Questions concerning computations performed on a quantum-computer. DO NOT USE THIS TAG just because the question concerns a computation of a quantum-system!
0
votes
1answer
76 views
how many qubit do we need to store “16”?
classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states
so how this ...
2
votes
0answers
39 views
What is three-photon interference?
Whilst reading this paper on a quantum processor that performs a type of matrix computation, I came across the concept of 'three-photon interference'. A quick Google search shows that this process is ...
7
votes
1answer
96 views
Positivity in the Pauli/Bloch/coherence vector representation
Suppose $\rho$ is an $n$-qubit state and $\vec{x}$ is a vector of coefficients in the Pauli representation (also called the Bloch or coherence vector). That is
$$
x_k = {\rm Tr}(\rho \sigma_k),
$$
...
2
votes
0answers
52 views
Creating matrix Hamiltonian for Feynman's CCNOT
I'm trying to read Quantum Mechanical Computer and to implement the CCNOT logical gate with Mathematica.
Since i wish to use the SWITCH implementation of the CNOT [Fig.8] i've realized that i need to ...
7
votes
1answer
109 views
How are qubits better than classical bit?
WHAT I KNOW:
classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states.
Now ...
0
votes
0answers
38 views
Deutsch-Jozsa algorithm [closed]
How many calls are required to determine is the function balanced or not on the classical computer with probability of error < 50%.
Ref: Deutsch-Jozsa algorithm.
1
vote
2answers
63 views
Qubit projections
Given the qubit:
$$\frac{|0\rangle+i|1\rangle}{\sqrt{2}}$$
What is the corresponding point on the extended complex plane and Bloch sphere?
How to perform calculations and get the point representing ...
0
votes
1answer
60 views
Two qubits problem [closed]
Given the 2 qubit state:
(a/b) |00> + (c/b) |01> + (c/b) |10> + (d/b) |11>
What is the probability that 2 qubits are equal?
Thanks much!
0
votes
0answers
45 views
Constructing a Toffoli gate from CNOT and single-qubit gates [closed]
Toffoli gate in terms of CNOT and single-qubit gates.
Thanks much!
0
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0answers
33 views
The physical implementation of quantum annealing algorithm
From that question about differences between Quantum annealing and simulated annealing, we found (in comments to answer) that physical implementation of quantum annealing exists (D-Wave quantum ...
1
vote
1answer
156 views
I am interested in learning Quantum Computing what should I do? [closed]
I wish to learn about quantum computing which seems to be a topic of hot research and overall just intrigues me. I have a strong background in discrete mathematics and number theory. And am a pretty ...
2
votes
1answer
89 views
Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$?
Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$, where $k$ is the number of "hits" in a total of $N$ possible values for $|\,x\rangle$?
If we know $k$, and know ...
3
votes
1answer
158 views
Studying Feynman articles nowadays
I'm curious to know if it's useful to study Feynman article "Quantum Mechanical Computer" nowadays.
I'm a computer scientist, and i don't know any of the literature in quantum computers. Since long ...
13
votes
3answers
373 views
Does quantum computing rely on particular interpretations of quantum mechanics?
It is my understanding that quantum computing relies on quantum superposition and entanglement to work--qbits must exist in all states simultaneously before giving a particular result when observed.
...
-2
votes
1answer
44 views
2 following gates, inverse circuit
I have a circuit that has 4 wires and 2 following each other Toffoli gates.
The first Toffoli gate occupies 3 wires from above, the following Toffoli gate occupies 3 wires from below.
What will look ...
1
vote
1answer
98 views
2 following gates, permutation matrix
I have a circuit that has 4 wires and 2 following each other Toffoli gates.
I have permutation matrix for each Toffoli gate (A and B).
Do I have to multiply that 2 matrices to get the entire ...
4
votes
0answers
61 views
fixed input qubit state to an arbirary pure state using two variable rotations and one fixed rotation
It is a theorem that any arbitrary unitary transformation in SU(2) can be factored into the following form:
$ O = U_X(\theta) U_Y(\phi) U_X(\delta) $
Where $U_X$ is a Bloch sphere rotation. I ...
9
votes
2answers
307 views
Entropy of a state subject to the action of a set of random unitaries
Suppose that we have a known set of unitaries $U_1,...,U_n$ randomly selected from the Haar measure and suppose that each unitary is applied with probability $\frac{1}{n}$ to some input state $\rho$ ...
10
votes
2answers
487 views
Basic questions in Majorana fermions
Why any fermion can be written as a combination of two Majorana fermions? Is there any physical meaning in it? Why Majorana fermion can be used for topological quantum computation?
0
votes
2answers
99 views
Quantum gate: Phase shift
I dont undestand how to apply a phase shift gate to a qubit. By example how to map $|\psi_0\rangle = \cos (30^\circ) |0\rangle + \sin (30^\circ) |1\rangle$ to $|\psi_1\rangle = \cos(-15^\circ) ...
1
vote
1answer
236 views
Hadamard gates and constructing them
Can anyone explain the process required to make a Hadamard gate that acts on 1st, 2nd and 3rd qbits?
For Hgates acting on the first qubit i realise the matrix is $H=\begin{pmatrix} ...
5
votes
1answer
57 views
Scaling of quantum error correction
I'm having a question regarding quantum error correction.
Using a large number of imperfect (but already very good) quantum gates, it is in theory possible to build an equivalent, error-corrected ...
1
vote
4answers
217 views
Quantum computers: are they possible or impossible?
I know quantum computers are very complicated and my question is is there any way in "Principle" to create one? Are there already quantum computers being created?
2
votes
2answers
494 views
How to apply a Hadamard gate?
How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
0
votes
2answers
134 views
Help on controlled quantum gates?
Obviusly a controlled-not gate is possible, is a not-controlled gate possible?
I need a gate to flip the first qbit and leave the second unchanged, but in literature I have never seen such a gate.
...
3
votes
2answers
190 views
Quantum Teleportation Fidelity
I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% ...
0
votes
0answers
47 views
Finding out resulting state [closed]
Suppose we have two qubits in the state $x|00\rangle+y|11\rangle $.
What is the resulting state of the second qubit in that case? Use and to denote and respectively.
3
votes
1answer
51 views
Reversible gates
Is it possible to make any gate reversible merely by retaining the input bits in the
output and introducing ancilla bits as necessary? That is, given an irreversible
gate with $k$ inputs and $l$ ...
7
votes
1answer
175 views
Computability of physics
As far as I understand a Universal Quantum Simulator can simulate any quantum system and thus anything that exists in the universe. Also, a quantum computer can implement such a quantum simulator. ...
2
votes
2answers
155 views
Constructing a Toffoli gate with 2-and 1-qubit gates?
I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how ...
3
votes
1answer
134 views
Quantum computing problem
Suppose that a qubit is in the state $|\varphi\rangle=a|0\rangle+\sqrt{1-a^2}|1\rangle$, where $a\in[-1,1]$.
If we first perform a standard basis measurement on this qubit and then perform a
...
1
vote
1answer
76 views
Uneven Quantum Measurement
$\newcommand{\ket}[1]{\left| {#1} \right> }$
I have no academic background in physics, but I'm attempting to study quantum computation.
I have read that a quantum system of two qubits is ...
0
votes
0answers
22 views
Finding all marked element by Grover search(not in superposition)
Quantum search enables square-sped up search for marked element. When there are multiple maked element, grover search provides only superposition of them. If I want to find all the marked elements, ...
6
votes
2answers
434 views
Quantum Computing Power Advantages
Currently, the world's fastest supercomputer runs at 17.59 Petaflops, which consumes 9 megawatts of electricity. A qubit-based quantum computer has the potential to operate much more quickly for some ...
2
votes
2answers
114 views
Non-destructive measurement of qbits
Yale news "New qubit control bodes well for future of quantum computing" (Original paper) says:
"The Yale physicists successfully devised a new, non-destructive measurement system for observing, ...
5
votes
3answers
117 views
Controlled-measurement of a quantum register
Given a state vector $\left[\alpha,\beta,\gamma,\delta\right]$ which is not known a priori, does there exist an operation, which I will call "controlled-measurement", which results in the ensemble
...
7
votes
4answers
182 views
If quantum computation is reversible, what is the point of Grover's search algorithm?
Wikipedia et al say the following about Grover's algorithm:
Although the purpose of Grover's algorithm is usually described as
“searching a database”, it may be more accurate to describe it as
...
14
votes
1answer
319 views
If the ground states of interacting QFTs are so complicated, how did Nature find them?
My question was inspired by trying to understand the paper Quantum Algorithms for Quantum Field Theories, by Jordan, Lee, and Preskill. The main result of that paper is that scattering experiments in ...
3
votes
1answer
109 views
Qubit, one or two complex numbers?
I'm currently reading up on quantum computing and it seems like I have found some contradiction about how to represent qubits.
It is often stated that a qubit is represented as $a|0\rangle + ...
1
vote
1answer
110 views
NOT Universal Operator and Computational basis
This is the relationship between density operator and Bloch vector:
$$\rho= \frac{1}{2}({\bf{\hat{1}}}+{\bf{b}}.\boldsymbol{\hat{\sigma}})$$
We define the NOT Universal Operator in the following way:
...
1
vote
1answer
118 views
How is a Qubit in two states under Superposition?
I have read a little about Quantum computing.
From what I understand, Quantum Superposition is when a qubit is in a state $\alpha|0\rangle$ + $\beta|1\rangle$, where $\alpha$ and $\beta$ are ...
3
votes
4answers
264 views
Why is quantum entanglement so important?
Entanglement also allows multiple states to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum ...
0
votes
1answer
101 views
Latest advances in experimental quantum processors?
I'm and undergraduate student and I'm doing a report on Quantum computing. As a conclusion of my report I'd like to highlight the latest experimental advances in Quantum Computing, especially in ...
3
votes
1answer
150 views
What is the basic idea behind how quantum computation is supposed to work?
As far as I know that QM is probability-based and Feynman proposed a quantum computer (QC) as an emulator for fast computation. Reading the introductory articles, I just do not get the essence of the ...
6
votes
1answer
191 views
Why do we want to entangle qubits?
The title is pretty much all I want to ask. Why are qubits entangled? To my knowledge (which isn't that deep) a quantum register can be realized without entangling the qubits.
1
vote
1answer
88 views
Using wavepackets instead of photons in quantum computer
Why does a photonic quantum computer require photons? Why wouldn't wave packets work just as well, better in fact since it would get away from the use of fragile single photons? (Article)
4
votes
1answer
193 views
How many states can a n qubit quantum computer store?
A classical computer composed of '0' or '1' transistors stores $2^n$ states.
Is it true that a quantum computer composed of '0' or '1' or '0 & 1' qubits stores $3^n$ states?
2
votes
4answers
163 views
Computer Science Modeling of Physical World
I am curious what efforts have been made to date to define virtual computer worlds based on the physics we know in the real world?
I think it would be awesome to say start off with an atom defining ...
4
votes
1answer
60 views
Do error checking costs of quantum computing shrink BQP?
BQP is the set of problems solvable in polynomial time for a given error tolerance, and it is suspected to be larger than P (and BPP, which is probably equal to P). However, inability for the gates to ...
3
votes
1answer
121 views
No cloning theorem and exclusive-or (XOR) operator
According to IBM's website,
[...]where we would [classically] have done an assignment (x=y), we instead initialize the target (x=0) and use exclusive or (x^=y).
This sounds like x is a copy ...
