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) ...
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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 ...
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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 $4$ ...
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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
$$\frac{1}{\sqrt{...
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Forming states of the form $\sqrt{p}\vert 0\rangle+\sqrt{1-p}\vert 1\rangle$
I'm curious about how to form arbitrary-sized uniform superpositions, i.e.,
$$\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 ...
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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♦
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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 ...
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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\...
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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♦
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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 ...
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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 ...
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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 ...
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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 ...
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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}...
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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 ...
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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 ...
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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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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 ...
