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Questions tagged [ising-model]

For questions about the Ising model, which describes ferromagnetism in terms of interactions between nearest-neighbors in a lattice. Quantum computing may have some advantages in characterizing solutions to various Ising models.

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6 votes
2 answers
496 views

Map a 4-body Ising Hamiltonian to a 2-body Ising Hamiltonian

I wonder if there exists a way to map the square of a 2-body Ising Hamtiltonian (which will make it 4-body) back to a 2-body Hamiltonian that has the same ground state? Let me explain what I mean by ...
Turbotanten's user avatar
4 votes
1 answer
466 views

Understanding of the transverse-field Ising model

I want to make sure whether I do understand the transverse Ising model correctly or not. The classical Ising model describes the interaction between spins in a grid and the state of spins can be ...
Kai-Chun Lin's user avatar
4 votes
0 answers
88 views

Quantum Ising model correlation function query

In this paper on quantum Ising model dynamics, they consider the Hamiltonian $$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$ and the correlation function $$\mathcal{G}...
John Doe's user avatar
  • 911
3 votes
2 answers
442 views

Does QAOA require that the problem Hamiltonian be an Ising Hamiltonian as a quadratic function of the spin variables?

In the context of QAOA, I often see the problem Hamiltonian being called an "Ising Hamiltonian", and shortly after, I that the Hamiltonian is a quadratic function of the spin variables. Is ...
underdog987's user avatar
2 votes
1 answer
41 views

Optimizing SymPy Implementation of prime factorization in form of QUBO

I'm trying to reproduce a paper on Prime Factorization. This paper converts the problem into a QUBO form, which then we can map it to an Ising Minimizer. I've basically done everything, and I've ...
Amirhossein Rezaei's user avatar
2 votes
0 answers
47 views

Can we easily find the ground states for one-dimensional ANNNI-like Ising models?

The Hamiltonian for a simple one-dimensional Ising model on a finite (linear) chain of $L$ spin-half particles might be: $$H = -J \sum_{i=0}^{L-1} \sigma_i^z \sigma_{i+1}^z.\tag{1}$$ The interactions ...
Mark Spinelli's user avatar
1 vote
1 answer
99 views

Combinatorial optimization problem via VQE instead of QAOA

I'm studying about the hybrid quantum algorithms and I have a question about the VQE and QAOA. It seems like QAOA is a part of VQE that use a certain ansatz for solving combinatorial optimization ...
William's user avatar
  • 162
1 vote
1 answer
87 views

Fully connected transverse field Ising

Can someone explain to me what a "fully connected transverse field Ising" is ? I know what a classical Ising model is and I think the transverse term refers to the magnetic field being ...
Duen's user avatar
  • 436
1 vote
1 answer
194 views

(When) must the ground state of a frustrated Hamiltonian be entangled?

I've only recently, and still only haphazardly and rather poorly, begun to understand Ising models with local interactions. I'm interested in particular in the simple one-dimensional Ising model with ...
Mark Spinelli's user avatar
1 vote
1 answer
63 views

About the formulation of an Ising Hamiltonian

I am reading the paper from Andrew Lucas, Ising formulations of many NP problems, and I am stuck with the formulation of the following Ising Hamiltonian: $$H = A \bigg( K - \sum_v x_v \bigg)^2 + B\...
Laura's user avatar
  • 59
1 vote
1 answer
58 views

3D toric code (2D + measurement errors) has higher threshold error rate $p_{\text{th}}$ than 2D?

I am doing simulations of the toric code using the statistical mapping worked out by Preskill et al., Topological Quantum Memory, [arXiv:quant-ph/0110143], where we find the phase boundary of an Ising ...
JoJo P's user avatar
  • 348
1 vote
0 answers
29 views

Who is currently working on coherent Ising machines (classical analog devices)?

Can you share some papers on that subject? Review papers would be highly appreciated. What are limitations in terms of connectivity between different spins?
sycramore's user avatar
  • 325
1 vote
0 answers
25 views

Quantum optimization and correlation function

If one imagines the nodes of the classical weighted graph as atoms, and paths between them as bonding strength, then to find the shortest path in the weighted graph, can one also look at the minima/...
user avatar
1 vote
0 answers
66 views

Global (Ising) Gates and ZX-calculus representation

I could find from this source -- but also from other works on ZX-calculus -- the following extract: This looks to me as a generalisation of a 2-qubit Ising gate to an $n$-qubit global Ising gate. ...
Daniele Cuomo's user avatar
1 vote
0 answers
89 views

Compilation of IBM's kicked-Ising experiment in terms of Pauli rotations

I'm following this paper which classically simulates a kicked-Ising experiment, in response to IBM's recent Nature paper. The quantum circuit in question consists of alternating layers of $R_{ZZ}\left(...
jth's user avatar
  • 368
0 votes
0 answers
48 views

The X-Y Hamiltonian with Jordan-Wigner Transformation

While exploring the Hamiltonian of the x-y model within the framework of quantum mechanics, I encountered the following transformation using the Jordan-Wigner transformation (JWT): \begin{align} H_{xy}...
amirhoseyn Asghari's user avatar
0 votes
1 answer
37 views

Is there any another method for adjusting transverse field? (D'wave)

By using QUBO formula, I can't take in Transverse field equation I was tried using of annealing schedule but it was failed . Is there any another method for adjusting transverse field? (I want to get ...
Cha's user avatar
  • 1
0 votes
0 answers
24 views

What is the closest experimental platform to $H=\sum_{ij} J^X_{ij}X_iX_j+J^Y_{ij}Y_iY_j+J^Z_{ij}Z_iZ_j$?

Consider the Hamiltonian $$H=\sum_{ij} J^X_{ij}X_iX_j+J^Y_{ij}Y_iY_j+J^Z_{ij}Z_iZ_j$$ where $X,Y,Z$ are Pauli spin operators and $J_{ij}^\alpha$ are arbitrary couplings that can be positive and ...
Nichola's user avatar
  • 391
0 votes
0 answers
27 views

Difference in the Order of Applying Quantum Gates in Qiskit

I've been experimenting with Qiskit and came across a scenario where I'm uncertain about the effects of the order in which I apply quantum gates. Imagine we have the Hamiltonian Which one would be ...
Hakan Akgün's user avatar
0 votes
0 answers
28 views

Observable for Absolute Overall Magnetization of an Ising Model

I am currently following this tutorial for generating a phase transition plot that has been generated in the same tutorial. In this tutorial's magnetization ...
Zee's user avatar
  • 391