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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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### Is a quantum while-loop possible?

I was wondering if it's theoretically possible to have a while loop that runs a bit like this: You initialize a set of qbits with the H-gate. You perform a set of operations on them. You check the ...
1 vote
121 views

### 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 ...
43 views

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

I am following this video 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 circuit) - doesn't that mean that the qubits ...
127 views

1 vote
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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: ...
60 views

### 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 $x \ne y$....
82 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 ...
293 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 ...
224 views

### 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 ...
1 vote
80 views

### 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 ...
870 views

### 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 ...
326 views

### 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
84 views

### 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 ...
1 vote
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. ...
222 views

### 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
46 views

### 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 ...
466 views

### 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 ...
1 vote
124 views

### 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 ...
66 views

### 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
200 views

### 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 ...
26 views

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 ...
1 vote
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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 ...
1 vote
745 views

### 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 ...
461 views

### 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 ...
599 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: ...