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).

Filter by
Sorted by
Tagged with
2
votes
0answers
27 views

In QAOA why do we need $m \log(m)$ repititions to get at least $F_{p}(\beta , \gamma) - 1$ with probability of $1 - 1/m$?

In the original QAOA paper from Farhi https://arxiv.org/pdf/1411.4028.pdf, it is stated in chapter 2 last paragraph (page 6) that: when measuring $F_{p}(\beta , \gamma)$ we get an outcome of at least ...
2
votes
1answer
19 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 $m$ ...
4
votes
1answer
34 views

In QAOA, why do we pick the initial Hamiltonian $B$ to be $\sigma_x$ applied to each qubit?

In QAOA 1, why do we pick the initial Hamiltonian $B$ to be $\sigma_x$ applied to each qubit? Would it be possible to pick $B$ to be an application of $\sigma_z$'s instead? Then $C$ and $B$ would be ...
1
vote
2answers
44 views

Quantum Approximate Optimization Algorithm for $p=1$

I was running instances of $3$-regular graphs with small number of vertices on Qiskit, and for $p=1$ the algorithm was giving always the exact solution for the MaxCut problem, after optimizing the ...
2
votes
1answer
43 views

Optimum Solution calculation for QAOA

In QAOA, for the MaxCut problem, one tries to find a good ratio, as close to 1 as possible, of $\epsilon = \frac{C_{approx}}{C_{opt}}$, where $C_{approx}$ is the approximate value of the cost function ...
1
vote
0answers
27 views

How to implement the Mixer of Quantum Alternating Operator Ansatz for Max-Independent-Set

I am trying to implement the Mixer of the Max-Independent Set from The Quantum Alternating Operator Ansatz. From this paper: https://arxiv.org/pdf/1709.03489.pdf in Chapter 4.2 page 15 to 17. For ...
2
votes
1answer
42 views

Papers on classical optimization in QAOA

Are there any papers on the classical optimization part of QAOA? What is the most efficient method now? And how is the classical optimization classified?
2
votes
1answer
86 views

How to solve QUBO problems in Q#?

Short version: I'm trying to solve a traveling salesman problem very similar to the traveling Santa example here: http://quantumalgorithmzoo.org/traveling_santa/, which is also included in the samples ...
4
votes
1answer
84 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 ...
1
vote
1answer
46 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 (...
2
votes
1answer
55 views

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}...
0
votes
1answer
63 views

Custom Mixer for QAOA: Error 'Operator' object has no attribute 'primitive_strings'

I like to use as custom Mixer Hamiltonian for solving the TSP using QAOA. The mixer and cost hamiltonians are described here: https://arxiv.org/pdf/1709.03489.pdf - Chapter 5.1. Therefore I need to ...
3
votes
1answer
70 views

How does the classical optimization of the angles $\gamma$ and $\beta$ in QAOA work?

I have been trying to implement QAOA with classical optimization of the angles $\gamma$ and $\beta$, but I I'm failing at the classical part. In paper Quantum Approximate Optimization Algorithm: ...
0
votes
0answers
23 views

How to construct Hamiltonian for combinatorial optimization problems and then convert into Pauli basis?

Suppose I have a portfolio optimization problem where I have to minimize, $$qx^T\sum x - \mu^Tx$$ where q is the maximum risk and x is {0,1}^n and $\mu$ are the expected returns. Now I have to convert ...
1
vote
1answer
58 views

Quantum Circuit Optimization with Machine Learning [closed]

I read some paper about Quantum Circuit Optimization but I am on a low level. And have some experience in ML. But what I don't understand is it possible that ML can help to optimize Quantum Circuits ...
1
vote
0answers
43 views

Deriving Expression For QAOA Optimal Trial State Parameters

I am going through the QAOA section in the Qiskit Textbook - QAOA and am stuck in one of the steps. In section 5.2, the method for getting the Optimal Trial State Parameters are discussed. I do not ...
1
vote
1answer
68 views

What is meant by “local minimum” in QAOA?

I am trying to understand what exactly happens in QAOA. I am reading this blog which says, We would be just repetitively applying $U_C$. But once we got into a state which is the eigenstate of $H_C$ ...
0
votes
1answer
79 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, ...
2
votes
0answers
34 views

What is the implication of locality in QAOA?

Suppose I am solving the TSP formulated as a QUBO problem using QAOA. I understand from the original paper that there is a parameter $p$ which sets the number of steps used in thealternating ansatz. ...
2
votes
1answer
110 views

Why do we transform a Boolean variable into a a Pauli Z matrix

Under Qiskit QAOA's tutorial (https://qiskit.org/textbook/ch-applications/qaoa.html), the authors specify that a cost function $C(x)$ representing the optimization objective of a Binary Combinatorial ...
4
votes
1answer
54 views

Resource recommendation on quantum simulations

I would like to know more about quantum simulations, so as to start on a few standard physical models (maybe particle in a box, harmonic oscillator, etc.) and then build up on more complex things. But ...
0
votes
0answers
44 views

QAOA with Qiskit: Is the initial state affected by the noise model?

I'm doing a simulation of the QAOA algorithm with noise via the QAOA class of Qiskit 0.19. Here's (part of) my code: ...
1
vote
1answer
66 views

Evaluated Standard deviation during QAOA/VQE optimization is always zero. Qiskit 0.19

I'm using qiskit 0.19.1, and I'm doing some simulation of QAOA, using the aqua class QAOA. I use a callback function in my program to see energy and std during optimization, but the evaluated standard ...
1
vote
0answers
28 views

Is there a limit to the size of problems that your simulators can run on Qiskit Aqua?

I'm trying to solve QUBO problems using Qiskit QAOA and VQE solvers. However, I have the experience that I can only solve small problems. I tried with both QAOA and VQE and both experience the same ...
0
votes
1answer
232 views

VQE for Beginners : Using Tutorial and Cirq

I have been following this tutorial: https://dkopczyk.quantee.co.uk/vqe/ I am using Cirq to try to teach myself VQE, replicate their results, and also try to understand more about ansatz for ...
3
votes
1answer
57 views

QAOA Belongs into VQE or the other way around?

I have been reading a couple of papers in the arxiv and wanted to get a clarification regarding the relation between these two methods; is one a subset of the other?
2
votes
1answer
56 views

What does the maximum of a Hamiltonian means (in a particular paper)?

In the paper Quantum Observables for continuous control of the Quantum Approximate Optimization Algorithm via Reinforcement Learning, an Hamiltonian is defined in order to solve the MAXCUT problem : $...
2
votes
1answer
96 views

What does the notation $U(B,\beta) = \prod_{j =1}^n e^{-i \beta \sigma_j^x} $ mean in the context of QAOA?

In the article Quantum Observables for continuous control of the Quantum Approximate Optimization Algorithm via Reinforcement Learning, the following notation is used to describe an Unitary operation ...
1
vote
1answer
74 views

VQE with error dim. mismatch using qiskit.aqua.vqe

when i try to call the VQE from qiskit I get an error of dimmismatch. The input matrix is of a 16x16 shape and I could not find out what where I introduce the error. In the picture The input matrix ...
3
votes
1answer
135 views

QAOA for MaxCut - Algorithm motivation

In the QAOA algorithm for MaxCut, the authors construct a very specific scheme where the qubits (corresponding to the vertices of the graph) are transformed using a sequence of unitaries $$|\gamma, \...
3
votes
0answers
82 views

Quantum algorithms, combinatorial optimization, and approximation bounds

Recently, I saw this article, Classical and Quantum Bounded Depth Approximation Algorithms where the author discusses the limitations of QAOA relative to classical approaches. In particular, they ...
8
votes
1answer
329 views

Is there a mistake in the VQE Ansatz in Cirq's tutorial?

I have been going through Cirq's VQE background tutorial and after examining the Ansatz it seems to me that the only layer that actually affects the final measurement is the rot_x_layer. The other ...
7
votes
1answer
1k 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 ...
2
votes
1answer
155 views

QAOA Maxcut for larger qubits

I am using QAOA to solve maxcut problem. It takes a very long time to simulate 10 qubits and I never get the results. Is there a way to simulate faster for larger qubit? Here is my code ...
1
vote
1answer
459 views

Backend Warning: The skip Qobj validation does not work for IBMQ provider. Disable it

I am using QAOA to solve the max-cut problem. On my machine, 10 qubits already takes a minute or two to simulate. I'm hoping that the ibmq-qasm-simulator could simulate 32 qubits faster than my laptop ...
1
vote
1answer
189 views

How to understand run_algorithm() inputs in qiskit

I'd like to better understand the Max-Cut algorithm from the qiskit tutorials. Particularly, the run_algorithm function inputs. The inputs are two dictionaries, but I can't find any documentation or ...
3
votes
1answer
86 views

How does the fact that the output of a quantum circuit cannot be efficiently simulated classically help for optimisation?

This question refers principally to the article where for a low-depth circuit QAOA, the output cannot be efficiently simulated classically. I am wondering how this kind of quantum supremacy matters ...
3
votes
0answers
60 views

QAOA and symmetry effects on the angles

In this paper, QAOA on Maxcut shows symmetries that allow them to restrict their search space intervals. But how do they find such intervals knowing that in the original QAOA angles $\gamma,\beta$ are ...
9
votes
1answer
412 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, ...
9
votes
1answer
1k views

What is the difference between QAOA and Quantum Annealing?

Edward Farhi's paper on the Quantum Approximate Optimization Algorithm introduces a way for gate model quantum computers to solve combinatorial optimization algorithms. However, D-Wave style quantum ...