New answers tagged quantum-gate
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CNOT gate on an entangled target qubit
The result of applying the $CNOT$ gate to an entangled state are below. Note only the target qubit is affected as you thought.
$CNOT_{02}|1\rangle \otimes (\frac{|{00}\rangle + |{11}\rangle}{\sqrt{2}})...
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Does the matrix representation of quantum gates depend on the basis?
Some other very good answers have been posted, and this answer is not really useful on it's own, but I think it adds something in conjunction with the others. Really, quantum gates should be thought ...
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CNOT gate when the target qubit is in entangled state
I'm assuming you have three qubits $q_0, q_1, q_2$.
$q_0, q_1$ are initialized in the Bell state: $|q_1q_0\rangle = \sqrt{1/2}(|00\rangle + |11\rangle)$.
$q_2$ is initialized in state $|1\rangle$, ...
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Does the matrix representation of quantum gates depend on the basis?
Yes, the matrix representation changes. For example, the Pauli $X$ gate in the standard basis is
$$
X\equiv \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}
$$
which you evaluate by taking your ...
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Does the matrix representation of quantum gates depend on the basis?
Say you have state $|\psi\rangle$ and you perform a change in basis by applying $V$:
$$|\phi\rangle = V |\psi\rangle$$
Now you want to apply some unknown unitary $W$ to $|\phi\rangle$ such that it has ...
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Simple successor gate
The easiest thing is to store intermediate results on ancilla qubits so that those results can be reused.
If you don't have any zero'd ancilla qubits, but do have qubits not being operated on right ...
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Can we learn anything interesting about a claw by taking the square-root-of-NOT of each qubit?
A direct calculation yields:
$$\left(\sqrt{\text{NOT}}\right)^{\otimes n}=\frac{1}{\sqrt{2^n}}\sum_{x,d}(-\mathrm{i})^{h(x\oplus d)}|d\rangle\!\langle x|$$
with $h$ being the Hamming weight. If $f$ is ...
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Universality for reversible classical computation
You do have to be a little careful on what you mean by "universal." The CCNOT (Toffoli) gate is universal in a stronger sense than the CSWAP (Fredkin) gate is, if only because CSWAP ...
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How does the propogation of bi-product operators through the CNOT gate in Gate Teleportation give this circuit?
Are you doing CX 2 3 or CX 3 2 when preparing the middle state? The corrections are for ...
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Apply parametric gate to quantum state in symbolic tensor representation
A pure sympy solution would be:
...
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Implementing the "Inplace Access to the Surface Code Y Basis" with neutral atom/shuttling platforms
In the introduction of the paper, it's noted that if you have non-local connectivity then you can perform $R_Y$ and $M_Y$ in constant depth by using a folded surface code. The circuit for doing so is ...
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Is there a "control-on-zero" CCNOT?
Since you also ask about availability on quantum hardware: Note that the control-on-zero is equivalent to a conventional controlled operation, but conjugated with Pauli $X$. For example:
equals
So ...
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