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How do the probabilities of each state change after a transformation of a quantum gate?
Quantum gates are represented by matrices, which represent the transformations applied to qubits (states).
Suppose we have some quantum gate which operates on $2$ qubits.
How does the quantum gate affect (not necessarily change it) the result of…
ItamarG3
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Is entanglement necessary for quantum computation?
Entanglement is often discussed as being one of the essential components that makes quantum different from classical. But is entanglement really necessary to achieve a speed-up in quantum computation?
DaftWullie
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How to implement the 4 Bell states on the IBM Q (composer)?
I would like to simulate the 4 "Bell States" on the IBM composer?
How can I best implement those 4 Bell states using the existing set of gates ?
Here below you see the definition of the 4 Bell states.
The first bell state can be easily implemented…
JanVdA
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How can we keep Schrödinger's cat alive?
We know, Schrödinger's cat inside the box is in the equal superposition state of both alive and dead. We can express its state as $$|\text{cat}_\phi\rangle= \frac{|\text{alive}\rangle+e^{i\phi}|\text{dead}\rangle}{\sqrt{2}} \hspace{10mm} \text{where…
Syed Emad Uddin
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What applications does Grover's Search Algorithm have?
Grover's Search algorithm is usually talked about in terms of finding a marked entry in an unsorted database. This is a natural formalism that lets it be applied directly to searching for solutions to NP problems (where a good solution is easily…
DaftWullie
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Are there results from quantum algorithms or complexity that lead to advances on the P vs NP problem?
On the surface, quantum algorithms have little to do with classical computing and P vs NP in particular: Solving problems from NP with quantum computers tells us nothing about the relations of these classical complexity classes1.
On the other hand,…
Discrete lizard
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Does a complete list of open quantum software projects exist?
An answer to
Is there any source which tabulates quantum computing algorithms for simulating physical systems? mentions the Quantum Algorithm Zoo, a list of quantum algorithms. Several answers to Programming quantum computers for non-physics majors…
agaitaarino
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Obtaining gate $e^{-i\Delta t Z}$ from elementary gates
I am currently reading "Quantum Computation and Quantum Information" by Nielsen and Chuang. In the section about Quantum Simulation, they give an illustrative example (section 4.7.3), which I don't quite understand:
Suppose we have the Hamiltonian…
brzepkowski
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What counts as an "ancilla" qubit?
I am getting confused about the meaning of the term "ancilla" qubit. It's use seems to vary a lot in different situations. I have read (in numerous places) that an ancilla is a constant input - but in nearly all of the algorithms I know (Simion's,…
Quantum spaghettification
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What do the off-diagonal elements of a density matrix physically represent?
For simplicity, let's take a density matrix for a single qubit, written in the $\{|0\rangle,|1\rangle\}$ basis:
$$ \rho = \begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10}^* & 1-\rho_{00} \end{pmatrix} $$
The diagonal elements give us the…
KnightShuffler
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How are gates implemented in a continuous-variable quantum computer?
I've mostly worked with superconducting quantum computers I am not really familiar with the experimental details of photonic quantum computers that use photons to create continuous-variable cluster states such as the one that the Canadian startup…
Mark Fingerhuth
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In a Quantum Turing Machine, how is the decision to move along the memory tape made?
Let, for a Quantum Turing machine (QTM), the state set be $Q$, and the alphabet of symbols be $\sum=\{0,1\}$, which appear at the tape head. Then, as per my understanding, at any given time while the QTM is calculating, the qubit that appears at its…
Prem
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How long does quantum annealing take to find the solution to a given problem?
Quantum annealing is an optimization protocol that, thanks to quantum tunneling, allows in given circumstances to maximize/minimize a given function more efficiently than classical optimization algorithms.
A crucial point of quantum annealing is the…
glS
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If quantum gates are reversible how can they possibly perform irreversible classical AND and OR operations?
Quantum gates are said to be unitary and reversible. However, classical gates can be irreversible, like the logical AND and logical OR gates. Then, how is it possible to model irreversible classical AND and OR gates using quantum gates?
Sanchayan Dutta
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Why must quantum computers be kept near absolute zero?
Online descriptions of quantum computers often discuss how they must be kept near absolute zero $\left(0~\mathrm{K}~\text{or}~-273.15~{\left. {}^{\circ}\mathrm{C} \right.}\right)$.
Questions:
Why must quantum computers operate under such extreme…
Didix
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