How is qaoa different from Goemans-Williamson algorithm?

How is qaoa different from Goemans-Williamson algorithm?

Unlike Goemans-Williamson algorithm, QAOA does not come with performance guarantees. QAOA takes the approach of classical approximate algorithms and looks for a quantum analogue that will likewise produce a classical bit string x ∗ that with high probability is expected to have a good approximation ratio α.

What kind of noise occurs during final measurement?

A simpler form of noise is that occurring during final measurement. At this point, the only job remaining in the circuit is to extract a bit string as an output. For an n n qubit final measurement, this means extracting one of the 2n 2 n possible n n bit strings.

How is measurement error mitigation done in Qiskit?

In Qiskit we mitigate for the noise by creating a measurement filter object. Then, taking the results from above, we use this to calculate a mitigated set of counts. Qiskit returns this as a dictionary, so that the user doesn’t need to use vectors themselves to get the result.

Which is the formula for the Hamiltonian in qaoa?

H = ∑ ( j, k) ∈ E1 2(1 − ZjZk). This means that the Hamiltonian can be written as a sum of m = | E | local terms ˆCe = 1 2(1 − Ze1Ze2) with e = (e1, e2) ∈ E.

How is the classical cost function written in qaoa?

Here Zi is read as the Pauli Z operator that acts on qubit i and trivial on all others, i.e. Zi = (1 0 0 − 1). This means that the spin Hamiltonian encoding the classical cost function is written as a | Q | – local quantum spin Hamiltonian only involving Pauli Z – operators.

How is qaoa used to solve combinatorial optimization problems?

QAOA takes the approach of classical approximate algorithms and looks for a quantum analogue that will likewise produce a classical bit string x ∗ that with high probability is expected to have a good approximation ratio α. Before discussing the details, let us first present the general idea of this approach.

How to find the maximal string in qaoa?

We want to find the n-bit string x for which C(x) is the maximal. This cost function can be mapped to a Hamiltonian that is diagonal in the computational basis. Given the cost-function C this Hamiltonian is then written as where x ∈ {0, 1}n labels the computational basis states | x⟩ ∈ C2n.

How to calculate the global profit function in qaoa?

By assigning xi = 0 or xi = 1 to each node i, one tries to maximize the global profit function (here and in the following summations run over indices 0,1,…n-1) C(x) = n ∑ i, j = 1wijxi(1 − xj). To simplify notation, we assume uniform weights wij = 1 for (i, j) ∈ E.