Questions tagged [gate-synthesis]
For questions about finding (short) gate sequences to implement a specific unitary operation, for example decomposing a complicated multi-qubit gate into a sequence of basic gates. It might apply to optimizing circuits with respect to length or depth or finding gate sequences to implement an algorithm.
221
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29
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Qiskit not efficiently compiling with new gate basis
I am using Qiskit to compile a small Qiskit circuit (shown below) with a gate basis consisting of Rigetti native gates:
RZ
...
0
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0
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28
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Solving variables in symbolic unitary to get a desired real-valued unitary using qiskit or qympy, qiskit-symb/pytket
I am trying to decompose a 4x4 unitary into 2 qubit circuit using U3 and CNOT gates but the circuit implementation qiskit gives me is not optimized. So I started looking at qiskit-symb and qympy to ...
- 1
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1
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129
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Is there a tool to decompose 4-Qubit unitaries (aka 16x16 matrices)?
I was wondering if there is a tool that can decompose such a matrix in gates on 4 qubits?
I found one for 3-qubit gates (9x9 matrices) in Cirq but nothing for bigger matrices.
(The matrix is not ...
- 105
1
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1
answer
51
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Implementation of a unitary operator scaled by a factor
Is it possible to implement a unitary operator scaled by a factor on a quantum computer?
Let's say the unitary operator is $U$:
$$U=\begin{bmatrix}
u_0 & u_1 \\ u_2 & u_3
\end{bmatrix}\...
- 311
0
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1
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55
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Realization of the gate $(I\pm U)/2$
The state after applying the Hadamard test (before measurement)
is $$\newcommand{\ket}[1]{|#1\rangle}\newcommand{\bra}[1]{\langle#1|}\ket{0}\frac{I+U}{2}\ket{\psi} + \ket{1}\frac{I-U}{2}\ket{\psi}.$$
...
- 311
2
votes
2
answers
75
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Better constant for linear depth incrementers
Currently working on some quantum arithmetic and was wondering if we have a better constant factor for a linear depth incrementer.
As an example (and the best I could currently find), Craig Gidney ...
- 53
2
votes
2
answers
54
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Calculating number of CNOT gates in Pauli evolution gate
How to calculate the number of CNOT gates for a Pauli exponentiation for given time?
I am performing Trotterization which involves performing Pauli evolution ...
- 391
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28
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BQSkit Selecting Starting Circuit Structure
Background
On the BQSKit repository, there is a nice example of using the qfactor algorithm to instantiate a 3-qubit Toffoli circuit. For this to work, however, it is first necessary to specify an ...
- 197
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4
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116
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$U_1\oplus U_2$ decomposable into $I\oplus U$ and 1-qubit gates?
TL;DR
Let $U_1, U_2, U$ be arbitrary 1-qubit quantum gates.
Can 2-qubit gates of the form $U_1\oplus U_2$ always be decomposed into a combination of controlled gates ($I\oplus U$) and single qubit ...
- 311
1
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1
answer
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How many gates are necessary to implement an arbitrary n-qubit permutation unitary?
How many gates are necessary to implement an arbitrary n-qubit permutation unitary, using only 1- and 2-qubit gates?
An n-qubit permutation unitary is a $2^n$ x $2^n$ unitary matrix where each entry ...
- 181
2
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1
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105
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How to retrieve a phase gate from a circuit made out of $CX$ and $T$
The extract below comes from this paper.
It is an example that shows a basic phase polynomial, related to the $CCZ$ gate.
It can also be written with $CX$ and $T$ gates.
I can't find the connection ...
- 1,998
3
votes
1
answer
112
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Is it possible to decompose a controlled gate with control qubit in the $|+\rangle$ state?
$\newcommand{\ket}[1]{\vert#1\rangle}\newcommand{\bra}[1]{\langle#1\vert}$
Given a quantum circuit with 2 qubits that executes a controlled gate $CU$ where the control qubit is in the $\ket{+}$ state, ...
- 311
0
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1
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52
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How can I shift elements around in my state vector according to a specific pattern?
Consider the statevector $|\psi_1\rangle=(a_0,...,a_{N-1})^T$.
My goal is to shift the elements around to end up with $|\psi_2\rangle=(a_{3N/4},...,a_{N-1},a_0,...a_{N/2},\vec{\phi})^T$ where $\vec{\...
- 521
1
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2
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How to find an equivalent circuit without ancilla qubits?
$\newcommand{\ket}[1]{|#1\rangle}$
I have the following quantum circuit:
(The inner qubits are both initialized to $|i\rangle$. $U$ is a arbitrary quantum gate.)
But I am only interested in the ...
- 311
3
votes
1
answer
173
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Clifford+T synthesis with imperfect T gates
From this paper, it has been nicely shown that the number of perfect $T$ gates required to simulate arbitrary single-qubit gates grows linearly with $\log(1/\epsilon)$, where $\epsilon$ is the error ...
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