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)
Questions tagged [superposition]
155 questions
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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 superposition. My first question is, of course,
is this…
Snowshard
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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) probability. However, superpositions seem to be a…
Norrius
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An impossible quantum adder claimed by a journal article?
In Quantum adder of two states that are themselves superpositions, I asked:
I have two states $|a\rangle = \frac{1}{\sqrt N}\sum_{i=0}^{N-1}|i\rangle|a_i\rangle$ and $|b\rangle = \frac{1}{\sqrt N}\sum_{j=0}^ {N-1} |j\rangle|b_j\rangle$,…
Paulske
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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 $4$ measurement results are possible (say,…
weekens
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How can we keep Schrödinger's cat alive?
We know, Schrödinger's cat inside the box is in the equal superposition state of both alive and dead. We can express its state as $$|\text{cat}_\phi\rangle= \frac{|\text{alive}\rangle+e^{i\phi}|\text{dead}\rangle}{\sqrt{2}} \hspace{10mm} \text{where…
Syed Emad Uddin
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Given circuits preparing $|\psi\rangle$ and $|\phi\rangle$, what's a circuit preparing $|\psi\rangle+|\phi\rangle$?
Given a quantum circuit $C_1$ that generates a state $\vert\psi\rangle$ and another circuit $C_2$ that generates $\vert\phi\rangle$, is there a way to construct a circuit that outputs
$$\frac{1}{\sqrt{2}}(\vert \psi\rangle +\vert\phi\rangle)$$
using…
Kolp
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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 through the Hadamard gate, it gets into superposition,…
CodeSandwich
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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 responsible for the exponential speed-up that quantum…
Ognyan Tsvetkov
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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 to do something similar in a quantum circuit, not…
Sayan Dey
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Superposition of quantum gates
In the standard model of quantum computation a gate is a unitary that acts on a subsystem. Physically, it can be implemented by some device. Now, any device is also a part of our quantum world, thus it has a quantum state. This quantum state, in…
Danylo Y
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Advantage of Hadamard gate over rotation about the X axis for creating superpositions
When I look at most circuits (admittedly small sample as I'm a beginner), the Hadamard gate is used a lot to prepare a superposition from say the $\mid0\rangle$ state.
But upon a little reflection, we can prepare a superposition using a…
Ntwali B.
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How accurate is this figure by TIME magazine?
Below is a figure from a TIME magazine edition. I have a few questions regarding this representation of quantum computing:
Is saying "0 and 1 at the same time" a correct statement? Isn't the qubit just in a superposition of both states, not "both…
Rydberg
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Is it right to think of superposition as just angle?
Based on my current understanding, a qubit is represented as a vector $(a, b)$ which satisfies $a^2 + b^2 = 1$. Classical bit one can be represented as $(0, 1)$ and bit zero can be represented as $(1, 0)$.
And then we can have things that cannot be…
Wong Jia Hau
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Summation of amplitudes
I was wondering how to create generalized entangled superpositions of qubits when I came to need of an algorithm to generate the following:
Suppose we have two $n$ qubit states, $$|\psi\rangle = \sum_X \alpha_X\ |X\rangle$$
and, $$|\phi\rangle =…
kichapps
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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 use the inverse of such a circuit to produce…
Sam Jaques
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