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Questions tagged [superposition]

Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation. (Wikipedia)

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What is the difference between superpositions and mixed states?

My understanding so far is: a pure state is a basic state of a system, and a mixed state represents uncertainty about the system, i.e. the system is in one of a set of states with some (classical) ...
Norrius's user avatar
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35 votes
4 answers
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Effects of quantum computing on parallel universes

I have heard a few times that one way of describing quantum computers is that they essentially use the computing power of their counterparts in alternate realities that they access through ...
Snowshard's user avatar
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22 votes
5 answers
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How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where: only $3$ of these $4$ ...
weekens's user avatar
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13 votes
3 answers
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Superposition of quantum circuits

Given a quantum circuit $C_1$ that generates a state $\vert\psi\rangle$ and another circuit $C_2$ that generates $\vert\phi\rangle$, is there a way to construct a circuit that outputs $$\frac{1}{\sqrt{...
Kolp's user avatar
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7 votes
3 answers
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Forming states of the form $\sqrt{p}\vert 0\rangle+\sqrt{1-p}\vert 1\rangle$

I'm curious about how to form arbitrary-sized uniform superpositions, i.e., $$\frac{1}{\sqrt{N}}\sum_{x=0}^{N-1}\vert x\rangle$$ for $N$ that is not a power of 2. If this is possible, then one can ...
Sam Jaques's user avatar
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1 vote
1 answer
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How does the induction step in the Grover-Rudolph scheme to prepare superpositions from probabilities work?

In https://arxiv.org/abs/quant-ph/0208112, the authors discuss a scheme to, given a discrete probability distribution $\mathbf p\equiv (p_i)_i$, under some assumptions on $\mathbf p$, prepare the ...
glS's user avatar
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5 votes
1 answer
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Is there a way to create a superposition of all the possible states?

If there're four qubits in my circuit, how can I arrange my gates so that the final output state is a superposition of all the possible states of 4 qubits? (there're 16 of them in total). I've tried ...
ZR-'s user avatar
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4 votes
2 answers
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How to superpose two composite qubit states?

Assuming we have two sets of $n$ qubits. The first set of $n$ qubits is in state $|a\rangle$ and second set in $|b\rangle$. Is there a fixed procedure that generates a superposed state of the two $|a\...
wang1908's user avatar
3 votes
1 answer
253 views

Can a single qutrit in superposition be considered entangled?

Often in quantum computing the idea of quantum superposition is introduced well before the concept of entanglement. I suspect this may be because our conception of (classical) computing privileges ...
Mark Spinelli's user avatar
1 vote
1 answer
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How does the uncomputation step work in the Grover-Rudolph scheme to prepare $\sum_i\sqrt{p_i}|i\rangle$?

In https://arxiv.org/abs/quant-ph/0208112, the authors discuss a scheme to, given a discrete probability distribution $\mathbf p\equiv (p_i)_i$, under some assumptions on $\mathbf p$, prepare the ...
glS's user avatar
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9 votes
2 answers
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What is the role of entanglement in quantum-computational speed-up?

The way I see it, there are three main quantum properties utilized in quantum computing - superposition, quantum interference, and quantum entanglement. I'm looking to understand which one is ...
Ognyan Tsvetkov's user avatar
9 votes
3 answers
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Does conditional gate collapse controller's superposition?

I've created a simple circuit in Q-Kit to understand conditional gates and outputted states on each step: In the beginning there is clear 00 state, which is the input The first qubit is passed ...
CodeSandwich's user avatar
9 votes
1 answer
657 views

How to distinguish between collapsed and uncertain qubits in a quantum circuit?

I have been through the Young's double slit experiment. It's a direct proof or instance of showing that a wave is collapsed via observation or measurement, and shows no interference patterns. I want ...
Sayan Dey's user avatar
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7 votes
1 answer
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How does the CNOT gate operate when the control qubit is a superposition?

If a control qubit is in superposition, how it will affect target qubit if it is collapsed or in superposition? Is it true that CNOT works only if the control bit collapsed to 1? Also, is it possible ...
Olexander Korenyuk's user avatar
5 votes
1 answer
251 views

Is it possible to tune the amplitude of superposition generated by Hadamard gates?

I had a question earlier about generating the superposition of all the possible states: Here. In that case, we could apply $H^{\otimes n}$ to the state $|0\rangle^{\otimes n}$, and each state has the ...
ZR-'s user avatar
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4 votes
1 answer
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Implementing state which is a superposition of unitaries applied to the same reference

I was wondering if there is exists an (efficient) way to implement the state $$|\Psi\rangle=\left(\sum_i^N c_i|{\psi_i}\rangle\right)=\left(\sum_i^N c_i\hat U_i\right)|{0.....0}\rangle$$ where $\hat{U}...
cheetah's user avatar
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3 votes
1 answer
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In the hidden subgroup problem for finite Abelian groups, where does the state $\frac{1}{\sqrt{|G|}}\sum_{g\in G} |g,0\rangle$ come from?

I am new to the concept of HSP. Previously, I saw how to solve hidden subgroup problem over $\mathbb{Z}_2^n$, which was Simon's algorithm. Over there the first step was to apply $H^{\otimes n}$, which ...
roydiptajit's user avatar
3 votes
1 answer
271 views

Quantum adder of two states that are themselves superpositions

I have two states $|a\rangle = \frac{1}{\sqrt N}\sum_{i=0}^{N-1}|i\rangle|a_i\rangle$ and $|b\rangle = \frac{1}{\sqrt N}\sum_{j=0}^ {N-1} |j\rangle|b_j\rangle$, with $i,j,a_i,b_j \in \mathbb{N}$. I ...
Paulske's user avatar
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1 vote
1 answer
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How to create a electron in a superpositon?

I am trying to understand how are qubits created and implemented in real life. I was unable to find much information about how electrons are kept or sent into a superposition of our wish which is of ...
D Star Let's Explore's user avatar
1 vote
1 answer
506 views

Does a CNOT quantum gate violate no cloning theorem? [duplicate]

I am a curious quantum computing learner. :) Once observe the CNOT gate: as you can see there it converts a |+> to |-> in the top or to say in another way it clones the |-> state. So does ...
D Star Let's Explore's user avatar
0 votes
3 answers
246 views

Represent qubit in a superposition [closed]

How do we represent a qubit $\vert 1 \rangle$ and put in a superposition (in dirac)?
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