code computations

I like making diagrams to describe computations. For the surface code, an excellent tool is 3d topological diagrams. Here is an example diagram (made by me in SketchUp): The basic idea is that white ...
7
votes
0answers
127 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 ...
7
votes
0answers
82 views

Status of hidden shift and hidden subgroup problems

We know that solving a hidden subgroup problem over a non-commutative group is a long standing problem in quantum computing even for groups like $D_{2n}$ (alternatively can be written as $\mathbb{Z}_n ...
7
votes
1answer
178 views

On the distribution of the fidelity of a random product state with an arbitrary many-qubit state

Consider an arbitrary $n$-qubit state $\lvert \psi \rangle$. How much do we understand about the probability distribution of the fidelity of $\lvert \psi \rangle$ with a tensor product $\lvert \alpha \...
7
votes
0answers
81 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 ...
7
votes
0answers
179 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 ...
7
votes
0answers
132 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, ...

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