Most Popular
1500 questions
8
votes
1 answer
How to construct Deutsch's gate or $\pi/8$ rotations using Toffoli+Hadamard?
It is known that Toffoli and Hadamard are Quantum Universal.
My question is - how to construct (an approximation of) the Deutsch's gate or the $\pi/8$ rotation using Toffoli + Hadamard?
I've seen several implementations of the Toffoli gate using…
GWB
- 111
- 2
8
votes
1 answer
What are the differences between the different transpiler optimization levels in qiskit
I am currently running a simple algorithm using Qiskit and I am running it for various transpiler optimization levels (0-3). I wish to know what exactly occurs differently when for example I run the algorithm with optimization level 1 as compared to…
Generic_dp
- 128
- 5
8
votes
2 answers
How can I fill a unitary knowing only its first column?
I have a unitary matrix that I want to construct. I only care what happens to the first computational state, so the first column is specified. So far, I've been assigning each question mark to a variable and solving $UU^T = I$ analytically. But this…
psitae
- 1,340
- 7
- 24
8
votes
1 answer
Explain the representation of the CNOT gate in ZX-calculus
In ZX-calculus, the CNOT gate is represented by this:
Can someone show me why this is true, using just the basic rewriting rules? All books/papers I have seen simply take it without proof, but I can't see why it is true.
NNN
- 363
- 1
- 9
8
votes
1 answer
Physical implementation of gates on IBM Q
There is a lot of quantum gates in IBM Q Composer, however, only few are implemented physically while others can be composed of them.
When one looks at description of a quantum processor in IBM Q interface, there is a list of basis gates. For…
Martin Vesely
- 13,891
- 4
- 28
- 65
7
votes
2 answers
Why can the QFT be replaced by Hadamard gates?
I'm studying Shor's Algorithm.
In the book, author explains QFT can be replaced by Hadamard gates?
Why this process is possible??
Thank you everybody. This is QPE. I attach part of book!!
유도경
- 309
- 1
- 5
7
votes
3 answers
How to run a qasm file on IBMQ device?
I can find many qasm examples.
How can I run them on different IBMQ devices?
peachnuts
- 1,373
- 1
- 7
- 15
7
votes
3 answers
Unentangling a qubit from a system: can we convert $\alpha|000\rangle+\beta|111\rangle$ into $\alpha|00\rangle+\beta|11\rangle$?
Let's say I start with the following arbitrary qubits:
$$
\color{red}{\vert Q_1 \rangle = \alpha_1 \vert 0 \rangle + \beta_1 \vert 1 \rangle}\\
\color{green}{\vert Q_2 \rangle = \alpha_2 \vert 0 \rangle + \beta_2 \vert 1…
M. Al Jumaily
- 812
- 1
- 6
- 19
7
votes
2 answers
Constructing a circuit for $C^1(U)$ for rotation operators with TWO single qubit gates and CNOT gate
This is the exercise 4.23 from Nielsen and Chuang, asking that if it is possible to construct $C^1(U)$ for $U=R_{x,y}(\theta)$ with TWO single qubit gates and CNOT gate. My answer is no, and I would like to argue in the following way.
First, we do…
fagd
- 965
- 4
- 12
7
votes
1 answer
How to interpret a 4 qubit quantum circuit as a matrix?
This is part of Simon Algorithm (Initial state + some Oracle function)
There is a post that explains how to interpret circuits (How to interpret a quantum circuit as a matrix?), but I'm not sure how to apply to the following circuit.
The first…
Felipe Rojo Amadeo
- 353
- 2
- 6
7
votes
4 answers
Are there Bell-like violations that can be observed without collecting statistics?
Observing the violation of Bell inequalities, be it in their original formulation, or in the nowadays more commonly used CHSH formulation, involves computing averages of specific experimentally measurable quantities. In the CHSH formulation, these…
glS
- 24,708
- 5
- 34
- 108
7
votes
1 answer
Uncomputation in quantum implementation of a classical algorithm
In Nielsens and Chuangs book, they present a way to implement a reversible version of any classical algorithm (section 3.2.5).
In short, they use Fredkin and other simple reversible gates to implement a circuit doing $(x, 0, 0, y) \rightarrow (x,…
Leander Behr
- 133
- 4
7
votes
1 answer
Decomposing a $(w+1)$-qubit permutation gate into $w$-qubit permutation gates, SWAPs and NOTs
Say I have a quantum circuit of $w+1$ qubits with a permutation gate (mapping computational basis states to computational basis states) that does the permutation $(i, i+1)(i+4, i+5)$ on $w+1$ qubits if $i$ is odd and the permutation $(i+1, i+2)(i+3,…
Sanchayan Dutta
- 17,497
- 7
- 48
- 110
7
votes
2 answers
Diagrammatic Quantum Reasoning: Proving the loop equation using yanking equations
I'm trying to study the book: Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning, and would like some help with Exercise 4.12:
The relevant equations are as follows:
As an aside, I would really appreciate it…
Mahathi Vempati
- 1,621
- 9
- 20
7
votes
1 answer
How to implement a Fredkin gate using Toffoli and CNOTs?
Inspired by a question Toffoli using Fredkin, I tried to do "inverse" task, i.e. to implement Fredkin gate (or controlled swap). In the end I implemented it with three Toffoli gates.
Firstly, I started with swap gate without control qubit which is…
Martin Vesely
- 13,891
- 4
- 28
- 65