Questions tagged [circuit-construction]
For questions about the construction of complex circuits using elementary quantum gates.
487
questions
2
votes
3answers
74 views
Find a circuit implementing a 3-qubit unitary matrix preparing $|b\rangle\simeq(0,c,c,c,c,c,c,0)$ with $c=1/\sqrt6$
I am trying to find a circuit to represent a 3 Qubit unitary matrix such that $U|0\rangle = |b\rangle$ for $b = \left[0~c~c~c~c~c~c~0\right]$, where $c = 1/\sqrt{6}$.
Although I am working in Qiskit, ...
2
votes
1answer
49 views
Representing Qubit Operator in Circuit
I am trying to represent a quantum circuit schematically with some operators in QISKIT. I know I can create some operator with Operator() in quantum_info from a ...
2
votes
1answer
41 views
Multiplication using nearest neighbour quantum gates
Let $A$ be an $n \times m$ matrix, and $x$ be an $m \times 1$ vector and $q$ be a number such that $q$ is polynomial in $n$.
Let us be given both $A$, $q$, and $x$ as input and let us also have a 2D ...
2
votes
1answer
56 views
Which backends implement the if-else operation?
On which backends (Basic, AER, Simulation, IBMQ) is the qiskit.circuit.controlflow.if_else Operation implemented currently?
I want to create a circuit depending on qubit states, e.g.:
...
0
votes
1answer
35 views
Encoding a block unitary matrix in a quantum circuit
My goal would be to implement the unitary matrix $M=\begin{bmatrix}U_{1} &0\\0&U_{0}\end{bmatrix}$ as a circuit for arbitrary $N \mathrm{x} N$ unitary matrices. It is trivial to show that if ...
1
vote
2answers
49 views
Is it true that $Ry(\pi/2)\sigma_zRy(-\pi/2)=\sigma_x$?
I saw in a qiskit document that said $Ry(\pi/2)\sigma_zRy(-\pi/2)=\sigma_x$ To confirm this I decided to create the matrix representations of these operations and multiply them together to see if I ...
4
votes
1answer
53 views
Native Gate Decomposition
TL;DR: I've got a very small set of gates to use and need to find efficient decompositions for $R_y$ and controlled $R_y$ gates. Does anyone have any better ideas than what I have?
I'm looking to ...
3
votes
0answers
57 views
How to impliment Projector Control-Not in Qiskit?
I want to impliment Projector Control-Not in Qiskit just like in this , which is a $|0\rangle\langle 0|$ projector found in the paper "Grand Unification of Quantum Algorithm" page 7. Also, ...
4
votes
1answer
65 views
Confusion with the number of CNOTs in a circuit
I am a bit puzzled on the following circuit. According to this Quantum Computing SE thread it holds that
$$
e^{i(Z\otimes Z)t} = {\rm CNOT} (I\otimes e^{iZt}){\rm CNOT} \qquad (1)
$$
As a result we ...
2
votes
1answer
50 views
Simulating the Ising-like model as a quantum circuit
We are interested in simulating the 1d Ising model Hamiltonian using a Quantum Circuit (QC). A similar question was posted before with no answers. Here we will assume, for simplicity, 3 lattice sites ...
1
vote
1answer
46 views
How to implement general 2-qubit gate in n-qubit system?
I am trying to implement a general 2-qubit gate in an n-qubit system (not using qiskit or cirq). Example: Consider 4 qubits. Assume we want to act a CX on qubit 2 as control and qubit 3 as target. The ...
1
vote
0answers
35 views
How to create this feature map?
In this paper, the following feature map is used:
$$x \to \vert\phi(x)\rangle = \frac{1}{\sqrt{2^k}}\sum_{i=0}^{2^k-1}\vert x\cdot g^i\rangle$$
But no circuit is provided. A theoretical description of ...
2
votes
1answer
32 views
Can the ancilla for Qiskit's mcx with mode="recursion" be dirty?
I think their implementation is close to the one from here which does use a dirty ancilla, but I just want to make sure
4
votes
2answers
286 views
Does there exists an algorithm to construct a quantum circuit given an arbitrary unitary?
Suppose there exists an algorithm that takes as input an arbitrary unitary matrix and produces as output a quantum circuit representing that matrix. Then in theory that algorithm could construct any ...
7
votes
2answers
147 views
What quantum gates admit a basis-independent interpretation of their action?
The SWAP gate swaps the state of the two qubits so that in the computational basis $|01\rangle \rightarrow |10 \rangle$ with a matrix representation given by:
\begin{bmatrix}
1 & 0 & 0 & 0 ...
4
votes
1answer
144 views
Given a $|W_8\rangle$, perform a CCCZ using stabilizer operations
I know it's possible to perform a CCZ operation using only stabilizer operations (Cliffords + Pauli measurements + classical feedback) by consuming a $|CCZ\rangle$ state, and that a $|W_4\rangle$ ...
3
votes
2answers
64 views
How to create superposition of states with fixed parity with a quantum circuit?
I'm searching for a circuit to generate, starting from the $|00\, ...\,0\rangle$ state, an arbitrary superposition of all states with either even or odd parity. The gate choice is irrelevant for now, ...
3
votes
1answer
77 views
How to create a Bell state with asymmetric amplitudes using single-qubit and CNOT gates?
Is there a systematic way - in terms of a quantum circuit with single qubit and CNOT gates - to create a bell state with asymmetric amplitudes, e.g.,
$$
\alpha |00\rangle + \beta|11\rangle
$$
where $\...
4
votes
1answer
38 views
What is the method to create arbitrary controlled circuits in Qiskit?
I am working on an implementation of an algorithm which uses ampitude estimation and amplification as a subroutine but we are not using qiskit but QuEST. QuEST doesn't have any direct method to ...
1
vote
0answers
31 views
How should I think about circuit metrics like "qubit count," "circuit depth," and "gate count" when dealing with the OpenQASM 3 `ctrl` modifier?
It seems like circuit metrics like qubit count, circuit depth, and gate count are pretty useful. Qubit count determines whether a it's even possible to run a program on resource-limited quantum ...
0
votes
0answers
29 views
How to perform controlled rotations similar to what is done in HHL
How does one do the conditional rotation based on a binary encoding of the input? The rotation of D_i^t has to be done in the image below and I know that similar rotations can also be found in HHL and ...
2
votes
2answers
80 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 ...
0
votes
2answers
81 views
How to multiply two vectors (kets) in qiskit?
Hi does anyone know how i could write a program to get the product of something like |1>|0>|0>?
2
votes
0answers
56 views
Could the Hamiltonian of a Rubik's Cube be simulated with a NISQ device?
Consider the four cells on each of the six faces of the 2x2x2 Rubik's cube (the pocket cube), with front, up, and right twists being labelled as $\langle F,U,R\rangle$.
Each move uses fifteen SWAP ...
2
votes
1answer
40 views
How to Construct Swap Gates from Permutation Matrix?
This is a follow-up question from here.
Let's say after an LUP decomposition, we have an 8x8 permutation matrix:
$ P^{-1} = \begin{bmatrix}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\
...
4
votes
1answer
74 views
Is there a higher dimensional Fredkin gate?
The Fredkin gate is CSWAP gate. Given a control register in $0$ or $1$, the gate does nothing or swaps two target registers respectively.
Is there a higher dimensional version of this gate? I have ...
0
votes
0answers
27 views
Measuring with a certain probability in Qiskit
I have the following quantum operation on two qubits:
$$ \mathcal{E}(\rho) = p \mathcal{T} \circ \mathcal{U}(\rho) + (1-p) \mathcal{U}(\rho) $$
where $p$ is some probability, $\mathcal{U}$ is some ...
0
votes
0answers
18 views
FRQI wrong interpretation
I try to use FRQI https://qiskit.org/textbook/ch-applications/image-processing-frqi-neqr.html with the same circuit.
Suppose I have the following image:
and the flatten representation is [0 100 200 ...
0
votes
0answers
21 views
FRQI for 8x8 image
I read the paper A flexible representation of quantum images for polynomial preparation, image compression, and processing operations and found a scheme for 2x2 images which looks like this:
I tried ...
1
vote
1answer
81 views
How to determine the basis state with maximum amplitude without measurement?
Suppose I have two quantum registers described respectively by the quantum states $| \psi_1 \rangle = \sum_i \alpha_i |i \rangle$ and $|\psi_2 \rangle = |0\rangle$. I would like to implement a CNOT ...
0
votes
1answer
56 views
Implement a square root of Swap gate in using qiskit [closed]
Does the √SWAP gate have a ready-to-use function on the Qiskit circuit library?
If not, how to implement it?
2
votes
0answers
64 views
Eigenvalues and energy levels of 1D Heisenberg model using real Quantum Computers?
The 1D Quantum Heisenberg model is
$$H_\textrm{Heisenberg} = -~J \sum_{\langle i\ j\rangle} \hat{S}_{i} \cdot \hat{S}_{j}$$
where each spin is an operator.
For simple cases, for example, a system with ...
0
votes
0answers
44 views
Four-qubit error correction code
$\newcommand{\ket}[1]{\left|#1\right>}$
Consider the following 4-qubit code which allows you to detect a bitflip and/or a phaseflip. The logical 0 and 1 are encoded as:
\begin{align*}
\ket{0}_{...
5
votes
2answers
170 views
Why isn't $Ry(\pi/2)$ gate equivalent to Hadamard gate?
I've been experimenting with quantum circuits and can't quite fathom how the difference between states comes together.
Speaking in terms of simulations using qiskit,...
1
vote
1answer
42 views
How many single and double qubit gates are required to create a uniform superposition of vertices of a Johnson Graph J(n,r)?
Can I in $\tilde{O}(r)$ number of gates (single and double qubit) create a uniform superposition of vertices of Johnson Graph $J(n,r)$? I would like to create a state $|\psi\rangle = \frac{1}{\sqrt{n \...
5
votes
1answer
60 views
Why do we care about the number of $T$ gates in a quantum circuit?
When reading this question and quickly reading some of the linked papers, I wondered why was the number of $T$ gates specified along the number of controlled-$X$ gates.
I've often read that ...
1
vote
1answer
55 views
What is the syntax for general control gate in stim
For a stabilizer code with the stabilizers in canonical form, an encoding circuit has the form
that's a product of hadamard gates and general control gates : $H_i C_i(U_i)$. For example for
the $[[5,1,...
0
votes
0answers
61 views
How can I create a Qiskit function producing a quantum circuit such that $\langle Z^{\otimes n}\rangle=J_{n-1}/2^{n-1}$?
Problem:
Create a function circ(n) that returns an $n$-qubits quantum circuit that, when measured in the $Z^{\otimes n}$ basis, should yield the following ...
1
vote
1answer
154 views
Getting non-Clifford after performing several Clifford gates in qiskit
I'm trying to test Clifford gates in qiskit according to the table in Fault-tolerant SQ, page 101. I tried 4 Cliffords in the test $$-X/2 - X -X/2,Y/2,X/2 - -X/2,Y/2,-X/2$$
using the following code
<...
0
votes
1answer
43 views
3
votes
1answer
73 views
How to implement a quantum array
I'm trying to implement a quantum array. That is one that stores qubits and can be indexed via qubits.
I can create one that handles setting values fairly easy. Have two registers, one for the ...
1
vote
1answer
105 views
Is it possible to perform $z$ rotation in Qiskit with just $x$ and $y$ rotations?
Is it possible to perform $z$ rotation in Qiskit with just $x$ and $y$ rotations?
I tried the following:
...
8
votes
2answers
392 views
Minimum number of 2 qubit gates to build any unitary
Any unitary $U$ acting on $N$ qubits can be decomposed in a finite product $U=U_1U_2...U_n$ where every $U_i$ acts on only 2 qubits, for example through decomposition in CNOT, phase shifts and 1 qubit ...
2
votes
2answers
261 views
What is the circuit for grover's algorithm if N is not a power of 2?
From the literature it seems that grover's algorithm works if $N$ is not a power of $2$. For instance, https://en.wikipedia.org/wiki/Grover%27s_algorithm
and
https://arxiv.org/abs/quant-ph/0005055
I ...
2
votes
4answers
531 views
How is a Toffoli gate built without using T gates?
Can someone tell me how to make a Toffoli gate without using T gates? Can we use $R_x$ and $R_y$. If yes, then how?
I tried many circuits but I was unable to create the CCNOT gate out of $R_x$, $R_y$ ...
3
votes
1answer
438 views
Controlled Z gate using Pauli rotation operators and Z tensor product Z
I am trying to construct a controlled Z gate using elementary gates. This is what I have so far: \begin{pmatrix}
-i & 0 & 0 & 0\\
0 & -1 & 0 & 0\\
0 & 0 & 1 & 0\\
...
3
votes
1answer
206 views
Qiskit's QFT not returning the expected state
I'm currently going through the lab problems for the Qiskit course here. I'm trying to finish lab set number 3 on QPE but I can't seem to get the desired output, even from the solution notebook. I'm ...
1
vote
0answers
60 views
What is the right way to teleport qubits on a real quantum computer?
I've been using the teleportation protocol to teleport qubits and then using Qiskit state tomography for reconstructing my qubits.
Using this circuit using open qasm I regularly obtain fidelity 0.9.
...
5
votes
1answer
141 views
BHT algorithm implementation
Summary of Method
Amplitude Amplification Summary
The BHT algorithm uses amplitude amplification, a nice generalisation of Grover's algorithm, where there is a subset $G\subset X$ of good elements in ...
1
vote
0answers
76 views
Quantum Circuits for Time-Series Data
I am currently working with a dataset with autocorrelated features, i.e, x(t) affects the value of x(t+1) which affects the value of x(t+2).
Suppose this is the circuit representing x(t):
Does ...
