24 votes

Effects of quantum computing on parallel universes

Regarding your first question, you are essentially asking about the validity of a position taken by David Deutsch - a founder of quantum computing! For example, in his book 'The Fabric of Reality', ...
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22 votes
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How can we keep Schrödinger's cat alive?

TL;DR: This is probably going to be disappointing. If a cat enters a superposition and we lose track of the relative phase $\phi$ then there is only one deterministic operation that returns to the $|\...
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18 votes
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What is the difference between superpositions and mixed states?

No, a superposition of two different states is a completely different beast than a mixture of the same states. While it may appear from your example that $\rho_1$ and $\rho_2$ produce the same ...
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15 votes
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Effects of quantum computing on parallel universes

Question 1 This description lies somewhere between the two extremes of a theory and mysticism, depending on how amiable one is to the concept. David Deutsch is vocal proponent of the former, Lee ...
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12 votes

How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Here is how you might go about designing such a circuit.$\def\ket#1{\lvert#1\rangle}$ Suppose that you would like to produce the state $\ket{\psi} = \tfrac{1}{\sqrt 3} \bigl( \ket{00} + \ket{01} + \...
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11 votes

What is the difference between superpositions and mixed states?

The short answer is that there is more to quantum information than "uncertainty". This is because there is more than one way to measure a state; and that is because there is more than one basis in ...
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11 votes

How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

I'll tell you how to create any two qubit pure state you might ever be interested in. Hopefully you can use it to generate the state you want. Using a single qubit rotation followed by a cnot, it is ...
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How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Break the problem in parts. Say we have already sent $\mid 00 \rangle$ to $\frac{1}{\sqrt{3}} \mid 00 \rangle + \frac{\sqrt{2}}{\sqrt{3}}\mid 01 \rangle$. We can send that to $\frac{1}{\sqrt{3}} \...
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10 votes
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How to distinguish between collapsed and uncertain qubits in a quantum circuit?

Consider a quantum circuit on one qubit initialized in the state $|0\rangle$ and consisting of two Hadamard gates where we can insert a measurement between the Hadamards. The input state is $|0\rangle$...
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9 votes

What is the difference between superpositions and mixed states?

Along with glS' post: A mixed state would be if you had a can of paint, but you weren't sure if it was blue or yellow. You know it is either one of the two, and once you pop the top and measure it, ...
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Is there a way to create a superposition of all the possible states?

Do you mean mapping the state $|0\rangle^{\otimes n} \to \dfrac{1}{\sqrt{2^n}}\sum_{i=0}^{2^n-1} |i\rangle $ ? If that is the case then you can just apply $H^{\otimes n}$ to the state $|0\rangle^{\...
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8 votes

Effects of quantum computing on parallel universes

In the many worlds interpretation (MWI) reality consists of a structure called the multiverse that looks like a collection of slightly interacting parallel universes in some circumstances: Deutsch, ...
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8 votes

Is a qubit always in superposition?

Superposition is a basis dependent concept. Namely the $|0\rangle$ and $|1\rangle$ states are commonly said not to be superposition states exactly because one of the two coefficients in the $\{|0\...
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Advantage of Hadamard gate over rotation about the X axis for creating superpositions

It's mostly about simplicity and adopted convention. In the end, this is basically the same question as "why should I pick a universal set of gates A rather than a universal set B?" (see here). ...
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7 votes
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How to superpose two composite qubit states?

Depending on what precisely your assumptions are about a, b, I think this is essentially impossible, and is something called the "no superposing theorem". Please see this paper.
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7 votes
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Can Toffoli operate on a qubit in superposition?

Control qubit can be in superposition, why not? This is how entangled qubits are created. But the circuit you have drawn does not entangle qubits, it actually does not change qubit states at all, and $...
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7 votes

Is it right to think of superposition as just angle?

That's not too far from the truth. You can always describe the probabilities of a two-outcome event like that: you have $p_1+p_2=1$ and thus defining $c_i\equiv\sqrt{p_i}$ you observe that $(c_1,c_2)$ ...
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7 votes

Superposition of quantum circuits

As Davit Khachatryan's answer points out, the task is impossible / ill-defined, since the desired target state is generally not normalized and it depends on the relative global phases of the two ...
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Does a CNOT quantum gate violate no cloning theorem?

Cloning means you have a unitary transforming $U$ that takes $|\psi\rangle|0\rangle $ to the $|\psi\rangle|\psi \rangle $ for all quantum states $|\psi\rangle$. That is, $$ U\big(|\psi\rangle|0\rangle ...
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6 votes
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How to read Dirac notation (without algebra)?

The dirac notation itself, the $|$ and $\rangle$ parts is simply a notation to remind you that you're dealing with quantum states. What you write inside this `ket' is completely arbitrary. In the ...
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6 votes
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Why do we use the quantum superposition for a period instead of factors in Shor's algorithm?

A QFT can't arbitrarily raise the probability of any state you want to any value you want. Once you create a superposition, you need to find some way to make destructive interference occur between the ...
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6 votes

How do 2 Hadamard gates act on a single qubit?

If you apply the same gate twice on a state $|\psi\rangle$ you will get out the state $|\psi\rangle$ if the hermitian of the gate is the same as the gate. In your case, you applied the Hadamard gate, $...
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6 votes

Is it right to think of superposition as just angle?

What you have described is a probabilistic bit, and is interesting in its own right, but not 'equal' to a proper quantum bit. A quick search gives for instance this talk (which I have not seen myself)....
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6 votes
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Can a single qutrit in superposition be considered entangled?

To talk about entanglement, you have to first identify subsystems. In your $d=4$ example, you defined an isomorphism $\mathbb{C}^4\simeq \mathbb{C}^2\otimes\mathbb{C}^2$ via the identification of ...
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6 votes
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How instantaneous is state preparation in a quantum register, if all possible superpositions are to be initialized equally?

We know that giving a single qubit starting in the state $|0\rangle$, which is a state one can initialize very fast with high fidelity, then we can put it in the superposition state $|\psi \rangle = ...
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5 votes
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How to measure superposition coefficients to determine state?

The idea is to apply a unitary transformation which will map these states to a different pair of orthogonal states which are easy to distinguish by measuring in computational basis. Let's construct a ...
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5 votes
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Forming states of the form $\sqrt{p}\vert 0\rangle+\sqrt{1-p}\vert 1\rangle$

As long as you want to set arbitrary states for a single qubit, like in your example, the solution is straightforward and it makes use of standard 2x2 $R_y$ gate. In there if you set $\theta = 2\...
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5 votes
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How to obtain arbitrary distribution in quantum database

According to this paper, A significant conclusion from this solution is that generically the generalized algorithm also has $O(\sqrt{N/r})$ running time Where 'r' is the number of marked states. ...
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5 votes
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Does conditional gate collapse controller's superposition?

$$ \begin{eqnarray*} \mid 0 0 \rangle &\to& \frac{1}{\sqrt{2}} \mid 0 0 \rangle + \frac{1}{\sqrt{2}} \mid 1 0 \rangle\\ &\to& \frac{1}{\sqrt{2}} \mid 0 0 \rangle + \frac{1}{\sqrt{2}} \...
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5 votes

Advantage of Hadamard gate over rotation about the X axis for creating superpositions

I think the major advantages of the Hadamard gate are "usability" stuff, as opposed to fundamental mathematical stuff. It's just easier to remember and simpler to apply. The Hadamard gate's marix is ...
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