Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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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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 either +1 or -1. The transverse-field Ising model…
Kai-Chun Lin
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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 an example. Suppose we have the following 2-body…
Turbotanten
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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} = \langle…
John Doe
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Is QUBO formulation actually useful for solving real-world problems?

Combinatorial optimization is often mentioned as a potential application of quantum computers. One of the main paradigms here is to reduce combinatorial optimization to an Ising problem, which is mathematically known as QUBO (quadratic unconstrained…
Nikita Nemkov
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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 obtained the final QUBO expression of page 3. My only…
Amirhossein Rezaei
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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 this required? If I tried to optimize a function of boolean…
underdog987
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How to map QUBO to Ising and account for the sign change in non-diagonal elements?

A question that has been bugging my mind in quantum annealing is: Assume we have a QUBO matrix $Q_{ij}$ with non-zero non-diagonal elements which have different signs, that is $Q_{ij}<0$ for some $i\neq j$ and $Q_{nm}>0$ for some $m\neq n$. How can…
Nikolaos Petropoulos
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What does a solvable Hamiltonian model mean?

I have recently been reading about simulating the dynamics of many body Hamiltonians by means of quantum computers and I am a bit confused about some terminology. I understand that if you are able to compute the eigenvalues and eigenvectors of an…
Josu Etxezarreta Martinez
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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. Especially considering that the 2-qubit case admits…
Daniele Cuomo
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(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 nearest and next-nearest neighbor interactions,…
Mark Spinelli
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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 are between adjacent qubits in the lattice. …
Mark Spinelli
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Determining the J matrix of the ISING Hamiltonian

I am reading from the paper of Utkarsh et al., Solving Vehicle Routing Problem Using Quantum Approximate Optimization Algorithm (arXiv). And I couldn't quite understand the notation to which the authors describe the formulation of the J matrix in…
yousef elbrolosy
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A highly space-efficient embedding of prime factorization problem using the Ising model

What's the idea? I'm trying to embed the prime factorization problem into the form of a PUBO. To do so, let $p$ and $q$ be two real positive numbers. We can represent these two numbers as binary numbers, which itself can be represented as vectors,…
Amirhossein Rezaei
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How does measurement based quantum computing (MBQC) behave under error propagation?

In the quantum circuit model, we know how to handle error propagation if we implement a unitary $U'$, which is $\varepsilon$-close to the ideal unitary $U$ and a state $|\psi'\rangle$, which is also $\varepsilon$-close to the ideal state…
Blau
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Converting a Quartic Term into Quadratic Form in QUBO for Prime Factorization

This is a continuation of this question and I encourage you to read that as well. I'm trying to embed the prime factorization problem into the form of a QUBO. To do so, let $p$ and $q$ be two real positive numbers. We can represent these two numbers…
Amirhossein Rezaei
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