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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118 views

How to derive $|0\rangle=\frac{1}{\sqrt{2}}(|+\rangle+|-\rangle)$?

When learning measurement basis, my teacher told us $|0\rangle=\frac{1}{\sqrt{2}}(|+\rangle+|-\rangle)$ and said that we can derive it ourselves. Along this, he also mentioned $|+\rangle=\frac{1}{\...
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How does superposition apply to quantum computing?

beginner here. I've always heard explanations on quantum computing, all about superposition, entanglement, etc. But how does superposition actually apply to quantum computing? Yeah, its "in ...
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What is the Schmidt decomposition for the 00 + 01 state?

If I try to write the two-qubit state $$ |\psi \rangle = \frac{|0 \rangle |0 \rangle + |0 \rangle |1 \rangle}{\sqrt{2}}$$ as $$ |\psi \rangle = \lambda_0 |\phi_0 \rangle |\phi_0 \rangle + \lambda_1 |\...
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How can one evaluation of $U_f$ in Grover's algorithm use only one query of $f$?

I am very much new to quantum computation and do not have a background in quantum mechanics, which I believe is at the root of my confusion around Grover's algorithm. Suppose that we have a search ...
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1answer
28 views

Gate Cost to Transform Superposition of Hamming weight 1 states to superposition of arbitrary basis states?

Say you have something like a general-coefficient $n$-qubit W-state, i.e., $$ |\psi\rangle\equiv\sum_{j=1}^n a_j X_{j}|0\rangle^{\otimes n} \ , $$ where $a_j$ are normalized complex coefficients. ...
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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 ...
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When writing data into qRAM, can I do it in a superposition state?

In general, quantum algorithms are said to be hybrid algorithms. Especially when storing data in qRAM, it seems to be done through classical calculations. Is it possible to write this part directly to ...
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Does Toffoli AND conjugate affect superposition if used in Shor's algorithm?

I have come across several papers that use Toffoli AND conjugate to minimize the T-depth. But since it contains a measurement, does it affect Shor's algorithm (in terms of interference, entanglement, ...
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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 ...
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How to read a Q sphere representation?

I'm trying to understand the Q-sphere representation of a 3-qubit system. I get that the 3-qubits are in a superposition of 2 different states. The first qubit (rightmost) is in a superposition of <...
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How to get a qubit into superposition?

I have a qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\right> + (\beta_1 + i\beta_2 )\left|1\right>$$ so if i give values $\alpha_1 + i\alpha_2 = 1 + 4i$ and $\beta_1 + i\...
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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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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 to describe the state of a qubit passing through two Hadamard gates? [duplicate]

Describe the state of the qubit at points A, B and C. How does this demonstrate that we need the “ket” (or the vector) representation of qubits, rather than just describing them in terms of ...
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What's the point of a measurement operator? [duplicate]

I was experimenting with quantum circuits in IBM Quantum Experience. I know that the Hadamard gate creates superposition in the qubit, so I created the following circuit: However, when I looked at ...
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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 ...
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How instantaneous is state preparation in a quantum register, if all possible superpositions are to be initialized equally?

Before the start of a quantum algorithm qubits need to be initialized into a quantum register. How fast can a quantum register of length $n$ be initialized in a way that all possible superpositions of ...
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1answer
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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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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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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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Can I switch $\alpha_0$ and $\alpha_1$ conditionally to $\alpha_0>0$ in a state $\alpha_0|0\rangle+\alpha_1|1\rangle$?

I have a single qubit $a$ in state $$ |s\rangle = \alpha_0|0\rangle + \alpha_1|1\rangle $$ $\alpha_0$ may be 0 whereas $\alpha_1$ is always positive and above $0$. Almost always $$\alpha_0 << \...
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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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1answer
138 views

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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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 satisfy $a^2 + b^2 = 1$. Classical bit one can be represented as $(0, 1)$ and bit zero can be represented as $(1, ...
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Do any two distinct pure states form a basis?

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}$ In ...
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Why don't I get what I expect when measuring with respect to a different basis?

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}$ If ...
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Is a qubit always in superposition?

I am introduced to ancilla qubits which are usually initialized to $\vert 0 \rangle$. It seems that an ancilla qubit is equivalent to the $0$ bit in classical computing as it will evaluate to $\vert 0 ...
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3answers
118 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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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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1answer
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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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2answers
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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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1answer
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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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1answer
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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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1answer
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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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1answer
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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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1answer
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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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Summation of amplitudes [duplicate]

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 = \...
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Reinforcement learning with a quantum agent [closed]

Is it an open question whether we can do reinforcement learning where the quantum agent is not present in the environment, that is, doesn't contribute noise to the environment? In a classical ...
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2answers
567 views

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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2answers
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How can I invert the least significant bit of a certain term of a superposed state?

Say I have $$\dfrac{1}{\sqrt{2}}\bigl(|1\rangle|221\rangle|0\rangle + |3\rangle|73\rangle|2\rangle\bigr).$$ How can I change that into $$\dfrac{1}{\sqrt{2}}\bigl(|1\rangle|221\rangle|1\rangle + |...