The quantum-computer tag has no wiki summary.
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Measuring Entangled Qubits
Suppose we have a pair of entangled qubits.
$$
|\psi\rangle = \frac{1}{ \sqrt{2} } ( |00\rangle + |11\rangle )
$$
Now we give one qubit to Alice and other to Bob. Alice measure the her qubit to ...
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CNOT gate output with both inputs in superposition
What is the output of a CNOT gate if both inputs are in superposition?
For example, what happens if:
$\left|x\right>=\alpha_x\left|0\right>+\beta_x\left|1\right>$
and
...
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0answers
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The role of state space composition in quantum computation
In a paper by Richard Josza and Noah Linden they argue that the way state spaces of composite systems are formed is a key aspect in the benefits of quantum computers. In (classical) phase space, two ...
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Is there a well defined quantum-computer architecture? [closed]
Do quantum computers have the same basic architecture as regular computers? D-Wave is selling a commercial quantum computer solution with a 512-qubit processor which is 10 square meters large at ...
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1answer
57 views
Hamiltonian reduction having constant of the motion
I have this $2^n*2^n$ matrix that represent the evolution of a system of $n$ spin.
I know that I can have only one excited spin in my configuration a time.
(eg: 0110 nor 0101 ar not permitted, but ...
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1answer
57 views
Ising spin vs Pauli spin matrices
Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
2
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1answer
196 views
Do quantum computers manufactured by D-Wave Systems, Inc. work? [duplicate]
D-wave claims to have built 128 qbit quantum computers which are commercially available?
What I don't understand is that have they really been able to do this given that the scientific community is ...
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1answer
85 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 ...
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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 ...
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1answer
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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
$$
x_k = {\rm Tr}(\rho \sigma_k),
$$
...
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Creating matrix Hamiltonian for Feynman's CCNOT [closed]
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
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1answer
124 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 ...
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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.
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2answers
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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 ...
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1answer
62 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!
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Constructing a Toffoli gate from CNOT and single-qubit gates [closed]
Toffoli gate in terms of CNOT and single-qubit gates.
Thanks much!
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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
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1answer
165 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 ...
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1answer
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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 ...
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1answer
163 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 ...
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392 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.
...
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1answer
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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 ...
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1answer
102 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 ...
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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 ...
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2answers
309 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 $\rho$ ...
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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?
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2answers
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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) ...
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1answer
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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} ...
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1answer
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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 ...
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4answers
230 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?
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2answers
529 views
How to apply a Hadamard gate?
How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
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2answers
140 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.
...
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2answers
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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% ...
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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
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1answer
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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 $l$ ...
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1answer
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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. ...
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2answers
175 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 ...
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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
...
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1answer
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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 ...
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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, ...
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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 ...
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2answers
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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, ...
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3answers
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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
...
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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
...
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1answer
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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 ...
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1answer
113 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 + ...
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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:
...
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1answer
131 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 ...
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4answers
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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 ...
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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 ...
