# 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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ...
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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 ...
1 vote
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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 ...
1 vote
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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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### 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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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, ...
1 vote
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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}{\...
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 ...