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HHL algorithm, how to decide n qubits to prepare for expressing eigenvalue of A?
I am trying to understand the HHL algorithm for solving linear systems of equations (Harrow, Hassidim, Lloyd; presented in arXiv:0811.3171 and explained on page 17 of arXiv:1804.03719). By reading some papers, I think I got rough idea but there are…
Bick
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Lower bound for Degenerate Codes?
According to (Macchiavello, Palma, Zeilinger, 2001; pg82) a lower bound of the encoding Hilbert space of a non degenerate code is given by the quantum version of the Hamming bound:
$$2^k \sum_{i=0}^t 3^i \begin{pmatrix} n \\ i\end{pmatrix}\le…
Quantum spaghettification
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Markov Chain expressed in Density Matrix formalism
Suppose we have two states of a system where I tell you that there is a probability $p_1$ of being in state $1$, and probability $p_2$ of being in state $2$. The total state can be written as a vector in $L^1$ normed space:
$$p=\begin{pmatrix}p_1 \\…
Connor Dolan
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Are there measuring standards (and units) for the identification of qubits?
The representation of bits in different technological areas:
Normal digital bits are mere abstractions of the underlying electric current through wires. Different standards, like CMOS or TTL, assign different thresholds to such signals: "if the…
AG-M
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In qubit/qudit terms, where is the experimental limit between S=3/2 and 2·S=1/2?
This question is inspired by "What is the difference between a qudit system with d=4 and a two-qubit system?", as an experimental follow-up.
Consider for illustration these two particular cases:
Molecular Spin Qudits for Quantum Algorithms, where…
agaitaarino
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Is it true that observing a quantum state will end the superposition of states? How can I not observe?
I have no background in quantum physics, and no understanding of most formulas used in this context. I'm not looking for an in depth answer, i'd just like to vaguely understand the concept.
The way i heard it, a superposition is [real/a neccessary…
bukwyrm
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Why or how is 'cat' state preparation via a C-not-not operation not fault tolerant?
On p490 of Nielsen and Chuang, 2010 the authors say that the preparation of the 'cat' state ($|000\ldots 0\rangle+|111\ldots 1\rangle$) is not Fault Tolerant. Below is my mock up of the diagram they draw for the preparation ($H$ and $C$-not-not *)…
Quantum spaghettification
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How does the extremality of a POVM reflect on its Naimark dilation isometry?
Let $\mu:\Sigma\to\mathrm{Pos}(\mathcal X)$ be some POVM, with $\Sigma$ the finite set of possible outcomes, and $\mathrm{Pos}(\mathcal X)$ the set of positive semidefinite operators on a finite-dimensional space $\mathcal X$. Write the components…
glS
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Upper Bounds for QMA Quantum Merlin Arthur, and QMA(k)
QMA (Quantum Merlin Arthur), is the quantum analog of NP, and QMA(k) is the class with $k$ Merlins. These are important classes when studying Quantum Complexity theory. QMA(k) is QMA with $k$ unentangled provers ($k$ Merlins), or BQP verfiers. These…
user3483902
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Quantum computing and blockchain technology
It is popularly stated that quantum computing could destroy and disrupt blockchain technology completely. How is quantum computing a threat to blockchain technology?
Chetan Warke
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What is the "no fast-forwarding theorem"?
As a newbie to Quantum, I was reading some of the articles and ran into a no-fast-forwarding theorem, which is described "Simulating the dynamics of a quantum system for time T typically requires Ω(T) gates so that a generic Hamiltonian evolution…
John Parker
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Can quantum computing provide advantages related to Hardware-Neural Networks?
The following question is related to this one: Will deep learning neural networks run on quantum computers?. I found it complementary and necessary because the previous answers are not completely related with my concerns.
Primarily, my question is…
SalvaCardona
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Explicit states with high $T$ count
It is well known, that the Clifford $+T$ gate set consisting of the gates $\lbrace H, S, CNOT, T \rbrace$ is universal for quantum computation, that is, for any n-qubit unitary $U:\left( \mathbb{C}^2\right)^{\otimes n} \rightarrow \left(…
Fritz Hefter
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What is a proof for the principle of deferred measurement?
Does anyone know of a proof for the 'principle of deferred measurement'?
Quantum Guy 123
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Why is depth complexity relevant?
Since gate complexity correspond to the number of gate for a given quantum circuit, it seems that depth complexity bring no more information about quantum complexity than gate complexity. So does gate complexity encompass depth complexity ?
adamaaa
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