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35 votes
Accepted

An impossible quantum adder claimed by a journal article?

it's from International Journal of Theoretical Physics - reputable journal Consider this paper your lesson in how reliable "reputability" is. Look at Figure 5 from the paper: Specifically ...
Craig Gidney's user avatar
26 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', ...
Mark Spinelli's user avatar
24 votes
Accepted

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 $|\...
Adam Zalcman's user avatar
  • 22.9k
23 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 ...
glS's user avatar
  • 25.4k
21 votes

How accurate is this figure by TIME magazine?

This figure is not accurate at all about quantum computers. This "try-every-case" thing is the standard boilerplate everyone puts in their popsci articles. But it's not at all how quantum ...
Craig Gidney's user avatar
16 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 ...
Jonathan Trousdale's user avatar
13 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 ...
Niel de Beaudrap's user avatar
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} + \...
Niel de Beaudrap's user avatar
11 votes
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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}} \...
AHusain's user avatar
  • 3,653
11 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, ...
Dot's user avatar
  • 111
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 ...
James Wootton's user avatar
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 $|0\rangle$...
Adam Zalcman's user avatar
  • 22.9k
9 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, ...
alanf's user avatar
  • 191
9 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 ...
Māris Ozols's user avatar
9 votes
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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^{\...
KAJ226's user avatar
  • 13.9k
8 votes
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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). ...
DaftWullie's user avatar
  • 58.8k
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\...
Paul Nation's user avatar
  • 2,239
8 votes

How accurate is this figure by TIME magazine?

I might not express the sentiment quite as strongly as some of the other answers. It is attempting to convey something, and what it is saying is not completely untrue, but is certainly skipping over ...
DaftWullie's user avatar
  • 58.8k
8 votes
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Why do we need Entanglement?

Almost every quantum state is entangled$^1$. It is therefore unsurprising that quantum algorithms bump into them every so often. In fact, an attempt to navigate the space of all quantum states without ...
Adam Zalcman's user avatar
  • 22.9k
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.
DaftWullie's user avatar
  • 58.8k
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 $...
kludg's user avatar
  • 3,214
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 $(c_1,c_2)$ ...
glS's user avatar
  • 25.4k
7 votes
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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 ...
KAJ226's user avatar
  • 13.9k
7 votes

What is the role of entanglement in quantum-computational speed-up?

Regarding question 1: I think it's rather difficult to attribute any particular quantum behavior to any one of these properties in isolation. They are all immediate consequences of describing a ...
jecado's user avatar
  • 1,196
7 votes

How accurate is this figure by TIME magazine?

Contrary to the answers by Craig Gidney and by Martin Vesely (the answer by DaftWullie is the most fair so far), nothing in the TIME magazine cartoon is wrong. "It is ultimately either 0 or 1 ...
user1271772 No more free time's user avatar
6 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 ...
Craig Gidney's user avatar
6 votes
Accepted

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 ...
Sam Jaques's user avatar
  • 2,076
6 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\...
Gianni's user avatar
  • 364
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 ...
DaftWullie's user avatar
  • 58.8k
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, $...
auden's user avatar
  • 3,459

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