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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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Can QAOA be considered as simulation of a quantum annealer on a gate-based quantum computer?

Quantum annealers are single purpose machines allowing to solve quadratic unconstrained binary optimization (QUBO) problems. QUBO problems have following objective function: $$ F=-\sum_{i<j}J_{ij}...
Martin Vesely's user avatar
17 votes
1 answer
3k views

Is VQE a class of algorithms or a specific algorithm?

Is VQE a class of algorithms or a specific algorithm? For example, is QAOA a VQE or is VQE an algorithm distinct from QAOA that solves the same class of problems? If VQE is a specific algorithm, what ...
Malcolm Regan's user avatar
7 votes
2 answers
191 views

Quantum annealing - studies showing empirical evidence for better performance in comparison with classical computers

Currently, it is not known wheter quantum anneling or algorithms like VQE and QAOA for general purpose quantum computers bring about any increase in computational power. However, there are some ...
Martin Vesely's user avatar
5 votes
1 answer
982 views

How does the performance of QAOA and VQE compare to Grover's?

I believe finding the optimal solution is guaranteed for Grover's Algorithm along with quadratic speed-up according to Nielsen and Chuang's book. I wonder if there is any statement regarding QAOA and ...
John Parker's user avatar
  • 1,111
14 votes
1 answer
1k views

Why exactly are variational algorithms considered promising?

There is obviously a great deal of work happening at the moment on variational quantum algorithms. However, I'm struggling to understand why exactly are they considered promising? Looking through some ...
Nikita Nemkov's user avatar
10 votes
1 answer
670 views

Barren plateaus in quantum neural network training landscapes

Here the authors argue that the efforts of creating a scalable quantum neural network using a set of parameterized gates are deemed to fail for a large number of qubits. This is due to the fact that, ...
asdf's user avatar
  • 503
9 votes
1 answer
2k views

QUBO, Ising Hamiltonians and VQA

I understand that usually the combinatorial optimisation problems are turned into QUBO, which has a very simple mapping to Ising Hamiltonians. Ising Hamiltonians in turn have the desired properties of ...
karolyzz's user avatar
  • 279
8 votes
1 answer
4k views

What's the role of mixer in QAOA?

In QAOA algorithm, two terms are being discussed; 1) clause or cost (C) Hamiltonian and 2) mixer consisting of pauli X gates. What is the role of this mixer? Not clear why it comes after the C. ...
John Parker's user avatar
  • 1,111
4 votes
1 answer
468 views

Is the cost Hamiltonian unitary in QAOA?

I am trying to implement QAOA and there are things I don't understand at all. The expansion of $H$ into Pauli $Z$ operators can be obtained from the canonical expansion of the cost-function $C$ by ...
Himera Ephemera's user avatar
4 votes
1 answer
2k views

Calculating the ground states of an Ising Hamiltonian on a real quantum computer

I have followed this tutorial and based on it, I've written the following function in qiskit, which can explicitly calculate the ground states of a transverse-field Ising Hamiltonian. ...
EventicTortoise's user avatar
4 votes
1 answer
246 views

Derivation of QAOA from AQC

In adiabatic quantum optimization we start with an initial Hamiltonian $H_0$ and then adiabatically evolve from $H_0$ to $H_P$ (problem hamiltonian) for a time $T$ according to \begin{equation}\label{...
nuemlouno's user avatar
  • 177
3 votes
1 answer
189 views

To find the best angles in QAOA why we do not optimize over a maximum ofall shots instead of a mean?

When finding the best angles for QAOA we optimize over $F_{p}(\beta , \gamma) = \langle \psi_p(\gamma,\beta)|C|\psi_p(\gamma,\beta)\rangle $. In each optimization step we simulate the circuit $m$ ...
Hannah's user avatar
  • 529
2 votes
1 answer
305 views

How to do the direct evaluation by hand in QAOA algorithm

In QAOA algorithm, for $p=1$ layer of gates and at most degree $d=3$, the expectation value can be calculated by hand. I think I can convince myself the idea of commutability. In this qiskit example, ...
M. Chen's user avatar
  • 173
2 votes
2 answers
312 views

TranspilerError: 'Number of qubits (40) in QAOA is greater than maximum (30) in the coupling_map'

Hi Ive been trying to solve a custom PO problem using QAOA and I ran into this particular error. As per my understanding,this is due to the limitation of the simulation hardware. But as per the ...
Lasal Hettiarachchi's user avatar
2 votes
2 answers
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 ...
jolene's user avatar
  • 219
2 votes
1 answer
275 views

How to use Initial States in Qiskits QAOA?

The class QAOA from qiskit: https://qiskit.org/documentation/stubs/qiskit.aqua.algorithms.QAOA.html has the parameter initial_state from the type InitialState. https://qiskit.org/documentation/apidoc/...
Hannah's user avatar
  • 529
1 vote
1 answer
333 views

An effective way to submit all the jobs for VQE/QAOA at a time to an IBMQ machine?

In Qiskit, I am solving a VRP for 5 nodes and it creates 20 variables for a QUBO. It runs in a 65 qubit machines (any machine below that many fails). Now, in such a typical solvers for optimization (...
Amitava Chakraborty's user avatar
0 votes
1 answer
131 views

Best way to compute $\langle a|B|a \rangle$ in Cirq, where a is a state obtained running circuit A. And B is a different Quantum Circuit

I am implementing RQAOA in Cirq. After running regular QAOA to find an optimal state a (This I have done successfully). I need to calculate $\langle a|Z_iZ_j|a\...
GuusH's user avatar
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