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Is Gil Kalai's argument against topological quantum computers sound?
In a lecture, recorded on Youtube, Gil Kalai presents a 'deduction' for why topological quantum computers will not work. The interesting part is that he claims this is a stronger argument than the argument against fault tolerant computing in…
Discrete lizard
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Are spin-glass problems NP (-complete)?
It is well known that finding ground states for spin-glass systems (Ising, XY...) is NP-hard (at least as hard as the hardest NP-problems) so that they can be efficiently used to solve other NP problems like the Traveling Salesman Problem.
My…
Wouter
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Does quantum computing threaten blockchain?
As per Wikipedia, blockchains are a way to maintain "a continuously growing list of records, called blocks, which are linked and secured using cryptography [... and] inherently resistant to modification of the data."
Blockchains are in current…
Daniel Tordera
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Why do we use the standard gate set that we do?
The typically used gate set for quantum computation is composed of the single qubits Cliffords (Paulis, H and S) and the controlled-NOT and/or controlled-Z.
To go beyond Clifford we like to have full single qubit rotations. But if we are being…
James Wootton
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What is the quantum circuit equivalent of a (delayed choice) quantum eraser?
Quantum computers are efficiently able to simulate any other quantum system. Hence there must be some sort of equivalent of a (possibly simulated) quantum eraser setup. I would like to see such an equivalent drawn as a quantum circuit, ideally in…
user1039
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Scalability of ion trap quantum computers
My understanding is that the magnetic fields needed to hold the ions in place in ion trap quantum computers are very complex, and for that reason, currently, only 1-D computers are possible, therefore reducing the ease of communication between…
auden
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Will deep learning neural networks run on quantum computers?
Deep Learning (multiple layers of artificial neural networks used in supervised and unsupervised machine learning tasks) is an incredibly powerful tool for many of the most difficult machine learning tasks: image recognition, video recognition,…
Bob Swain
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How does approximating gates via universal gates scale with the length of the computation?
I understand that there is a constructive proof that arbitrary gates can be approximated by a finite universal gate set, which is the Solovay–Kitaev Theorem.
However, the approximation introduces an error, which would spread and accumulate in a long…
M. Stern
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How to approximate $Rx$, $Ry$ and $Rz$ gates?
Quantum Inspire is a quantum computing platform provided by QuTech. It consists of two real quantum processors - Starmon-5 and Spin-2. Whereas it is possible to use rotation gates $Rx$, $Ry$ and $Rz$ on Spin-2 processor, Starmon-5 gate set consist…
Martin Vesely
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How to compactly represent multiple qubit states?
Since access to quantum devices capable of quantum computing is still extremely limited, it is of interest to simulate quantum computations on a classical computer. Representing the state of $n$ qubits as a vector takes $2^n$ elements, which greatly…
Kiro
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What is the difference between the "Fubini-Study distances" $\arccos|\langle\psi|\phi\rangle|$ and $\sqrt{1-|\langle\psi|\phi\rangle|}$?
I sometimes see the "Fubini-Study distance" between two (pure) states $|\psi\rangle,|\phi\rangle$ written as
$$
d(\psi,\phi)_1=\arccos(|\langle\psi|\phi\rangle|),
$$
for example in the Wikipedia page.
Other sources (e.g. this paper in pag. 16), use…
glS
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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 $\mathbb{Z}_n \rtimes \mathbb{Z}_2$) for general $n$. What…
Root
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Does the trace distance have a geometric interpretation?
Consider the trace distance between two quantum states $\rho,\sigma$, defined via
$$D(\rho,\sigma)=\frac12\operatorname{Tr}|\rho-\sigma|,$$
where $|A|\equiv\sqrt{A^\dagger A}$.
When $\rho$ and $\sigma$ are one-qubit states, the trace distance can be…
glS
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Why doesn't the Gottesman-Knill theorem render quantum computing almost useless?
The Gottesman-Knill theore states (from Nielsen and Chuang)
Suppose a quantum computation is performed which involves only the following elements: state preparations in the computational basis, Hadamard gates, phase gates, controlled-NOT gates,…
user2723984
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Is swap gate equivalent to just exchanging the wire of the two qubits?
Is swap gate equivalent to just exchanging the wire of the two qubits?
if yes why not just switching the wire whenever we want to apply a swap gate?
Sam
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