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1500 questions
7
votes
0 answers
Can we distill magic states with arbitrary angle $\theta$?
There seems to be numerous work about the distillation protocol of the $T$-magic state
$$
\frac{1}{\sqrt{2}}(|0\rangle+e^{i\pi/4}|1\rangle).
$$
Similarly, I am wondering if it is possible to distill a $\theta$-magic…
Yunzhe
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7
votes
1 answer
What are reviews on the search for good quantum LDPC codes?
Can anyone provide a link for an up-to-date review of the current situation in researching good quantum LDPC codes and prospects?
I am interested in questions like:
Does the quantum computing community believe this research will provide practical…
Yaron Jarach
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7
votes
2 answers
Can you give an intuitive idea behind how the Minimum Weight Perfect Matching (MWPM) decoder work?
The Minimum Weight Perfect Matching (MWPM) decoder seems to be the most popular choice for decoding error syndromes in Surface Code quantum error correction. Can anyone give an intuitive idea of how it works, with an example?
Aubrey Sharansky
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7
votes
1 answer
Is it possible to perform search with $O(\sqrt{N})$ copies of a "resource" state rather than an oracle?
Suppose that we wish to find $x$ s.t. $f(x) = 1$. Instead of having access to an oracle like $U_f: |i\rangle \mapsto (-1)^{f(i)}|i\rangle$ or $U_f: |i\rangle|z\rangle \mapsto |i\rangle|z\oplus f(i)\rangle$, suppose we have access to copies of a…
shashvat
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7
votes
1 answer
Were quantum computers conjectured to factor large numbers before Shor developed his algorithm?
Peter Shor has given wonderful accounts of the development of his algorithm, with a lot of detail on the activity in the field at around the early-mid 90's. He's been very free about emphasizing that his algorithm was inspired by Umesh Vazirani's…
Mark Spinelli
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7
votes
1 answer
Worst Bell inequality violation with non-maximally entangled state?
I'm familiar with CHSH game and the strategy that allows Alice and Bob to succeed with a probability of $$\frac{1+\tfrac{1}{\sqrt 2}}{2}\approx 85\%$$ if they share a maximally entangled state such as $\lvert\Phi_+\rangle$ and use the measurements…
Franklin Pezzuti Dyer
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7
votes
1 answer
Fidelity concentration bound for random stabilizer states
Let $|\Phi\rangle$ be a normalized vector in $\mathbb{C}^d$ and let $|\psi\rangle$ be a random stabilizer state. I am trying to compute the quantity
$$\mathsf{Pr}\big[|\langle \Phi|\psi \rangle|^2 \geq \epsilon \big].$$
Note that if $|\psi\rangle$…
BlackHat18
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7
votes
1 answer
Do non-stabilizer codes have integer weight enumerator?
Consider an $ ((n,K=2^k,d)) $ non-stabilizer code. The weight enumerator coefficients are
$$
A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2
$$
where $ \Pi $ is the projector onto the code subspace.
Are the $ A_j $…
Ian Gershon Teixeira
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7
votes
3 answers
Does Google's error correction paper invalidate Gil Kalai's arguments?
In his paper "The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims", Gil Kalai argues that quantum advantage will never be reached. For NISQ devices in particular, he argues that for a large variety of…
Tristan Nemoz
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7
votes
1 answer
Generating random, but non-uniform state
I would like an algorithm that generates a random state, sampled according to some probability distribution which is not uniform in Hilbert space. Assume though that I have at my disposal a uniform (i.e. Haar) random state generator. How do I do…
nervxxx
- 520
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7
votes
2 answers
How to increase the probability of successful measurement to find out the largest amplitude?
I have built a state
$$A|0\rangle = |\Psi \rangle = \sum _n c_n |n\rangle$$
Where $A$ is a circuit.
And I need to known, where is the largest $|c_n|$.
I find out that, I can simply do many measurements to find out which one is the largest.
However,…
Alexis
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7
votes
2 answers
Why can quantum walks not approach a stationary distribution
In Child's notes on quantum walks, he claims (section 16.6) "Since a quantum walk is a unitary process, we should not expect it to approach a limiting quantum state, no matter how long we wait."
But why should this be true? I understand that quantum…
SescoMath
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7
votes
1 answer
If a quantum algorithm requires a measurement, how can we use that as a subroutine in another quantum algorithm?
Some algorithms (like period finding), use one or more measurement step. The post measurement state is then acted upon by another set of gates to complete the algorithm.
If I imagine this as blackbox algorithm $f$ which takes $x$ as input and…
ssj009
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7
votes
2 answers
How does quantum teleportation work with mixed shared states?
I am given the scenario that instead of the two parties (A & B) sharing the bell state $|\phi_+\rangle$ they share the mixture $\rho_\lambda = \lambda|\phi_+\rangle\langle\phi_+|+(1-\lambda)\frac{\mathbb{1}}{2}\otimes \frac{\mathbb{1}}{2}$ in the…
Luca Ion
- 73
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7
votes
1 answer
How to derive the quantum Fisher information from the relative entropy?
The quantum relative entropy (QRE) between two states $\rho$ and $\sigma$ is given by
$$
S(\rho\|\sigma)=\operatorname{Tr}(\rho\ln\rho)-\operatorname{Tr}(\rho\ln\sigma)
$$
Now if $\rho$ and $\sigma$ are infinitesimally related i.e,…
m1rohit
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