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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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 ...
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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 ...
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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 ...
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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 ...
glS♦
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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 ...
glS♦
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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♦
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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 $\...
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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....
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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 ...
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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 ...
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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 ......
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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 $U_P$ ...
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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 ...
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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 ...
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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 ...
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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:
...
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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 ...
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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 ...
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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 ...
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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 $|+ \...
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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 $|\...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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, ...
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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://...
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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}{\...
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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 ...
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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}\...
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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 ...
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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:
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Given a quantum state, can you generate a uniform superposition over its computational basis vectors with nonzero amplitude?
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 ...
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Why use superpositions to write states even when they are not entangled?
I am reading book "Dancing with Qubits. How quantum computing works". I had learned the rule of entangled state: when quantum state is separable(i.e. it can be written as such a tensor ...
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Can you construct a 3-qubit XOR state?
I'm wondering if it is possible to build a 3-qubit quantum circuit that creates the following pure state: $$\frac{1}{2}\left(|000\rangle+|011\rangle+|101\rangle+|110\rangle\right)=\frac{1}{2}\left[1,0,...
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Does quantum superposition allow to apply an algorithm to all bits possibly in one shot?
From what I understood, quantum programming can solve some algorithm exponentially faster.
Thanks to the superposition, unlike a classic bit, which can be either 0 or 1, a qubit can be both 0 and 1.
...
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How does superposition in a quantum register work?
When I put each single qubit within a quantum register using Hadamard gates in superposition, how does it work that the whole register quantum-state is in superposition?
On the math-level the register-...
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Surface Code Eigenstates as Circles
I learned that logical $|0\rangle$ of surface code, is an eigenstate, where all stabilizers are +1 value, and since the z-stabilizer is enforcing an even amount of edged in each node, and the x-stab ...
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How to obtain the state $|0\rangle+|1\rangle$ from $|0\rangle$ via Pauli gates?
Could somebody explain in which way are we able to achieve superposition with Pauli $X$, $Y$, $Z$ matrices? In case of Hadamard gate $H$ we change coefficients to $1/\sqrt{2}$ directly, in case of $X$ ...
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Understanding phase kickback caused by the CNOT gate
Applying the CNOT gate to the state |+-⟩ would result in the state |--⟩ as per:
What has occurred is a "phase kickback". The relative negative phase from the target qubit has transferred to ...
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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) ...
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