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 ...
- 20.7k
2
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 ...
- 757
2
votes
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
2
votes
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 ...
- 83
2
votes
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
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
1
vote
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
1
vote
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
1
vote
Accepted
Conditioned gates with multiple classical bits
You can use bit_xor function from the newly added classical expressions module
...
- 9,052
1
vote
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 ...
- 384
1
vote
What do the values in a unitary matrix represent/what do they mean? How do you figure out what gate a unitary matrix represents?
I don't know what your background is, but I find it helpful to come at this from the starting point of classical probability:
Imagine you have a two state system (such as a coin). It can either be ...
- 55.7k
1
vote
What do the values in a unitary matrix represent/what do they mean? How do you figure out what gate a unitary matrix represents?
Every unit vector in your Hilbert Space corresponds to a valid quantum state. Multiplying that matrix with your vector is just the linear transformation.
It is like, given that all possible states, ...
- 1,311
1
vote
Accepted
The expectation values for the values of both qubits
You can find the single-qubit expectation values by tracing out the degrees of freedom of the other qubit. Mathematically, this corresponds to $\rho_A = \text{Tr}_B(|{\psi}_{AB}\rangle\langle{\psi_{AB}...
- 179
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