Linked Questions

4 votes
1 answer
143 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 ...
user39726's user avatar
4 votes
1 answer
442 views

Is the cost Hamiltonian unitary in QAOA?

I am trying to implement QAOA and there are things I don't understand at all. The expansion of $H$ into Pauli $Z$ operators can be obtained from the canonical expansion of the cost-function $C$ by ...
Himera Ephemera's user avatar
4 votes
1 answer
366 views

Simulate Hamiltonians with Pauli operations (controlled time evolution)

I had a question last week regarding the simulation of Hamiltonians composed of the sum of Pauli products: How can I simulate Hamiltonians composed of Pauli matrices? I'm having a follow-up question: ...
ZR-'s user avatar
  • 2,388
3 votes
1 answer
814 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 ...
Marion's user avatar
  • 625
3 votes
1 answer
540 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/...
Rehaan Ahmad's user avatar
2 votes
1 answer
245 views

Showing that $e^{i \sigma_z \otimes \sigma_z t} = \text{CNOT}(I \otimes e^{i \sigma_zt})\text{CNOT}$

While working on circuit construction for Hamiltonian simulation using this answer as reference, I'm unable to see how the following equation is true: $$ e^{i \sigma_z \otimes \sigma_z t} = \text{CNOT}...
epelaez's user avatar
  • 2,875
2 votes
1 answer
264 views

Decomposition of 2-qubit Hamiltonian into standard gate set for QAOA

I try to decompose ansatz into gate set in order to create a circuit in qiskit for QAOA algorithm. I don't understand how represent parametrized 2 qubit ansatz as circuit. $ H{_B} = \sum_{j=1}^{n} {\...
Masamune's user avatar
2 votes
1 answer
120 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?
Schrödinger314's user avatar
2 votes
1 answer
140 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,I want to try hamilton simulation and I have the ...
Despriobaby's user avatar
2 votes
1 answer
436 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 ...
Luca 's user avatar
  • 35
2 votes
1 answer
119 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?
Nobrega's user avatar
  • 33
1 vote
1 answer
326 views

In the HHL alghoritm, how can I transform my hermitian matrix into a unitary operator?

I'm studying the HHL algorithm and I'm trying to do an his implementation but, there are some points that I don't understand how I can transform my hermitian Matrix into its unitary operator? In ...
Simona99's user avatar
  • 180
1 vote
1 answer
108 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 ...
sotowa's user avatar
  • 131
2 votes
0 answers
74 views

From QUBO problem to quantum circuit [duplicate]

Can you describe how to convert some QUBO problem $$f(x_1, ..., x_n) = \sum\limits_{1 \le i < j \le n} \alpha_{i,j} \, x_i \, x_j$$ into its equivalent quantum circuits? Is it preferrable to start ...
incud's user avatar
  • 701
2 votes
0 answers
95 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 ...
Hannah's user avatar
  • 529

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