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13
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1 answer
General parametrisation of an arbitrary $2 \times 2$ unitary matrix
From Nielsen & Chuang's Quantum Computation and Quantum Information (QCQI):
Since $U$ is unitary, the rows and columns of $U$ are orthonormal, form which it follows that there exist real numbers $\alpha$, $\beta$, $\gamma$ and $\delta$ such that $$…
Tech Solver
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3 answers
Approximating unitary matrices
I currently have 2 unitary matrices that I want to approximate to a good precision with the fewer quantum gates possible.
In my case the two matrices are:
The square root of NOT gate (up to a global phase)
$$G = \frac{-1}{\sqrt{2}}\begin{pmatrix} i…
Adrien Suau
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13
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2 answers
Quantum Supremacy: How do we know that a better classical algorithm doesn't exist?
According to the Wikipedia (Which quotes this paper https://arxiv.org/abs/1203.5813 by Preskill) the definition of Quantum Supremacy is
Quantum supremacy or quantum advantage is the potential ability of
quantum computing devices to solve problems…
P. C. Spaniel
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3 answers
Are correlations stronger than those allowed by quantum mechanics possible?
We know how a quantum correlation setup can help us with a better probability of winning games like the CHSH. But what is the upper bound that physics can allow? Is it the quantum correlation setup? Or can we exceed them in general sense to get much…
Siddhant Singh
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13
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2 answers
Where do we put error correction code in quantum circuit?
First of all : I am a beginner in quantum computing.
I would like to have a resource (or an answer if it is not complicated) explaining where we put the error correction codes in a quantum circuit.
Indeed, I know we have different possible errors…
Marco Fellous-Asiani
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13
votes
2 answers
Can we speed up the Grover's Algorithm by running parallel processes?
In classical computing, we can run the key search (for example AES) by running parallel computing nodes as many as possible.
It is clear that we can run many Grover's algorithms, too.
My question is; it possible to have a speed up using more than…
kelalaka
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13
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5 answers
Advances on imperfect quantum copying
It is known by the no-cloning theorem that constructing a machine that is able to clone an arbitrary quantum state is impossible. However, if the copying is assumed not to be perfect, then universal quantum cloning machines can be generated, being…
Josu Etxezarreta Martinez
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13
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3 answers
Which programming language is suitable for a beginner?
I understand there are a lot of programming languages (e.g. Q#, Qiskit, etc.)
Which one is suitable for someone that just started learning programming and doesn't know anything about quantum mechanics?
Daniel Mana
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13
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1 answer
Significance of Clifford operations from quantum error correction perspective
In the literature on QECC, Clifford gates occupy an elevated status.
Consider the following examples which attest to this:
When you study stabilizer codes, you separately study how to perform encoded Clifford gates (even if these aren't applicable…
Tanmay Singal
- 170
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13
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How are magic states defined in the context of quantum computation?
Quoting from this blog post by Earl T. Campbell:
Magic states are a special ingredient, or resource, that allows quantum computers to run faster than traditional computers.
One interesting example that is mentioned in that blog post is that, in…
glS
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13
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2 answers
Is the "Quantum Volume" a fair metric for future, elaborate, high value quantum computations?
A metric called the "quantum volume" has been proposed to somehow compare the utility of different quantum computing hardware. Roughly speaking, it measures their worth by the square of the maximum depth of quantum computations it permits but limits…
user1039
13
votes
0 answers
What is the Generalized Quantum Stein's Lemma and why is it important?
I'm sensing a lot of buzz about potential re-proofs of the Generalized Quantum Stein's Lemma - a generalization of the quantum counterpart to the classical Stein's Lemma, which is of some importance in statistical inference and hypothesis…
Mark Spinelli
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13
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1 answer
Does the quantum coherence in the FMO complex have any significance to quantum computing (on a biological substrate)?
The quantum effects of the FMO complex (photosynthetic light harvesting complex found in green sulfur bacteria) have been well studied as well as the quantum effects in other photosynthetic systems. One of the most common hypotheses for explaining…
TanMath
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13
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1 answer
Advantage of simulating sparse Hamiltonians
In @DaftWullie's answer to this question he showed how to represent in terms of quantum gates the matrix used as example in this article. However, I believe it to be unlikely to have such well structured matrices in real life examples, therefore I…
FSic
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2 answers
Hamiltonian simulation with complex coefficients
As part of a variational algorithm, I would like to construct a quantum circuit (ideally with pyQuil) that simulates a Hamiltonian of the form:
$H = 0.3 \cdot Z_3Z_4 + 0.12\cdot Z_1Z_3 + [...] +
- 11.03 \cdot Z_3 - 10.92 \cdot Z_4 + \mathbf{0.12i…
Mark Fingerhuth
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