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Based on comment by DaftWullie and my experience with the algortihm, it seems that a title of the article is misleading. The authors claim that algorithm they proposed is efficient. However, this is true only partialy. The authors devised only part of an algorithm for solving TSP. In particular, they are able to calculate length of a Hamiltonian cycle ...


2

One thing that I noticed. If cu3 gate from $q[2]$ to $q[0]$ is some $U$, then the cu3 from $q[2]$ to $q[0]$ should be $U^2$ in the phase estimation algorithm, but the comparisons of operators with the help of numpy.array showed me that it's not true here. I tried to implement by replacing cu3 part of the QASM code with the following: cu3(1.6, -1.12, 2.03) q[...


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The objective of the portfolio optimization problem is to trade off expected return ($\mu^T x$) with the risk taken ($x^T \Sigma $x). This could be achieved by introducing a constraint on the risk, e.g. $x^T \Sigma x \leq R$, for an acceptable risk level $R$ and then maximize the return under this constraint. However, this is not a QUBO, i.e., it cannot be ...


2

I have not read the full details of the paper, but have attempted to skim over the most relevant bits to the question (i.e. I could easily have missed something). As I read the paper, they are doing some calculation with a fixed size of input, and they repeat it many times (see equation 58). They ask how many times do you have to repeat it to get the same ...


2

Hamiltonian is the basic building block for VQE algorithm. Basically, we try to minimize the expectation of the Hamiltonian to find the lowest eigenvalue of the Hamiltonian matrix which is apparently very useful for many problems ranging from chemistry to finance. Find more details on: https://arxiv.org/pdf/1907.04769.pdf


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I changed the stock parameter to a list of strings and added the line stockmarket = StockMarket.NASDAQ as such: num_assets = 4 # Generate expected return and covariance matrix from (random) time-series stocks = ['MSFT', 'DIS', 'NKE', 'HD'] data = WikipediaDataProvider( token="xeesvko2fu6Bt9jg-B1T", ...


1

The budget constraint is only added as a penalty term (multiplied by ‘penalty’ coefficient) in the Hamiltonian and does not enforce equality. This means the objective function is $$ \text{min}_{x\in\{0,1\}^n} \hspace{0.5em} q x^T \Sigma x - \mu^T x + \text{penalty} \cdot (B - 1^T x)^2$$


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Several quantum circuit representations for common distributions are given in uncertainty models. For generic probability distributions, you can train a quantum circuit representation using quantum generative adversarial networks. For a respective tutorial, please see here.


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The quick answer to your problem is to install Qiskit Aqua directly from GitHub instead of via pip. On the lastest master version, this bug is fixed. You can do this using git clone https://github.com/Qiskit/qiskit-aqua cd qiskit-aqua pip install . more detailed instructions are given on Qiskit's webpage. As to why you're getting this error: This comes ...


1

The Ising model is a formulation of your problem. Variables are variables $s_i$ that can take +1/-1 values. $$ \begin{equation} \text{E}_{ising}(s) = \sum_{i=1}^N h_i s_i + \sum_{i=1}^N \sum_{j=i+1}^N J_{i,j} s_i s_j \end{equation} $$ For a quantum form, we use spin operators $\sigma^z$, giving you an Ising Hamiltonian, whose eigenvalues correspond to the ...


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Please have a look at article Transformation of quantum states using uniformly controlled rotations, chapters 1 and 2. These provides you with construction of general rotation gate controlled by $n$ qubits with different rotations angles for each basis state $|x\rangle$. You also might be interested in some of these articles on quantum computers application ...


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There are many Qiskit notebooks on quatum computers application in different areas, including finance, in IBM Q web interface. For application in finance, click on icon Qiskit Notebooks, then folder Advanced -> Aqua -> Finance. Here is also website dedicated to quantum computing application in finance: Quantum for Quants.


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There are tutorials for a lot of the Qiskit Aqua functions kept in the tutorials repository, and I think this talks about the finance problem you are interested in. All of these tutorials are also available on the IBM Q Experience where you can run them in a browser.


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