New answers tagged quantum-gate
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Does the $\text{CNOT}$ gate activate if the control qubit is $-|1⟩?$
Yes, it would. It is sometimes better to think in the vector-matrix representation than in the dirac notations.
$$|1\rangle = \begin{bmatrix}
0\\
1
\end{bmatrix}\,.$$
Now,
$$Z|1\rangle = -|1\rangle =...
- 1,311
1
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Does the $\text{CNOT}$ gate activate if the control qubit is $-|1⟩?$
Yes.
Think of the $-|1\rangle$ state as a superposition of basis states $|0\rangle$ and $|1\rangle$ (albeit a weird one). In this case, you can apply the general rule for the CNOT gate acting on ...
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general way to decompose a CZ gate on $n$-qubit system
Yes absolutely it is possible! This algorithm may not use the optimal number of gates, but it gets the job done.
You may have heard of the SWAP gate which effectively switches the positions of two ...
- 96
1
vote
Accepted
Problem with the mathematical definition of the eigenvalue algorithm on a specific exercise
Calculate the wavefunction step by step by applying each gate in sequence
$$
\begin{align}
|000\rangle&\xrightarrow{H\otimes H}\frac12\sum_{a,b=0}^1|a\rangle|b\rangle|0\rangle\tag1\\
&\...
- 20.8k
3
votes
Accepted
Decomposition of a $4 \times 4$ unitary matrix
That paper appears to do their rotations in a very strange order. The method you're interested in is how to use Givens rotations to perform a QR decomposition (see, e.g. https://en.wikipedia.org/wiki/...
- 55.7k
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Decomposition of a $4 \times 4$ unitary matrix
Note the following: if we have a vector with 2 entries $\begin{bmatrix} a \\ b \end{bmatrix}$, then we can use a unitary matrix to change the second entry to $0$. Namely, set $r = \sqrt{|a|^2 + |b|^2}$...
- 208
2
votes
Accepted
How much complexity is required to implement $\text{C$_\Pi$NOT}$ gate?
I suspect that depends on $\Pi$. There will be easily categorised cases where you can.
For example: $\Pi$ projects onto a subset of basis states for which there exists an efficient classical ...
- 55.7k
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What role does Landauer's principle play in quantum reversibility?
Actually, classical physics is also reversible, whether you're considering classical dynamics or considering it as the limit of quantum physics (which is reversible).
The means for neither classical ...
- 1,994
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Equivalence checking of quantum circuits up to error
Sam's link to the posting on tcs answers the OP's question - but here's some other comments that were hinted at here and there.
The exact classical problem is coNP-complete as this reduces to ...
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Accepted
Frequency of qubits in qiskit simulators
The qubit frequency is not encoded into the noise model. You can however attach noise to the delay gate. See here.
- 841
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Netlist of the transpiled circuit in Qiskit
It very much depends on what do you mean by a netlist.
If you are searching for a human-readable serialization format of a non-dynamic circuit, I would recommend you OpenQASM 2
...
- 5,573
5
votes
Accepted
When is the square root of a Clifford gate a Clifford gate?
TL;DR A simple sufficient condition is: if the order $r$ of a given Clifford $U$ and the root's degree $n$ are relatively prime, then $U$ has an$^1$ $n$th root.
Let $r$ be the order of $U$, i.e. the ...
- 20.8k
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Phase accumulation for multiple Rabi driving pulses
Good question! Your first equation mixes a couple of abstractions that we typically sweep under the rug, so let's start by taking a step back. When we apply a control pulse to a qubit, it's usually ...
- 1,380
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Simulator able to run SwitchCase in qiskit?
The latest version of Qiskit Aer (version 0.13) supports SwitchCaseOp. So, if it's OK to run your circuit locally, you can use Aer simulators:
...
- 9,097
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Accepted
Conditioned gates with multiple classical bits
You can use bit_xor function from the newly added classical expressions module
...
- 9,097
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Conditioned gates with multiple classical bits
This can be done quite easily. For instance, take the case where you have two classical bits $c_1, c_2$ and would like to implement $X^{c_1+c_2}$ on a qubit $q$. Clearly, applying $X^{c_1}$ followed ...
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votes
Accepted
If_test() - Dynamic Circuits in qiskit
It appears there's a misunderstanding regarding the use of if_test and _else constructs in your code. In Qiskit, these ...
- 755
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Accepted
Constructing a two 3-qubit state involving either X, Y or Z rotation gate
One way to achieve this is the following way.
Initialise 1 qubit in the $|0\rangle$-state and rotate along the $Y$-axis to
\begin{equation}
\frac{1}{2}|0\rangle+\frac{\sqrt{3}}{2}|1\rangle.
\end{...
- 179
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How to fix two flip-bit errors in a 3 qubit input
I was able to figure it out now via taking 3 ancilla qubits instead of 2 and figuring out the invariant in case 2 bits are flipped.
- 69
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Regarding the inductive proof that any Clifford gate can be made of Hadamard, phase and c-not
This question is about the second part of the cited exercise. The first part is the single qubit case. In the second part, one is basically supposed to prove by induction that with the given ...
- 13
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Time evolution of Hamiltonian
I found out, that one can do that using the $Z$-rotations instead of $X$-rotations because the $Z$-rotation is already diagonal. that makes it way easier to see what $e^{\sigma^{z}}$ should be. So one ...
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