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1500 questions
10
votes
1 answer
Time Entangled Quantum Blockchain
This answer cites a paper[$\dagger$] which purposes a quantum blockchain using entanglement in time.
"The weakness is that the research only presents a conceptual design." - QComp2018
How could a quantum blockchain which leverages time entanglement…
user820789
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10
votes
2 answers
How to check if a matrix is a valid density matrix?
What conditions must a matrix hold to be considered a valid density matrix?
PiMan
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10
votes
1 answer
Barren plateaus in quantum neural network training landscapes
Here the authors argue that the efforts of creating a scalable quantum neural network using a set of parameterized gates are deemed to fail for a large number of qubits. This is due to the fact that, due to the Levy's Lemma, the gradient of a…
asdf
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10
votes
2 answers
Measuring in standard basis meaning
What does it mean to measure a qubit (or multiple qubits) in standard basis?
PiMan
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10
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2 answers
Why did D-Wave choose the Chimera graph the way they did?
D-Wave makes use of a $(n,k=4)$-Chimera structured graph in their computers. Meaning a $n\times n$ grid of unit cells, with each unit cell consisting of a complete bipartite graph on $2k=8$ nodes ($4$ for each side), also called $K_{4,4}$.
Why did…
nippon
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10
votes
2 answers
What quantum gates admit a basis-independent interpretation of their action?
The SWAP gate swaps the state of the two qubits so that in the computational basis $|01\rangle \rightarrow |10 \rangle$ with a matrix representation given by:
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1…
user97154
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10
votes
1 answer
Proof of an Holevo information inequality for a classical-classical-quantum channel
Suppose I have a classical-classical-quantum channel $W : \mathcal{X}\times\mathcal{Y} \rightarrow \mathcal{D}(\mathcal{H})$, where $\mathcal{X},\mathcal{Y}$ are finite sets and $\mathcal{D}(\mathcal{H})$ is the set of density matrices on finite…
Stephen Diadamo
- 155
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10
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0 answers
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" state.
Here, with eight cells on each face (apart from the…
Mark Spinelli
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10
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2 answers
How does the spectral decomposition of the Choi operator relate to Kraus operators?
In Nielsen and Chuang's QCQI, there is a proof states that
Theorem 8.1: The map $\mathcal{E}$ satisfies axioms A1, A2 and A3 if and only if
$$
\mathcal{E}(\rho)=\sum_{i} E_{i} \rho E_{i}^{\dagger}
$$
for some set of operators…
Sherlock
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10
votes
1 answer
What is the set of generators for the qutrit Clifford group?
According to this article, any Clifford gate, acting on $n$ qubits, can be generated by Hadamard, CNOT, and S gates.
What are the set of generators for qutrit Cliffords?
BlackHat18
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votes
1 answer
Good references to learn magic state distillation for fault tolerance
I need to learn magic state distillation procedure and their application to fault-tolerance.
One of the original paper on this subject is the following: https://arxiv.org/pdf/quant-ph/0403025.pdf
I am wondering if there are more recent and pedagogic…
Marco Fellous-Asiani
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10
votes
3 answers
Do any specific types of qudits other than qubits and qutrits have a name?
For example, has anyone seen something like:
"quqrit" for a 4-level system[1], or
"qupit" for a 5-level system[2] ?
1 From "quad" or "quart" since "tetra" would be qutrit, which is already a 3-level system.
2 From "penta" since "quint" would…
user1271772 No more free time
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10
votes
1 answer
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 some period. In fact, time crystals are quantum…
Martin Vesely
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10
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1 answer
Are there connections between long-range entanglement and topological quantum computation?
Long-range entanglement is characterized by topological order (some kinds of global entanglement properties), and the "modern" definition of topological order is the ground state of the system cannot be prepared by a constant-depth circuit from a…
Yupan Liu
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2 answers
Is the Kraus representation of a quantum channel equivalent to a unitary evolution in an enlarged space?
I understand that there are two ways to think about 'general quantum operators'.
Way 1
We can think of them as trace-preserving completely positive operators. These can be written in the form
$$\rho'=\sum_k A_k \rho A_k^\dagger \tag{1}$$
where…
Quantum spaghettification
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