All Questions
Tagged with textbook-and-exercises circuit-construction
19
questions
0
votes
2
answers
73
views
Help finding mistake when modifying $T$ injection protocols
I am a little confused about where I am going wrong when computing the action of the following circuit:
My understanding is that the CNOT gate acts on the second qubit as a control and the first ...
- 631
2
votes
1
answer
492
views
Construct a two-qubit quantum gate with given action using the gates ${CNOT, H, T}$
Using the gates ${CNOT, H, T}$, construct a 2-qubit gate that acts as follows on the
computational basis
$ |0⟩⊗|0⟩ = |0⟩⊗|0⟩ $
$ |0⟩⊗|1⟩ = e^{pi*i/4}|0⟩⊗|1⟩ $
$ |1⟩⊗|0⟩ = e^{pi*i/4}|1⟩⊗|0⟩ $
$ |1⟩⊗|1⟩ ...
- 373
1
vote
2
answers
450
views
Creating a Qiskit circuit based on output states
I am trying to create a Qiskit circuit that:
starting in state |00⟩ generates a 1/2 * (|00⟩ - |01⟩ - |10⟩ + |11⟩)
state
starting in state |10⟩ generates a 1/2 * (|00⟩ + |01⟩ - |10⟩ -|11⟩) state
...
- 279
2
votes
1
answer
300
views
Creating a Qiskit Circuit sending $|00\rangle$ to $|1,-\rangle$ and $|11\rangle$ to $|0,-\rangle$
I am trying to create a circuit in Qiskit that performs the following transformations:
starting in state |00⟩ generates a √(2)/2 * (-|10⟩+|11⟩) state
starting in state |11⟩ generates a √(2)/2 * (|00⟩-|...
- 279
2
votes
0
answers
307
views
Creating maximally-entangled state in quantum circuits using Qiskit
I am trying to create a function in Qiskit that, given an integer n, returns a circuit of that size in which all qubits at the output are entangled together in a maximally-entangled state.
Some ...
- 279
2
votes
2
answers
314
views
How to create a quantum circuit transforming $α|00⟩ + β|11⟩$ to $β|00⟩-α|01⟩+β|10⟩+α|11⟩$
Starting from an unknown state $α|00⟩ + β|11⟩$, where $\alpha,\beta$ are properly normalized, how can I create a circuit that transforms that state to a $\frac{1}{\sqrt{2}} (β|00⟩-α|01⟩+β|10⟩+α|11⟩)$ ...
- 279
0
votes
1
answer
137
views
How to create a quantum circuit checking whether two functions $f$ or $g$ are of the same type?
I want to create a quantum circuit that checks whether two functions f and g are of the same type, i.e., constant or balanced, or not. In other words, the output of the circuit should output 1 if both ...
- 183
2
votes
1
answer
444
views
Is there a way to prove that the number of gates in Exercise 4.22 of Nielsen and Chuang's book is the smallest possible number?
I've been going over Nielsen and Chuang's Quantum Computation and Quantum Information and I ran into Exercise 4.22, which says,
Prove that a $C^{2}(U)$ gate (for any single qubit unitary $U$) can be ...
- 359
3
votes
2
answers
329
views
Compute the output of this Approximate Quantum Cloning three-qubit circuit
Above is a circuit for "Approximate Quantum Cloning"
The preparation state is given by $$|\psi\rangle =\alpha|0\rangle+\beta|1\rangle$$
The gates labelled $\theta_i$ denote single qubit ...
- 121
3
votes
1
answer
729
views
How to generate a quantum circuit from the quantum state $|1000\rangle+|0100\rangle+|0010\rangle+|0001\rangle$?
I am trying to understand the steps of how make a state preparation circuit from a quantum state.
For making my question more clearer, for example, for the state is $\frac{|00\rangle+|11\rangle}{\...
- 493
4
votes
1
answer
651
views
How do you represent a Hadamard gate as a product of $R_x$ and $R_y$ gates?
I'm looking for a representation of Hadamard gate that uses only $R_x(x)$ and $R_y(y)$ gates. The values $x$ and $y$ may be the same, but they don't necessarily need to be.
- 43
7
votes
3
answers
1k
views
Partial Cyclic Permutation with only Toffoli and CNOT gates?
I have been trying to solve this puzzle of constructing this transformation from CNOT and Toffoli gates as mentioned in NC page 193 (Ex 4.27)
Here is what I have done:
First observation is it has 8 ...
- 975
6
votes
1
answer
2k
views
How to construct a controlled-Hadamard gate using single qubit gates and controlled phase-shift?
How can I construct a controlled-Hadamard gate using single qubit gates and controlled phase-shift?
I am stuck in this and any help would be appreciated.
user14639
2
votes
1
answer
126
views
How does feedback work in simple Grovers algorithm where $n=4$?
In this example implementation of Grovers Algorithm from the Qiskit Textbook which solves a $2\times 2$ sudoku puzzle:
https://qiskit.org/textbook/ch-algorithms/grover.html
The circuit iterates twice (...
- 23
3
votes
2
answers
194
views
Optimizations in quantum circuits
In a paper called On quantum circuits employing roots of the Pauli matrices, I found this figure, where I couldn't understand the equality in the circled circuits. I need an explanation of how the ...
- 61