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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47 views

How to calculate Alpha and Beta values for QAOA Max-cut problem manually?

I'm new to Quantum Computing. I came across solving the Max-cut problem using QAOA. For example, if I have a $U3$ gate with parameters $U3(0,0, \gamma_{XYZ})$ gamma parameter at $p=X$ between logical ...
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1answer
71 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 ...
3
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38 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 ...
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31 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 ...
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1answer
39 views

QAOA not returning solution for simple clustering problem

I am following University's of toronto QML course and there's a section where QAOA is applied to cluster a set of vectors by mapping the clustering problem into a Maxcut problem. Unfortunately qiskit'...
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1answer
111 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. ...
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1answer
105 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. ...
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23 views

QAOA Circuit for MWIS

Hi thanks for taking a quick look! I’ve got a question of how weights are implemented in the angles for gates in the QAOA. I'm trying to solve the Maximum Weighted Independent Set Problem This is the ...
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1answer
52 views

Why do we seek to maximise $F_{p}(\gamma, \beta)=\langle\gamma, \beta|H_{C}| \gamma, \beta\rangle$?

The question is simple: why do we seek to maximise $F_{p}(\gamma, \boldsymbol{\beta})=\langle\gamma, \boldsymbol{\beta}|H_{C}| \gamma, \boldsymbol{\beta}\rangle$? How does maximising this value ...
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1answer
48 views

Is there a matrix whose sum with the canonical Mixing Hamiltonian in Qaoa is proportional to the identity matrix?

Does there exist a Hermitian matrix, $K$ s.t $B^\prime = B + K$ satisfies $(B^\prime)^2 = c\cdot I$, where $B = \sum_{i=1}^{n}\sigma_x^{(i)}$, $\sigma_x^{(i)}$ is the Pauli X matrix acting on qubit $i$...
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1answer
56 views

How to create an observable: 'Identity \tensor Pauli gate' in Cirq

I am working on an implementation of the RQAOA algorithm on the Maxcut problem in Cirq. My graph G has n vertices. And after running a QAOA circuit with n qubits I obtain a state gammabeta (a vertical ...
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48 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\...
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2answers
103 views

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 ...
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2answers
135 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 ...
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1answer
82 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 ...
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47 views

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 ...
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2answers
203 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 ...
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35 views

Interpret graph nodes as qubits

I am trying implement MAXCUT using QAOA. I have a graph with edges defined by an edges set. My edges set looks a bit like this: ...
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113 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 [1][3]. While I ...
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134 views

Why does QAOA achieve quantum supremacy in an algorithmic sense?

In the paper Quantum Supremacy through the Quantum Approximate Optimization Algorithm the authors claim (last sentence of page 15): "If [...] the QAOA outperforms all known classical algorithms ...
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Properties of QAOA

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 ...
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1answer
66 views

Initial state definition for QAOA

There are a few options already discussed and suggested how to pass the initial state to the QAOA module. I tried all but no one works in my case. Maybe, there are any other ideas? So, I created the ...
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2answers
76 views

Quantum Machine Learning in NISQ era

I know that quantum algorithms can be useful for machine learning ("ML") methods, and vice versa. For example if we use QAOA we can use for the optimization part different types of ML ...
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37 views

Is the problem Hamiltonian in QAOA and AQC always a phase Hamiltonian?

In QAOA and AQC the problem Hamiltonian is always a Phase Hamiltonian (meaning only phases are added) Is that part of the QAOA and AQC definition or it is only used because it is convenient and work? ...
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1answer
61 views

Is $\gamma \in [0,2 \pi]$ or $\gamma \in [0,\pi]$ in $CU1(2\gamma)_{(i,j)} $?

When wanting to find the groundstate of this Hamiltonian with QAOA: \begin{equation} H_{C} =\sum_{i }^{n}(1 - Z_{i})/2 + \sum_{\{i,j\}\in \overline{E} } - 2(1 - Z_{i})(1 - Z_{j})/4 \end{equation} ...
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1answer
64 views

Qiskit: getting QAOA expectation

Suppose I run the Qiskit's QAOA algorithm. qaoa = QAOA(operator=qubit_operator, p=p, optimizer=optimizer) result = qaoa.run(quantum_instance) There is a built-in ...
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1answer
70 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/...
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124 views

Implemented QAOA returns wrong result

I try to apply QAOA algorithm to find minimal energy state of the Hamiltonian: $H_A = \frac{1}{2}\sigma_z^1 + \frac{1}{2}\sigma_z^1\sigma_z^2$ It is expected that with p=2 my variational should ...
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1answer
78 views

Why QAOA with $p \rightarrow \infty $ gives the optimal solution?

In the QAOA paper, it is shown that the optimal value of the p-ansatz $M_p$ converges to $\max_z C(z)$ as $p \rightarrow \infty$ on page 10. The proof is to relate to QAOA by considering the time-...
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1answer
71 views

Can QAOA solve a constraint optimization problem?

Can QAOA solve a constraint binary optimization problem? QAOA is short for Quantum Approximate Optimization Algorithm. I read the information https://qiskit.org/textbook/ch-applications/qaoa.html. But ...
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247 views

qiskit: Traveling Salesman Problem using QAOA fails for more than 3 cities

I tried to implement the traveling salesman problem (TSP) using QAOA with qiskit. I worked with this qiskit QAOA tutorial and this qiskit minimum eigen optimizer tutorial, where they implement a TSP ...
2
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1answer
85 views

Decomposition of 2-qubit Hamiltonian into standard gate set for QAOA

I try to decompose ansatz into gate set in order to create a circuit in qiskit for QAOA algorithm. I don't understand how represent parametrized 2 qubit ansatz as circuit. $ H{_B} = \sum_{j=1}^{n} {\...
2
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1answer
67 views

Why does the problem Hamiltonian of QAOA always consist of $Z$ and $I$ gates?

I noticed that in QAOA the problem hamiltonian always consists of $Z$ and $I$ gates. But isn't QAOA a form of Adiabatic Programming? Where the idea is just to go from one ground state to another? Does ...
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1answer
54 views

Classical optimisation of angles in QAOA for TSP gets stuck in local minima?

I have been trying to implement a QAOA for solving a traveling salesman problem (TSP) using qulacs and python. However, even for ...
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52 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 ...
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1answer
68 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 $m$ ...
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1answer
79 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 ...
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2answers
71 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 ...
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1answer
69 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 ...
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41 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 ...
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1answer
65 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?
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1answer
157 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 ...
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1answer
342 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 ...
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1answer
83 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 (...
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1answer
142 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}...
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1answer
160 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
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1answer
143 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: ...
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32 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 ...
2
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1answer
81 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 ...
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63 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 ...