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5 votes
Accepted

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

There is a technique known as perturbation gadgets (google the term and you'll find plenty of papers) about how to build many-body operations using two-body ones. The key is introducing some ancilla ...
DaftWullie's user avatar
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4 votes
Accepted

Combinatorial optimization problem via VQE instead of QAOA

VQE is more general algorithm allowing to look for ground state of a general Hamiltonian. On the other hand, QAOA is intended only for finding ground state of Ising Hamiltonian. So, we can say that ...
Martin Vesely's user avatar
3 votes

Fully connected transverse field Ising

I would guess that it means $$ H=\sum_{n=2}^N\sum_{m=1}^{n-1}Z_nZ_m+\lambda\sum_{n=1}^NX_n, $$ i.e. the Ising terms act between every pair of qubits.
DaftWullie's user avatar
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3 votes
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(When) must the ground state of a frustrated Hamiltonian be entangled?

In the Ising model, I don't think frustration is the key feature. Let's start with an arbitrary Ising model with no transversal field. (I'll let you have arbitrary interactions, and arbitrary ...
DaftWullie's user avatar
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3 votes

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

QAOA can be applied to Ising models that contain higher order terms; see this paper and this paper. QAOA applied to higher order Ising models does not necessarily require the use of ancilla qubits, ...
Elijah Pelofske's user avatar
2 votes

About the formulation of an Ising Hamiltonian

The square comes from the definition of the Hamilton $H_A$ given in equation (8) of the referenced paper. This term is described by "... is an energy which provides a penalty if the number of ...
Mathias's user avatar
  • 133
2 votes

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

Hard to say where you're going wrong, but indeed, introducing measurement errors into the system should make $p_{\text{th}}$ lower. One helpful reference might be the following phase diagram computed ...
squiggles's user avatar
  • 965
2 votes

Understanding of the transverse-field Ising model

Your Hamiltonian is not transverse. In your Hamiltonian, your magnetic field monomial $-\sum_{i}h_{i}\sigma_{i}^{z}$ is in the same direction as (longitudinal with) your interaction terms $-\sum_{ij}...
Mark Spinelli's user avatar
1 vote

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

The answer by DaftWullie is useful for more general Hamiltonians, but since you are working specifically with the Ising Hamiltonian, then you do not need auxiliary qubits or perturbations which are ...
user1271772 No more free time's user avatar
1 vote

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

QAOA is designed to work with Ising Hamiltonians only. This means that the algorithm can be employed for optimization of only quadratic problems which are related directly to Ising Hamiltonians. ...
Martin Vesely's user avatar

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