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I view QAOA as an algorithm for solving (approximately) a special class of problems, namely combinatorial problems and VQE as a possible subroutine to QAOA (but not necessarily as in the case of MaxCut). Let me explain The VQE - Variational Quantum Eigensolver - solves the problem of approximating the smallest eigenvalue of some Hermitian operator $H$ which ...

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You're right in the sense that the cost unitary, which is composed of all the $Z$ and $CZ$ gates does not affect the underlying probabilities of measuring a specific state by itself, however when we apply the mixer (the layer of $Rx$ gates), the probabilities are changed, due to these added phases. Let's look at a basic example, to convince you that ...

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I think there are two ways that you could denote the same thing. The first is what is done here: $$\prod_{j =1}^n e^{-i \beta \sigma_j^x}$$ The second is $$\bigotimes_{j-1}^ne^{-i \beta \sigma^x},$$ which I imagine is what you're thinking of. In the first expression, note the subscript on the Pauli matrix. This means that it's an operator over all $n$ ...

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What motivated this construction is mentioned in the original paper (section VI): adiabatic quantum computing. This construction is basically a Trotterized version of the evolution by the time dependent hamiltonian: $$H(t) = (1-t/T)B + (t/T) C$$ where T is the total runtime. The Trotterized evolution consists of alternately applying $U_{C}$ and $U_{B}$. ...

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First: The paper references [37] for Levy's Lemma, but you will find no mention of "Levy's Lemma" in [37]. You will find it called "Levy's Inequality", which is called Levy's Lemma in this, which is not cited in the paper you mention. Second: There is an easy proof that this claim is false for VQE. In quantum chemistry we optimize the parameters of a ...

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There are a few ways to speed up this execution in Aqua. One way in the case of noiseless simulation is to use SLSQP instead of Cobyla, which we've noticed empirically seems to converge faster in noiseless environments. Another is to set skip_qobj_validation=True in the QuantumInstance init. I would start with these two and see how they do. QAOA in general ...

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One of the advantages, as stated in the paper you linked, is that with QAOA you can increase the precision arbitrarily, whereas QA will only find the solution with probability 1 as $T \to \infty$ which is impractical. In addition if $T$ is too long you're likely to not find the solution as the probability is not monotonic. I believe an example of this can be ...

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In the article you mentioned it is said that classical algorithms can beat some cases of (quantum ) QAOA's as is proved in this article. So finding cases where quantum QAOA can still beat classical algorithms and can run on NISQ devices with low depth circuits is still exciting and promissing. The article uses plausible conjectures from complexity theory to ...

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There is a parameter when instantiating a QuantumInstance() called skip_qobj_validation. This parameter is set to True by default. When creating the QuantumInstance, you can set it to False, and that will get rid of the warning. q_instance = QuantumInstace(skip_qobj_validation=False)

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That tutorial was recently updated. In it you'll find a more familiar way to declare and execute algorithms. ee = ExactEigensolver(qubitOp, k=1) result = ee.run() The problem section of the older declarative form of Aqua execution (which is gradually being moved away from) is a way for the Aqua UI to display a list of algorithms applicable to a user-...

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