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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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How does Grover's operator work - specifically applying the H gate in the operator

I am following this video (https://www.youtube.com/watch?v=0RPFWZj7Jm0) and the professor applies an H gate at the start of the reflection operator (one H gate was applied at the beginning of the main ...
Colin Benaissa's user avatar
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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
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How to create the state $(n!)^{-\frac{1}{2}} \sum_{\pi \in S_n} | \pi, \pi (G) \rangle$ when $G$ is an undirected graph and $\pi$ a permutation

Let $G=([n],E)$ be an undirected graph, which is represented by a $n \choose 2$ bit string, by indicating for each $i < j$ if $(i,j) \in E$. We also denote the state $| G \rangle$ as the $n \choose ...
Gabi G's user avatar
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How can a third party learn the coefficient of a shared $2n$-qubits state using a classical message from each one?

Suppose Alice and Bob share the $2n$-qubits state $$|\phi _{x,y,b} \rangle = \frac{1}{2}(|x\rangle + (-1)^b |y\rangle)$$ where $x,y$ are $2n$-length strings of $0$ and $1$, $b$ is a bit, and $x \ne y$....
Gabi G's user avatar
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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
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is a mixed states really a statistical mixture?

$\DeclareMathOperator{\Tr}{Tr}\newcommand{\ket}[1]{|#1\rangle}\newcommand{\bra}[1]{\langle#1|}$Let consider the pure state $$ \ket{\psi_{1}}=\dfrac{\ket{0}+\ket{1}}{\sqrt{2}} $$ whose density matrix ...
yosh's user avatar
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How many times the circuit need to run when i use get_stateVector in qiskit

In qiskit,i use get_statevector method to get the statevector from my circuit. What i want to know is how many times the circuit need to run. Does is it only one? ...
qin guang's user avatar
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How to create a electron in a superpositon?

I am trying to understand how are qubits created and implemented in real life. I was unable to find much information about how electrons are kept or sent into a superposition of our wish which is of ...
D Star Let's Explore's user avatar
2 votes
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What is qubit decoherence?

If I have understood correctly, in time a single qubit in superposition will collapse on it's own to the $|0\rangle$ or $|1\rangle$ state, but I thought it only collapsed when measured. How is the ...
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CNOT gate effect on 2 qubits

If the CNOT gate applies a NOT on the target qubit if the control qubit is a 1 and the control qubit was in superposition (for example in the $|+\rangle$ state), wouldn't this break the superposition ...
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Can quantum superposition be thought of as a quantized version of classical bits?

A classical bit is represented by either 0 or 1. However a superposition state is combination of 0 and 1 both with some probability ($|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$). Does it mean that ...
Arnab Chatterjee's user avatar
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What happens if I superimpose my quantum computer?

Background So here's a question I had. Let's say I have a quantum mechanical system which obeys the Schrodinger equation. $$ \hat H \psi = \hat T \psi + \hat V \psi $$ where $\hat H$ is the ...
More Anonymous's user avatar
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Are equiprobable state same as superposition state

How qc.h(0) qc.h(1) helps quantum circuit qc=QuantumCircuit(2) to put the given qubits in a equiprobable states? Are ...
Khilesh Chauhan's user avatar
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What's an example of a superposition $\sum_i \sqrt{p_i}|i\rangle$ that cannot be prepared efficiently?

As also discussed in (How does the induction step in the Grover-Rudolph scheme to prepare superpositions from probabilities work? and How does the uncomputation step work in the Grover-Rudolph scheme ...
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How does the uncomputation step work in the Grover-Rudolph scheme to prepare $\sum_i\sqrt{p_i}|i\rangle$?

In https://arxiv.org/abs/quant-ph/0208112, the authors discuss a scheme to, given a discrete probability distribution $\mathbf p\equiv (p_i)_i$, under some assumptions on $\mathbf p$, prepare the ...
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How does the induction step in the Grover-Rudolph scheme to prepare superpositions from probabilities work?

In https://arxiv.org/abs/quant-ph/0208112, the authors discuss a scheme to, given a discrete probability distribution $\mathbf p\equiv (p_i)_i$, under some assumptions on $\mathbf p$, prepare the ...
glS's user avatar
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Superposition of circuits (d-level case)

In this post: Superposition of quantum circuits, the two states are qubits. Is it possible to generalize this question to two qudit case? ie, given quantum circuits $C_1$ and $C_2$ that generates $\...
Irene's user avatar
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Quantum Computer Basics [closed]

I am a newbie to Quantum Computing world. My collage professor asked me to do presentation on quantum computing. I have read many articles online but still I think I am not satisfied with what I found....
Poojan Solanki's user avatar
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Does Rx(θ) applied on pure states create superposition?

I'm struggling to find if $\text{Rx}(\theta)$ gate would convert a pure state qubit $|0\rangle$ to a superposition $\cos( \theta) |0\rangle + \sin(\theta) |1\rangle$. A definitive answer with ...
user1587566's user avatar
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Are entanglement and superposition necessary and sufficient for quantum universality?

A set of quantum gates is universal when it can approximate any unitary operation with arbitrary precision. These unitary operations are used in quantum algorithms, in a general sense, manipulating ...
grav.field's user avatar
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How to "eliminate" some components of the state vector?

I have $n*k$ qubits. At the very beginning the length of the state vector is $2^{nk}$. After some manipulations (Qiskit circuit) I reduce it to $k^n$ and it looks like $a|1...\rangle +a|0...\rangle ......
Maurice Clerc's user avatar
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Given a unitary $U_p:|0\rangle\to\sum_\omega\sqrt{P(\omega)}|\omega\rangle$, what does $|0\rangle$ represent exactly?

Consider a random variable $X$ on a probability space $(\Omega, 2^\Omega, P)$. Let $H_\Omega$ be a Hilbert space with basis states ${| \omega \rangle}_{\omega \in \Omega}$, and fix a unitary $U_P$ ...
Simon's user avatar
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Why are we only interested in the linear combination $|\phi\rangle = a |0\rangle + b |1\rangle$?

They say superposition enables qubit to live in linear superposition of two states. I.e. \begin{equation} |\phi\rangle = a|0\rangle + b |1\rangle \end{equation} Why are we interested only in linear ...
QuanTUM's user avatar
3 votes
2 answers
995 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
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Question on circuit function evaluation

In this question, from what I understand, the circuit on the right hand side can not be evaluated for f(0) so depending on value of y, we will have two different f(0)s so this equality of circuits ...
Sanjana's user avatar
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SX operator and superposition

I am running some tests using the probabilities we get from statevector to assert values in qiskit. For instance, with two qubits and a hadamard gate on the first one we have: ...
neilson's user avatar
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Can a quantum computer break a hash function?

I was watching this video by veritasium, https://www.youtube.com/watch?v=-UrdExQW0cs I'm curious on whether or not a quantum computer could break a hash function. I'm not really sure how hash ...
Carson Ouckama's user avatar
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How can I produce the state $\frac{1}{\sqrt{2}^N} (|1,0^{N-1}\rangle + |01,0^{N-2}\rangle + ...+|0^{N-1},1\rangle)$ [duplicate]

Let's say my algorithm starts with the qubit state $|0^N\rangle$. Is there a possibility to end up in a superposition where every component is made of a bitstring containing exactly an $1$ at on ...
kerf's user avatar
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8 votes
5 answers
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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 ...
Rydberg's user avatar
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Understanding the Hadamard gate and what is meant by qubits [duplicate]

I'm trying to understand the Qiskit documentation in order to see if there are differences in notation from my quantum mechanics lecture notes. The Hadamard Gate transforms $ |0 \rangle$ into $|+ \...
bsaoptima's user avatar
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Can qubit ever be in non-superposition state other than the instance its measured?

For a qubit to be in "actual state" $\psi=\alpha_0|0\rangle+\alpha_1|1\rangle$ cannot be viewed as the qubit is either in $|0\rangle$ or $|1\rangle$ with probability of $|\alpha_0|^2$ or $|\...
AjaiS's user avatar
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2 votes
1 answer
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Implementation of quantum Hadamard gate using electron spins?

The Hadamard gate performs the following operation on an incoming electron spin: What is a realistic laboratory way of implementing a Hadamard gate that will change a known electron spin into one ...
James's user avatar
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How does QPE work if target register is in superposition of eigenstates?

In regular Quantum Phase Estimation algorithm the target register shall be in the eigenstate of the investigated operator. If it's the case, then applying controlled operator $U$ we can get its phase ...
EugeneB's user avatar
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230 views

Can you construct a quantum circuit where all qubits are initially in a superposition, but there is still entanglement?

The most basic example of entanglement is when we have 2 qubits, where q0 is in the |+> state and connects to q1 (which is in the |0> state) with a cnot gate: The state is entangled, as the ...
Benedict Bien's user avatar
1 vote
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31 views

Modeling light transfer through every path with superpositioning

So I asked a question about this topic earlier but since then, I did more digging into this problem. Researchers at Berkeley experimented with a theory of photosynthesis happening using Quantum ...
Levent Ozbek's user avatar
1 vote
1 answer
52 views

Store/load superposition state of a qubit into/from classical register

I know this question looks ridiculous. But I simply want to know if possible to store/load a superposition state into classical register from qubit. Specifically two bit of classical register. ...
Muhammad Ikhwan Perwira's user avatar
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2 answers
201 views

Is this state a superposition in the standard basis?

This is a very basic question, but I am wondering how does one determine if the state is in a superposition in the standard basis? What I know is a state is in superposition iff ⍺ and β are both ≠ 0, ...
Dawn's user avatar
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Quantum Algorithm to Solve a Maze

I am trying to understand the paper "Quantum Algorithm to Solve a Maze - Converting the Maze Problem into a Search Problem" by Debabrata Goswami and Niraj Kumar (here the reference https://...
janbo's user avatar
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3 votes
2 answers
108 views

Preparing a superposition state modulo $k$

Consider being given the description of a function $f: \{0, 1\}^n \rightarrow \{0, 1\}^m$ and the binary representation of an integer $k$. Is the state \begin{equation} |\psi_{f, k}\rangle = \frac{1}{\...
Tom Clancy's user avatar
5 votes
1 answer
327 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
22 votes
1 answer
3k views

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
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3 votes
1 answer
282 views

Quantum adder of two states that are themselves superpositions

I have two states $|a\rangle = \frac{1}{\sqrt N}\sum_{i=0}^{N-1}|i\rangle|a_i\rangle$ and $|b\rangle = \frac{1}{\sqrt N}\sum_{j=0}^ {N-1} |j\rangle|b_j\rangle$, with $i,j,a_i,b_j \in \mathbb{N}$. I ...
Paulske's user avatar
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2 votes
3 answers
582 views

CNOT entangling a third qubit and how measurement impacts entanglement

I'm trying to understand entanglement, superposition and the effects of measurement on entangled qubits a bit better. About entanglement: I know that the circuit below will entangle the two qubits: ...
neilson's user avatar
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Why doesn't reading the ancilla qubit in Quantum Error Correction kill entanglement?

In Quantum Error Correction we have ancilla qubits (in gray) that will be entangled with the pair of bits we want to check. Because we don't want to directly measure the "main" qubits (in ...
neilson's user avatar
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QiskitError: 'Sum of amplitudes-squared does not equal one.'

I'm coding a 429 element length string to compare to other same length strings, but I keep getting that error. I used ljust to fill the string to a 512 element ...
LJZB's user avatar
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1 vote
1 answer
459 views

Multiple Hadamard gates Transformation on N qbits

I am newbie to quantum computing and having a bit confusion regarding the action of Hadamard gate on multiple qbits which are already in superposed state (I well understand how it works for qbits ...
aneela's user avatar
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1 answer
511 views

How does a Hadamard gate impact the initial/previous values of a Qubit? [closed]

I've been studying Quantum Computing and one thing that intrigued me is: given a qubit q1 with an initial value x, when I apply a Hadamard gate on it, then it goes to superposition, so the probability ...
neilson's user avatar
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0 answers
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Mark a state if it is part of another register

I am wondering something, especially about Grover algorithm: imagine I have a quantum register $a$ and a quantum register $b$ of equal length. Then, suppose I apply some algorithms on $a$ s.t. it is ...
Asimonu's user avatar
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2 votes
0 answers
49 views

When physically implementing superposition in a Transmon, what is the actual driving amplitude used in the microwave pulses by Qiskit?

I had been playing around with Qiskit Pulse, and I managed to run several single qubit circuits, however throughout these processes, I recurringly came across the driving amplitude and the signal ...
Aniket Chatterjee's user avatar
4 votes
1 answer
292 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