A computation model which relies on quantum-mechanic phenomena, such as entanglement and superposition. This generalizes the probabilistic model of computation.
Questions tagged [quantum-computing]
263 questions
43
votes
6 answers
Why and how is a quantum computer faster than a regular computer?
I'm currently reading a book (and a lot of wikipedia) about quantum physics and I've yet to understand how a quantum computer can be faster than the computers we have today.
How can a quantum computer solve a problem in sub-exponential time that a…
Tom
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19
votes
6 answers
Is Quantum Computer analog?
We used to have analog computers several decades ago. Modern days computers are Digital. What about Quantum computers? Is it analog or digital? I am asking this since qubit can be many things at the same time.
gpuguy
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10
votes
2 answers
Applying a multi qubit quantum gate to specific qubits
A controlled not gate matrix looks like this:
$$\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
\end{bmatrix}$$
That works great when you only have two qubits and you want to use the first qubit as the control,…
Alan Wolfe
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9
votes
3 answers
How to apply a 1-qubit gate to a single qubit from an entangled pair?
Reading about superdense coding I came upon a calculation I can not understand.
We have an EPR entangled pair of qubits $\frac{1}{\sqrt2}(|00\rangle + |11\rangle)$ and we want to apply a Pauli X gate to the first of the entangled qubits. On…
3yakuya
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7
votes
1 answer
What happens to multi-qubit quantum state after one of qubits is measured?
If we have a quantum state consisting of (let's say) 3 entangled qubits and we read the value of one of them, what happens to the probabilities of the remaining possible states?
For example, if we have three entangled qubits and have an amplitude…
3yakuya
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6
votes
1 answer
Does the order in which qubits are measured matter in quantum computing?
I’ll define my question more specifically:
Lets suppose we have an $n$ bit quantum computer, with qubits labelled $q_{1},…,q_{n}$, and let $b$ be any bit string of length $n$ (let’s assume we’ve labelled each qubits’ states $0$ and $1$ so that we…
Alex Michael
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6
votes
1 answer
Does a Hadamard Gate have uses outside of pure and evenly mixed states?
The standard usage cases for the Hadamard gate seem to be passing a pure $|0\rangle$ or $|1\rangle$ state in to get an even amplitude (probability) mixed state which has either matching or mismatching phase.
The other use of course, is to take such…
Alan Wolfe
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4
votes
1 answer
what’s wrong with this quantum key distribution scheme?
I’m reading about the BB84 quantum key distribution scheme, and I’m surprised that it’s conceptually more complicated than seems necessary to me. What’s wrong with this conceptually simpler scheme?
Alice chooses two random strings $x,y \in \{…
user56834
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4
votes
1 answer
Showing that Hadamard is its own inverse
Im trying to work out that a Hadamard transform H (a unitary matrix) is its own inverse by applying it twice to an arbitrary state $|x⟩$:
$$H|x⟩ = \frac{1}{\sqrt{2^n}}\sum_{y \in \{0,1\}^n}(-1)^{x \cdot…
Mal
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4
votes
1 answer
Tensor Product in Quantum Computation
I can not understand the following equality $$\langle ij|(|0\rangle \langle 0|\otimes I)kl \rangle= \langle i|0\rangle \langle 0|k \rangle \langle j|I|l \rangle?$$
Also to estimate phase $\phi$ in Nielsen & Chuang book, I can not understand why…
user12290
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4
votes
2 answers
Hadamard gate on entangled qubit
TL;DR: If you have two entangled qubits in the state $|00\rangle + |11\rangle$, what is the result of applying the Hadamard gate on the second qubit, and why?
I am trying to understand $\text{PSPACE} \subseteq \text{QIP}(3)$ (Watrous, 2003), and…
Winks
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4
votes
1 answer
Does entangling 100 qubits require a 2^100 X 2^100 Hadamard gate?
Suppose I have 100 qubits that I want to entangle and put into superposition. To do so I construct a Hadamard gate to do this. By definition, the Hadamard is going to be a 2^100 X 2^100 matrix - which is huge.
How does one go about actually…
C Shreve
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4
votes
1 answer
Controlled NOT gate a type of measurement?
I'm trying to understand the theory of quantum computing, and I'm a bit confused on a particular circuit:
Would the controlled NOT gate be a type of measurement, causing Q1 to be either |0> or |1>, or would the circuit be in a superposition of the…
Sam Kennedy
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3
votes
1 answer
What would remain of Quantum Computing if quantum states were real numbers?
This question is motivated by my attempt to understand quantum computing and the source of its computational power.
Quantum statest are described by complex numbers. That is, 1 qubit is described by 2 complex numbers, one for each state (actually 1…
user56834
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3
votes
1 answer
Shor's algorithm and offset elimination
I am wondering if the second Quantum Fourier Transform (QFT) in Shor's algorithm is necessary. I am probably missing a point but it seems that an offset elimination function would suffice to determine the period?
QFT eliminates the offset value and…
acevik
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