Linked Questions

8
votes
2answers
1k views

Can arbitrary matrices be decomposed using the Pauli basis? [duplicate]

Is it possible to decompose a hermitian and unitrary matrix $A$ into the sum of the Pauli matrix Kronecker products? For example, I have a matrix 16x16 and want it to be decomposed into something ...
6
votes
3answers
388 views

Quantum circuit to implement matrix exponential

I want to build a circuit which will implement $e^{iAt}$, where $ A= \begin{pmatrix} 1.5 & 0.5\\ 0.5 & 1.5\\ \end{pmatrix} $ and $t= \pi/2 $. We see that $A$ can be written as, $A=1.5I+0.5X$. ...
5
votes
2answers
131 views

Representation of rotation operators $e^{-i\theta(I-Z_1\otimes Z_2 \otimes Z_3)}$ about arbitrary axis for $3$ qubits

I was wondering in how to interpret and represent the operator $e^{-i\theta(I-Z_1\otimes Z_2 \otimes Z_3)}$ for a 3 qubit system in a circuit using qiskit. I was thinking I could just perform an ...
4
votes
1answer
276 views

How to decompose a multi-target controlled gate?

I'm trying to replicate with qiskit the results of this paper in which basically they implement a quantum version of the Principal Component Analysis applying Quantum Phase Estimation algorithm in ...
1
vote
2answers
131 views

Problem with commutation of $e^{-iH_1t}$ and $e^{-iH_2t}$, where $H_1$ commutes with $H_2$

I'm given with a Hamiltonian, $H=H_1+H_2$, where $H_1=\sigma_x\otimes\sigma_z$ and $H_2=\sigma_y\otimes\sigma_y$, and want to built a circuit which will implement $e^{-iHt},t=\pi/6$. We see that as $\...
2
votes
1answer
89 views

Question Regarding Simulating Hamiltonian With Quantum Circuit

There have been a few other questions about this section of Nielsen and Chuang, but when working through the output of the circuit, there are some inconsistencies that are probably due to some mistep/...
2
votes
1answer
73 views

The maximum depth possible on quantum computers

I hope you don't mind me having two questions. Firstly, I was running a Qiskit HHL simulation on a 12x12 matrix and a 12x1 vector, leading to a 16x16 matrix after expansion, and it resulted in a ...
1
vote
1answer
41 views

Rotation of multi-body interaction in quantum circuit

In quantum circuit, how do you implement the rotation of multi-body interaction, such as $e^{-i\theta\sigma_z^1\sigma_z^2\sigma_z^3}$? I already know the case of less than two-body interaction, but I ...
2
votes
1answer
64 views

How to perform a time evolution of a quantum state with Qiskit Aqua?

How can we perform a time evolution of a quantum state for a given Hamiltonian with qiskit Aqua operator flow? I'm interested in it due to its higher efficiency.
1
vote
1answer
57 views

Is there a tool to get the quantum circuit corresponding to a sparse matrix?

If I know a sparse matrix, is there any tool that allows me to get the corresponding quantum circuit directly? If not what should I do? For example´╝îI want to try hamilton simulation and I have the ...
2
votes
1answer
34 views

How do I find the matrix and circuit equivalent to this transformation?

First I would like to find the matrix corresponding to the transformation and then implement it with rotational gates. How can I do it?
1
vote
1answer
28 views

Good book/paper for finding an ansatz via Trotterization?

Is there a good book or paper where they describe how to get the ansatz and gates from a Hamiltonian?
0
votes
0answers
7 views

How to implement the Mixer of Quantum Alternating Operator Ansatz for Max-Independent-Set

I am trying to implement the Mixer of the Max-Independent Set from The Quantum Alternating Operator Ansatz. From this paper: https://arxiv.org/pdf/1709.03489.pdf in Chapter 4.2 page 15 to 17. For ...