# Questions tagged [qaoa]

For questions about the Quantum Approximate Optimization Algorithm (QAOA), first introduced in Farhi, Goldstone, Gutmann 2014 (https://arxiv.org/abs/1411.4028).

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### Qiskit compute mean expectation value

I want to calculate the mean expectation value of an PauliSumOp within qiskit after I executed a QAOA Circuit. My approach is the following: ...
124 views

### Understanding QAOA from Basics/scratch

Recently after working on QAOA with finance and graph coloring problems. I have started exploring the QAOA from scratch. I would like to understand the QAOA derivation mathematically and have started ...
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### What are the important parameters when it comes to VQE algorithms in qiskit?

So I wrote an algorithm for a quadratic problem (qubo) and try to solve it. My question is why I don't get the correct results when running my algorithm on a quantum computer like IBM_manila. In the ...
478 views

### Why do we decompose the hamiltonian into Pauli strings to measure the expectation value?

Measuring the expectation value of a hamiltonian is an essential step in some algorithms like QAOA. I noticed that the procedure always starts with decomposing the hamiltonian into a sum of Pauli ...
148 views

### Why does QAOA's performance monotonically increase as p increases?

From A Quantum Approximate Optimization Algorithm - Farhi et al. The Quantum Approximate Optimization Algorithm has the key feature that as p increases the approximation improves. We contrast this to ...
145 views

### Why do we add the cost function as a phase in QAOA?

For QAOA, my understanding is that after we derive our cost Hamiltonian: $H_c|x$>$=C(x)x$ where $C(x)$ is the cost function on input x. We exponentiate it: $e^{-iH_c\theta}$, so we can simulate ...
112 views

### How to optimise QAOA

I have a similarly naive question about the classical part of the optimisation in the Quantum Approximate Optimization Algorithm. Specifically, the cost function is given prescribed as \begin{align} ...
406 views

### How to theoretically compare the complexity of quantum and classical algorithms?

I am working on reducing an NP class problem to a QUBO so can be solved with QAOA. I know that there is not a practical way to compare the performance as there is no QPU with enough qubits. I am doing ...
1 vote
239 views

### Tweak the parameter p of QAOA in qiskit

I am solving a QUBO using QAOA. It works flawlessly with default parameters for smaller instances of the problem, but my RAM is saturated when I try to solve a problem of size 15. I suspect this can ...
392 views

### QUBO defined in Qiskit/DOcplex: how to solve it using Pennylane?

I have a complex Integer Linear Programming model defined in DOcplex/Qiskit representing a combinatorial optimization problem. Using the Qiskit utils, it is possible to covert it to either an Ising ...
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### Statevector Simulation of QAOA always finds exact solution

My question is simple: does applying QAOA with a statevector simulation always result in a perfect solution? I'm trying to calculate the best $\gamma$ & $\beta$ that solve certain problems but my ...
396 views

### What exactly happening in QAOA in a general way?

So I know that in QAOA we have the two hamiltonians. Mixer and Cost Hamiltonian. Lets start: First we have our Qubits which get in the Superposition if we add the Hadamard Gate. Then we have the both ...
132 views

### IBM Qiskit QAOA gate implementation question

In section $5.2$ of the QAOA chapter in Qiskit textbook, section $5.2$, state preparation uses the gate $U_{k,l}(\gamma) = e^{\frac{i \gamma}{2} (1-Z_k Z_l)}$. Later, in section $5.3$, this gate is ...
1 vote
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### Will there be any difference in solution for a weighted and unweighted graph? I mean is there any relation between weight and solution?

I was working on max-cut problem. To do I have been given a graph of unweighted version, and I have to convert it into weighted version. I did it using qiskit. Now I was playing around the code, hence ...
2k views

### Qiskit: Taking a QUBO matrix into `qubit_op'

I'm trying to solve the maximum independent set problem using Qiskit and the QAOA. I've a nice QUBO Matrix for this simple path graph: as so: My question is, how do I convert this into a general ...
891 views

### Solving higher-order (unconstrained) binary optimization problems with QAOA without quadratization

I am aware that it's possible to use QAOA to solve QUBO problems. However, I've recently seen some sources mentioning the possibility of solving HOBO/HUBO problems using QAOA as well . While I ...
The QAOA algorithm consists of two elements: The outer loop, basically a classical optimization algorithm The quantum circuit, taking $2p$ parameters (where $p$ is the number of layers, where each ...