All Questions
Tagged with gate-synthesis mathematics
6 questions
36
votes
5
answers
12k
views
How to derive the CNOT matrix for a 3-qubit system where the control & target qubits are not adjacent?
In a three-qubit system, it's easy to derive the CNOT operator when the control & target qubits are adjacent in significance - you just tensor the 2-bit CNOT operator with the identity matrix in ...
- 1,459
5
votes
1
answer
2k
views
How can you decompose Grover's diffusion operator into gates?
I know how Grover's diffusion operator works ($U_s = 2|s\rangle\langle s|-I$) with the inversion around the mean. However, I want to implement it in simpler gates, to use the algorithm. How can I do ...
glS♦
- 26.9k
13
votes
2
answers
2k
views
Automatic compilation of quantum circuits
A recent question here asked how to compile the 4-qubit gate CCCZ (controlled-controlled-controlled-Z) into simple 1-qubit and 2-qubit gates, and the only answer given so far requires 63 gates!
The ...
- 17.8k
0
votes
0
answers
44
views
How are multi-qubit gates extended into larger registers? [duplicate]
Implementing a single-qubit gate in a multi-qubit register is relatively easy. For example, this gate:
This is equivalent to $I \otimes H \otimes I$. If the $H$ gate was on the first bit, it would be ...
- 17.8k
3
votes
1
answer
131
views
Doing maths with controlled-half NOTs
In Quantum Computation with the simplest maths possible there is a section titled "Doing maths with a controlled-half NOT" which covers a reversible-(N)AND circuit with controlled-half NOTs.
What ...
- 17.8k
9
votes
2
answers
704
views
Is there a general method to implement a 'greater than' quantum circuit?
I am interesting in finding a circuit to implement the operation $f(x) > y$ for an arbitrary value of $y$. Below is the circuit I would like to build:
I use the first three qubits to encode $|x⟩$, ...
- 17.8k