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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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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 ...
Snowshard's user avatar
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31 votes
3 answers
7k views

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) ...
Norrius's user avatar
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22 votes
5 answers
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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 $4$ ...
weekens's user avatar
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22 votes
1 answer
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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}\...
Paulske's user avatar
  • 457
17 votes
1 answer
4k views

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{...
Syed Emad Uddin's user avatar
13 votes
3 answers
992 views

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{...
Kolp's user avatar
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9 votes
2 answers
869 views

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 ...
Ognyan Tsvetkov's user avatar
9 votes
1 answer
657 views

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 ...
Sayan Dey's user avatar
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9 votes
3 answers
883 views

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 ...
CodeSandwich's user avatar
8 votes
5 answers
4k views

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 ...
Rydberg's user avatar
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8 votes
3 answers
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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 ...
Ntwali B.'s user avatar
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8 votes
2 answers
383 views

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, ...
Wong Jia Hau's user avatar
8 votes
4 answers
840 views

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 ...
Danylo Y's user avatar
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7 votes
3 answers
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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 ...
Sam Jaques's user avatar
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7 votes
1 answer
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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 ...
Olexander Korenyuk's user avatar
7 votes
0 answers
56 views

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 = \...
kichapps's user avatar
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6 votes
2 answers
888 views

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 ...
M. Al Jumaily's user avatar
6 votes
4 answers
2k views

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 ...
dhiraj suvarna's user avatar
6 votes
1 answer
121 views

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 + \...
brzepkowski's user avatar
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5 votes
2 answers
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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 ...
linker's user avatar
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5 votes
1 answer
676 views

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 ...
ZR-'s user avatar
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5 votes
3 answers
4k views

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 ...
THALLAPALLI TEJASWINI's user avatar
5 votes
1 answer
376 views

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 ...
M. Al Jumaily's user avatar
5 votes
1 answer
209 views

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 $\left|0\right>$ ...
Shung-Ching's user avatar
5 votes
1 answer
252 views

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 ...
ZR-'s user avatar
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5 votes
1 answer
328 views

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 ...
FSic's user avatar
  • 879
4 votes
2 answers
613 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\...
wang1908's user avatar
4 votes
1 answer
355 views

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 ...
Matthew Giles's user avatar
4 votes
1 answer
396 views

Deutsch's algorithm makes no sense

Here are the 4 classical functions over $1$ bit we're examining, $f(x) = \{0,1\}, x \in\{0,1\}$: identity (balanced) -> $f(x) = x$: \begin{bmatrix}1&0\\0&1\end{bmatrix} negation (balanced) ...
Ognyan Tsvetkov's user avatar
4 votes
1 answer
121 views

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 ...
develarist's user avatar
4 votes
1 answer
244 views

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 ...
Tudor's user avatar
  • 143
4 votes
1 answer
76 views

Can quantum algorithms include conditional jumps/change an instruction pointer?

From what I've seen (in talks for a general physics audience, but I'm not in the field of quantum computing), all or most quantum algorithms are fixed sequences of instructions applied to registers ...
Jim Pivarski's user avatar
4 votes
1 answer
317 views

Are there Clifford gates that preserve some computational basis states while otherwise generating superpositions?

Consider a two-qubit Clifford gate that maps $|00\rangle$ to $|00\rangle$, up to a phase. Can it map at least one of the other computational basis states $|10\rangle, |01\rangle, |11\rangle$ into a ...
user196574's user avatar
4 votes
1 answer
138 views

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}...
cheetah's user avatar
  • 433
4 votes
1 answer
354 views

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 $\vec x=(x_1,x_2, ...,x_n)^T$ ...
beatbrot's user avatar
4 votes
1 answer
283 views

Given a quantum state, can you generate a uniform superposition over its computational basis vectors with nonzero amplitudes?

Given an arbitrary $|\psi\rangle=\sum_{i=0}^n\alpha_i|i\rangle$, $K=\{i\mid \alpha_i\not=0\}$, and $k=\vert K\vert$, is it possible to generate the state $\frac{1}{\sqrt k}\sum_{i\in K}|i\rangle$? I ...
FlamtapShuckle's user avatar
4 votes
1 answer
119 views

If 3 polarizer experiment to teach quantum superposition can be explained classically, should it not be used to explain Quantum Mechanics?

Here is the link to the Dirac's three polarizer experiment. https://www.informationphilosopher.com/solutions/experiments/dirac_3-polarizers/ When a 90$^o$ and 0$^o$ polarizers are placed in front of ...
Chetan Waghela's user avatar
4 votes
1 answer
139 views

What does it mean to be in a superposition of eigenstates in a LC oscillator?

In superconducting qubits, we use a circuit with a specific type of inductor and quantize the Hamiltonian. Because it's an anharmonic oscillator, we say that it has states -- $|0\rangle$ and $|1\...
snickers_stickers's user avatar
4 votes
1 answer
650 views

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 <...
Van Peer's user avatar
  • 577
4 votes
1 answer
438 views

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: ...
Craig Gidney's user avatar
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4 votes
0 answers
134 views

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 ...
pioneer's user avatar
  • 169
3 votes
5 answers
3k views

The heart of all of quantum physics is superposition

I am going to teach an introductory course on quantum information and I thought about this statement that I want to give at the very beginning. Would you agree on that? From my perspective, every ...
relativeentropy's user avatar
3 votes
2 answers
738 views

Does the X (NOT) gate affect superpositions at all?

Does "NOT" gate have any effect on qubit in superposition state? After applying Hadamard gate on qubit seems like the "NOT" gate doesn't have any effect on it. Could somebody ...
Michael Torston's user avatar
3 votes
3 answers
362 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}{\...
Claire's user avatar
  • 669
3 votes
2 answers
482 views

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 ...
user820789's user avatar
  • 3,302
3 votes
2 answers
984 views

Why do we need Entanglement? [duplicate]

My question is why do we need entanglement at all? If we can hold $n$ bits in superposition, wouldn't we still be able to surpass a supercomputer once we had say over 100-bits? Is it because we need ...
Moo's user avatar
  • 153
3 votes
1 answer
253 views

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 ...
Mark Spinelli's user avatar
3 votes
3 answers
448 views

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 ...
Techmaster21's user avatar
3 votes
3 answers
745 views

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 ...
Woody1193's user avatar
  • 331
3 votes
1 answer
306 views

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|↓...
Logan's user avatar
  • 79