# 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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### Testing superposition states in Q#

I am learning Q# so, as I often do, I am writing some unit tests to play with quantum gates. I was able to write these tests for X gate: ...
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### CNOT in reversible computing and entanglement

We have a classical reversible circuit $U$ implementing a classical boolean function $f: \left\{0, 1\right\}^n \to \left\{0, 1\right\}$, which also takes some $a$ ancilla bits, and has side effect of ...
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### How to create a Quantum circuit to implement the generation of 3-qubit uniform superposition wavefunction

I want to know experimentally or circuit wise diagram to know how to create a circuit that will produce 3-qubit uniform superposition wave function Can somebody help me in that Thank you in advance
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### Which entangled qubit is measured in this example?

Sorry, I am a newbie to quantum computing. I am reading an overview paper (released just a week ago) titled Advances in Quantum Deep Learning: An Overview (Garg & Ramakrishnan, 2020). I am stuck ...
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### Are superpositions of an infinite number of states realizable?

I first encounted this idea in Constructing finite dimensional codes with optical continuous variables where it mentions "superpositions of an infinite number of infinitely squeezed states" in the ...
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### What are the two measurements per box being done in the Bell Tests in the IBM Quantum Experience “Entanglement and Bell tests” Section

I am confused as to what is being measured in the boxes in the example drawings shown on the Entanglement and Bell Tests section in the IBM Q Experience: https://quantum-computing.ibm.com/docs/guide/...
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### Effect of Pauli X gate on minus state using bloch sphere

As I understood, the X gate flips the state around : $X(|0\rangle) = |1\rangle$. It can also be visualized with a $\pi$ rotation around the $x$ axis in the Bloch sphere. I have no problem with that. ...
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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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### Can Toffoli operate on a qubit in superposition?

I understand that CNOT and Toffoli (CCNOT) gates are not universal for quantum computation since they (alone) cannot create superposition. Moreover, it is totally possible to perform a CNOT operation ...
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### What is the diference between classic probabilities and quantum probabilities? [closed]

So, I'm really trying my best to understand how quantum computers work. This is how I think they work: There is a set of qubits; Then an algorithm is put in action by the use of quantum gates that ...
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### Is quantum superposition state a truth or an assumption?

Please, be patient with my question I already read that there is a heuristic that makes superposition a fact of reality. In addition, this superposition, when observed, it has a state of 0 or 1. ...
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### Can quantum parallelism be turned on and off?

The qubit is able to take on multiple states at once, unlike the bit. This property I know is superposition, but is this property perpetual (always on) or optional (controlled to be on or off only ...
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### What does superposition do for quantum probabilistic sampling?

The idea of a qubit being able to exist for several values between 0 and 1 (superposition) makes it sound like it can do alot for probabilistic math problems, but for one task that comes instantly to ...
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### What is the difference between superposition of $|0\rangle$ and superposition of $|1\rangle$ at physical level?

If we apply Hadamard gate 2 times on a qubit $|0\rangle$ then we will get $|0\rangle$. So there must be something else which is unique for both $|1\rangle$ and $|0\rangle$ which is constant even in ...
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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 do quantum states collapse to the right answer?

I am a computer engineer and have recently started understanding quantum computers. I am still struggling to wrap my head around some concepts. One such query is the following - It is said that ...
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### How many combinations can 'n' qubits have?

With $4$ bits there are $2^4=16$ combinations. How many combinations can you have with $4$ qubits (assuming they are all superimposed)? EDIT: As per here, the argument is that if a qubit can hold ...
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### How do 2 Hadamard gates act on a single qubit?

When I perform $2$ Hadamard $H$ gates on a single qubit, why is the probability of getting $0$ as the outcome 100%? Why is it not 50% 0 and 50% 1 instead? Why is the second $H$ gate not putting the ...
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### How to amplify a specific part of the quantum state

I understand that, according to amplitude amplification, I can amplify states according to a partition over the state space. However, suppose I want to amplify or de-amplify a specific portion of the ...
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### How would I construct an Ising Hamiltonian for binary linear programming?

So I am preparing for an exam and stumbled upon this question which I am unable to answer: The problem Binary Integer Linear Programming tries to find a binary vector $\vec x=(x_1,x_2, ...,x_n)^T$ ...
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### Deriving a state vector from a stabilizer state's generators

When I run a stabilizer simulator such as Scott Aaronson's CHP simulator (defined in https://arxiv.org/abs/quant-ph/0406196), one of the possible outputs is a stabilizer table. For example: ...
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### How to implement such a gate where one input bit is zero and the other is one and the output should be one?

I have created 10 qubits, where I have set 2 in superposition by applying Hadamard gate to each of the 2 qubits. So the 2 qubits state can be $|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle$. I ...
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### How to measure superposition coefficients to determine state?

There was a problem at the Winter 2019 Q# codeforces contest (that is now over), which I cannot find a mathematical solution for. The problem goes like this: You are given 3 qubits that can be in one ...
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### Why do we use the quantum superposition for a period instead of factors in Shor's algorithm?

I understand in Shor's algorithm we use quantum computers to find the period of a function which can then be used to find N, and we increase the probability of observing the state with the correct ...
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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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### What's the meaning of applying $U_{\text{div}}$ to a register in superposition?

$\newcommand{\qr}{|#1\rangle}$Say I begin with $10$ q-bits $\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}$ forming a register $B$. Name these q-bits as $b_9, ..., b_2, b_1, b_0$. ...
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### Is there a relation between the factorisation of the joint conditional probability distribution and Bell inequality?

[I'm sorry, I've already posted the same question in the physics community, but I haven't received an answer yet.] I'm approaching the study of Bell's inequalities and I understood the reasoning ...
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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 ...
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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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### Compact encoding of Boolean formula as oracle

As in the title, I have a doubt regarding the implementation of a boolean formula used as an oracle for a quantum algorithm. The problem is that so far I could reproduce the formula as a quantum ...
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 $4$ ...