Unanswered Questions

700 questions with no upvoted or accepted answers
17
votes
0answers
787 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, ...
16
votes
0answers
305 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 ...
11
votes
0answers
166 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 ...
10
votes
0answers
193 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 $r^{"}$....
10
votes
0answers
78 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 ...
9
votes
0answers
174 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
172 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 ...
9
votes
0answers
137 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 ...
9
votes
0answers
161 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 ...
8
votes
0answers
144 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 ...
8
votes
0answers
120 views

What is the probability $\Pr(||U-I||_{op}<\varepsilon)$ of a Haar-random unitary being close to the identity?

If one generates an $n\times n$ Haar random unitary $U$, then clearly $\Pr(U=I)=0$. However, for every $\epsilon>0$, the probability $$\Pr(\|U-I\|_{op}<\varepsilon)$$ should be positive. How can ...
8
votes
0answers
100 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 ...
8
votes
1answer
198 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 \...
8
votes
0answers
58 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 ...
8
votes
0answers
86 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 ...

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