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8 votes
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Why do we need Entanglement?

Almost every quantum state is entangled$^1$. It is therefore unsurprising that quantum algorithms bump into them every so often. In fact, an attempt to navigate the space of all quantum states without ...
Adam Zalcman's user avatar
  • 22.9k
5 votes

Does Rx(θ) applied on pure states create superposition?

In Nielsen and Chuang it is given that the matrix represntation of $R_X(\theta)$ is $$R_X(\theta) = \begin{pmatrix} \cos\frac\theta2 & -i\sin\frac\theta2 \\ -i\sin\frac\theta2 & \cos\frac\...
slimmerikko's user avatar
4 votes
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What is qubit decoherence?

When we measure a qubit in superposition, we interact with the system, causing it to collapse into either $|0\rangle$ or $|1\rangle$, with certain probabilities determined by the coefficients in the ...
banercat's user avatar
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4 votes
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What happens if I superimpose my quantum computer?

You're looking for Quantum computations without definite causal structure, where the order of the gates acting on your quantum system is controlled by another quantum system that can be in a ...
Quantum Mechanic's user avatar
4 votes
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Can quantum algorithms include conditional jumps/change an instruction pointer?

That's an interesting question! Running any classical algorithm First, let us say a word about the fact that quantum computers can run classical algorithms. As you've correctly intuited, what is ...
Tristan Nemoz's user avatar
  • 6,462
4 votes
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is a mixed states really a statistical mixture?

$\DeclareMathOperator{\Tr}{Tr}\newcommand{\ket}[1]{|#1\rangle}\newcommand{\bra}[1]{\langle#1|}$The math that you have done is correct, and so is your general understanding of mixtures and density ...
tpws's user avatar
  • 145
3 votes

The heart of all of quantum physics is superposition

@relativeentropy, since you are interested in knowing from a pedagogical perspective, It would be great to look at superposition from purely mathematical ground. Superposition is not an exclusive ...
Manish Kumar's user avatar
3 votes
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How to create a electron in a superpositon?

But I am not clear how to keep the electron in a particular superposition of our wish. (for e.g.: $1/\sqrt 2 |0\rangle + 1/\sqrt 2 |1\rangle$). Consider a Stern-Gerlach apparatus with it's field in ...
hft's user avatar
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3 votes
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Are equiprobable state same as superposition state

Superposition states of a qubit are usually of form $$| \psi \rangle = a |0\rangle + b |1\rangle $$ where probabilities of getting state $|0\rangle$ and$ |1\rangle$ after a $Z$-measurement are $$p(0) =...
FDGod's user avatar
  • 2,401
3 votes

The heart of all of quantum physics is superposition

I've answered a related question (What is the role of entanglement in quantum-computational speed-up?) in the past, where I argue that superposition is merely derivative of the more fundamental "...
jecado's user avatar
  • 1,186
3 votes

How to create the state $(n!)^{-\frac{1}{2}} \sum_{\pi \in S_n} | \pi, \pi (G) \rangle$ when $G$ is an undirected graph and $\pi$ a permutation

Surprisingly, the way to make a uniform superposition of all permutations is by using a sorting network. You make random shuffle states by sorting! Weird, right? This was figured out in "Improved ...
Craig Gidney's user avatar
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2 votes
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How to create the state $(n!)^{-\frac{1}{2}} \sum_{\pi \in S_n} | \pi, \pi (G) \rangle$ when $G$ is an undirected graph and $\pi$ a permutation

What you're missing is that if there is an efficient classical circuit to compute $\pi(G)$ from a binary representation of $\pi$, then it means that you are able to build the oracle: $$\mathcal{O}|\pi,...
Tristan Nemoz's user avatar
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2 votes
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How can a third party learn the coefficient of a shared $2n$-qubits state using a classical message from each one?

Get Alice and Bob to measure all their qubits in the $X$ basis, and send the $\pm 1$ results to Charlie. The combined answer is a bit string $w$. Charlie discards all the results associated with ...
DaftWullie's user avatar
  • 58.7k
2 votes
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CNOT gate effect on 2 qubits

Interestingly, the CNOT will not only keep the superposition, but in your example it will actually entangle the qubits! That is because, as DaftWullie says, you apply the operator linearly. Let us ...
sheesymcdeezy's user avatar
2 votes

CNOT gate effect on 2 qubits

This is a classical description of what controlled-not does which helps you think through the logic. However, controlled-not does not measure the control qubit, so it does not learn what state the ...
DaftWullie's user avatar
  • 58.7k
2 votes

Can quantum superposition be thought of as a quantized version of classical bits?

Adding a little bit of background/context to @banercat's answer: The comparison between classical and quantum bits can be a useful analog to understand why the (reversible) operations on a universal ...
ChristianM's user avatar
2 votes

Can quantum superposition be thought of as a quantized version of classical bits?

Does it mean that creating superposition actually quantizes the classical bit ? Creating a superposition state goes beyond the classical notion of bits. In the pure theoretical side of quantum ...
banercat's user avatar
  • 763
2 votes

Given a quantum state, can you generate a uniform superposition over its computational basis vectors with nonzero amplitudes?

TL;DR: No. Assuming we only have a single copy of $|\psi\rangle$, the transformation is prohibited by linearity of quantum mechanics. That said, it can be done if we have multiple copies of $|\psi\...
Adam Zalcman's user avatar
  • 22.9k
2 votes

How does the uncomputation step work in the Grover-Rudolph scheme to prepare $\sum_i\sqrt{p_i}|i\rangle$?

The uncomputation is performed by simply running the same unitary used to generate the $|\theta_i\rangle$ states in reverse. We could describe what's going on more abstractly as follows: Start with ...
glS's user avatar
  • 25.4k
2 votes

The heart of all of quantum physics is superposition

In his famous lectures on quantum mechanics, Richard Feynman described superposition as "the heart of quantum mechanics". He also stated that "no one has ever been able to define the ...
Brian John Flanagan's user avatar
1 vote

The heart of all of quantum physics is superposition

In my presentation on application of quantum computation in finance, I put emphasize naturaly on superposition as very imporant concept. Take for example Toffoli gate. It can be used as a classical ...
Martin Vesely's user avatar
1 vote

The heart of all of quantum physics is superposition

Superposition on its own seems a bit reductive. Because the concept does not enclose every mechanics. I am especially thinking at (1) entanglement, (2) non-locality and (3) tunnelling. A quantum ...
Daniele Cuomo's user avatar
1 vote

How many times the circuit need to run when i use get_stateVector in qiskit

It depends on whether you are simulating an ideal circuit or a noisy circuit. For ideal circuits, the number of shots shouldn't have any effect on the result. On ...
Egretta.Thula's user avatar
1 vote

How does the induction step in the Grover-Rudolph scheme to prepare superpositions from probabilities work?

Consider as a toy example a discrete distribution with four outcomes $p_0,p_1,p_2,p_3$. Start from $m=0$, which means $i=0$, and $|\psi_0\rangle=|0\rangle$. The state for $m=1$ would instead be $$|\...
glS's user avatar
  • 25.4k
1 vote

Why are we only interested in the linear combination $|\phi\rangle = a |0\rangle + b |1\rangle$?

A qubit is defined as living in a 2-dimensional Hilbert space. This means one cannot define more than 2 linearly independent basis states. Since $|0\rangle$ and $|1\rangle$ are linearly independent (...
Quantum Mechanic's user avatar

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