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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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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(Quantum Computing/Machine Learning) Estimate of the absolute value of the probability amplitude of |0⟩ in the superposition?

You are given a source of an unknown qubit state. You make measurements in the computational basis, that is, your measurement is $\{|0\rangle \langle0|,|1\rangle \langle 1|\}$. You observe that you ...
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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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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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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 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 + |...
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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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How to read Dirac notation (without algebra)?

I have no idea how to read Dirac notation. $$\left|↑↑ \right\rangle \tag{1}$$ $$\left|↑↓\right\rangle+\left|↓↑\right\rangle \tag{2}$$ $$\left|↑↓\right\rangle-\left|↓↑\right\rangle \tag{3}$$ $$\left|↓...
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How to prepare a superposed state where its terms are elements of a sequence?

Define the recursive sequence $x_{i+1} = x_0 x_i \mod 21$, where $x_0 = 2$, and hence $x_1 = x_0 x_0 = 4$, and so on, generating the sequence $[2, 4, 8, 16, 11, 1]$, where the brackets mean it cycles ...
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Is qubit superposition a basis-dependent concept?

The qubit $a\left|0\right>+b\left|1\right>$ is a superposition w.r.t. the basis $\left\lbrace\left|0\right>,\, \left|1\right>\right\rbrace$ because it may collapse to $\left|0\right>$ ...
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What is the post measurement state given an input and the outcome measurement?

Given a two-qubit state of equal superposition, what is the post-measurement state (should be the same number of qubits that have changed as a result of the measurement) on one of the two qubits and ...
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CNOT gate - control qubit is in 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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How to prepare a superposed states of odd integers from $1$ to $\sqrt{N}$?

$\newcommand{\q}[2]{\langle #1 | #2 \rangle} \newcommand{\qr}[1]{|#1\rangle} \newcommand{\ql}[1]{\langle #1|} \newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} \newcommand{\round}[1]{\left\lfloor #...
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How to properly write the action of a quantum gate implementing an operator $U$ on the superposition of its eigenvectors?

Let's say, that we are in the possession of a quantum gate, that is implementing the action of such an operator $$ \hat{U}|u \rangle = e^{2 \pi i \phi}|u\rangle $$ Moreover, let's say, that this ...
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What's the meaning of applying $U_{\text{div}}$ to a register in superposition?

$\newcommand{\qr}[1]{|#1\rangle}$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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Advantange 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 ...
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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 ...
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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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How to obtain arbitrary distribution in quantum database

I was working on the Grover's algorithm and the most common example is for a unitary distribution in a quantum database, for example: $|\psi\rangle = \frac{1}{2}|00\rangle + \frac{1}{2}|01\rangle + \...
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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) ...