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If a quantum error correcting code can correct every single-qubit $X$ and $Z$ error, can it also correct every single-qubit $Y$ error?
Let $\mathcal{C}$ be a given arbitrary $n$ qubit quantum error correcting code which can correct any single qubit $X$ error and any single qubit $Z$ error, i.e., $\{X_i\}_{i=1}^n$ & $\{Z_i\}_{i=1}^n $.
Should this code also be able to correct…
FDGod
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7
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Are there practical benefits of using qudits over qubits?
It's clear from foundational research that qudits can provide an enhanced control of the Hilbert space over qubits, and I've encountered references that highlight improved robustness and noise tolerance in quantum protocols such as QKD when using…
banercat
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7
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What are "completely positive" and "CPTP" quantum maps?
I am studying quantum computing a little bit by myself, and I have simple questions.
I didn't find a clear definition of what is a completely positive and trace-preserving (CPTP) map. The best I've found was here .
To summarize it -
Let $\,T:H\to H…
X0-user-0X
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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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Is every $ ((11,2,5)) $ code equivalent to the $ [[11,1,5]] $ stabilizer code?
Two codes are said to be equivalent if their code spaces are related by a non-entangling gate, i.e., a gate from $U(2)^{\otimes n} \rtimes S_n$, the local unitaries together with permutations.
It is proven in Corollary 10 of Quantum Codes of Minimum…
Ian Gershon Teixeira
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7
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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
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2 answers
How to derive the state of a qubit after a partial measurement?
I am trying to solve a problem from the course "Quantum Information Science I" of MIT Open Learning Library, but I get stuck.
Here is the problem. Consider the below circuit where the meter sign denotes the measurement with $\{|0\rangle,|1\rangle\}$…
Stéphane
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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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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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Difference between a star graph state and GHZ graph state
I saw in a class that star state and GHZ state are local-Clifford equivalent (Hadamard on n-1 qubits for a n star state).
But then, when I wanted to draw a GHZ state and check on the litterature whether or not I got it right, it seemed as a lot of…
MohamedSU
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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
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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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2 answers
Clarification on state prep for quantum phase estimation
I have a question about how to prepare a state $|\psi\rangle$ for quantum phase estimation (QPE). My question is about whether the state prepared in QPE has to be the exact eigenstate of the operator or whether it is sufficient for applications to…
Callum
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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…
Sergio Escobar
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