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How many logical qubits are needed to run Shor's algorithm efficiently on large integers ($n > 2^{1024}$)?
First, I know there are differences in logical qubits and physical qubits. It takes more physical qubits for each logical qubit due to quantum error.
Wikipedia states that it takes quantum gates of order $\mathcal{O}((\log N)^2(\log \log N)(\log…
LeWoody
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Relation between quantum entanglement and quantum state complexity
Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds to a higher quantum state complexity, or a…
XXDD
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General construction of $W_n$-state
Two of the most well known entangled states are the GHZ-state $|\psi\rangle = 1/\sqrt{2}\left( |0\rangle^{\otimes n} + |1\rangle^{\otimes n}\right)$ and the $W_n$-state, with $W_3 = 1/\sqrt{3}\left(|100\rangle + |010\rangle + |001\rangle\right)$.…
nippon
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What do they mean by "qubit can't be copied"?
What does it mean by ''qubit can't be copied'' ?
In a note, it is saying that:
Copying a qubit means $$U|\psi\rangle_A|0\rangle_B=|\psi\rangle_A|\psi\rangle_B$$
i.e; applying a unitary transformation on the qubit state. It is explained as, if the…
tarit goswami
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Are there any examples of anyone applying quantum algorithms to problems in computational biology?
As the title suggests, I'm searching for published examples of quantum algorithms being applied to problems in computational biology. Clearly the odds are high that practical examples don't exist (yet) – what I'm interested in is any proof of…
Greenstick
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What use has quantum computing been?
Most of us on this site believe that quantum computing will work. However, let's play devil's advocate. Imagine that we suddenly hit some fundamental stumbling block that prevented further development towards a universal quantum computer. Perhaps…
DaftWullie
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What is a Haar random quantum state?
Can somebody please explain me what is a Haar random state? I am not able to find any friendly resource to read about it.
Shweta Aggrawal
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Jones Polynomial
There are many fairly standard quantum algorithms that can all be understood within a very similar framework, from Deutsch's algorithm Simon's problem, Grover's search, Shor's algorithm and so on.
One algorithm that seems to be completely different…
DaftWullie
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How to permute (reshuffle) an n-bit input?
I am interested in a quantum algorithm that gets as input an n-bit sequence and that produces as output a reshuffled (permuted) version of this n-bit sequence.
E.g. if the input is 0,0,1,1 (so n=4 in this case) then the possible answers…
JanVdA
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Grover's Algorithm and its relation to complexity classes?
I am getting confused about Grover's algorithm and it's connection to complexity classes.
The Grover's algorithm finds and element $k$ in a database of $N=2^n$ (such that $f(k)=1$) of elements with $$\sim \sqrt{N}=2^{n/2}$$
calls to the oracle.
So…
Quantum spaghettification
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Is acting with a positive map on a state not part of a larger system allowed?
In the comments to a question I asked recently, there is a discussion between user1271772 and myself on positive operators.
I know that for a positive trace-preserving operator $\Lambda$ (e.g. the partial transpose) if acting on a mixed state $\rho$…
Quantum spaghettification
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Is it true to say that one qubit in an entangled state can instantaneously affect all others?
When a qubit is measured, there is a ‘collapse of the wave-function’ as a result is randomly chosen.
If the qubit is entangled with others, this collapse will also effect them. And the way it affects them depends on the way we chose to measure our…
James Wootton
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Does a study guide exist that starts from a "purely CS background" and advances towards "making a new quantum programming language"?
I am from a computer science background and I find it difficult to decide on the resources I should focus on while learning quantum computing, since there is so much to read/watch. My ultimate goal is to make a programming language acting as an…
Kushajveer
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What is the difference between "code space", "code word" and "stabilizer code"?
I keep reading (e.g. Nielsen and Chuang, 2010; pg. 456 and 465) the following three phases; "code space", "code word" and "stabilizer code" - but am having a difficult time finding definitions of them and more importantly how they differ from one…
Quantum spaghettification
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What does quantum error correction code notation stand for?
I understand the notation for classical error correcting codes. E.g., "Hamming(7,4)" stands for a Hamming code that uses 7 bits to encode blocks of 4 bits.
What does the notation for quantum error correcting codes mean? E.g., there is a paper that…
Alexander Pozdneev
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