The title sounded interesting, so I read it during my travel time. First of all, it is a toy model with 4 nodes and the size is very small and the results are not good, but it is an interesting paper with an interesting approach. <h1>Experimental evaluation of quantum Bayesian networks on IBM QX hardware</h1><a href="https://arxiv.org/search/quant-ph?searchtype=author&amp;query=Borujeni%2C+S+E" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500);">Sima E. Borujeni </a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&amp;query=Nguyen%2C+N+H" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500);">Nam H. Nguyen </a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&amp;query=Nannapaneni%2C+S" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500);">Saideep Nannapaneni </a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&amp;query=Behrman%2C+E+C" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500);">Elizabeth C. Behrman </a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&amp;query=Steck%2C+J+E" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500);">James E. Steck </a><a href="https://arxiv.org/abs/2005.12474" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500);">https://arxiv.org/abs/2005.12474 </a> OverviewThis paper describes an IBM machine implementation of a Bayesian network model that expresses causality in terms of conditional probability, which is like implementing a quantum computer model that corresponds to the probability amplitude of a quantum computer, combining interest rates, markets, and the oil market to implement causality in stock prices. Problem SetupVery simple problem setup, IR is the interest rate, SM is the stock market, SP is the stock price, and OI on the right side is the oil industry. Each node takes 01 or some binary value, the probability of which is determined by the conditional probability of the previous node, and the table below shows the correspondence. The first node has a fixed probability of 01 for IR and OI, respectively. <img src="https://assets.blueqat.com/public/uploads/us-east-2:4805ff4b-c3cc-4344-b165-86544c34d0bf/2022/09/29/2005-12474-pdf (1).png"/><a href="https://arxiv.org/pdf/2005.12474.pdf" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500); background-color: rgb(255, 255, 255);">https://arxiv.org/pdf/2005.12474.pdf </a> Solving with Quantum CircuitsThe solution is simple: probability is implemented using RY gates. Conditional probabilities can also be implemented with CRY gates, allowing the angle of the CRY gate in the 0 and 1 cases to be adjusted. <img src="https://assets.blueqat.com/public/uploads/us-east-2:4805ff4b-c3cc-4344-b165-86544c34d0bf/2022/09/29/2005-12474-pdf2.png"/><a href="https://arxiv.org/pdf/2005.12474.pdf" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500); background-color: rgb(255, 255, 255);">https://arxiv.org/pdf/2005.12474.pdf </a> We want to achieve conditional probability when the previous node is 0. If it is 0, the CRY gate will not respond, so we intentionally apply X to make it 1, then let CRY act on it, and then use X to restore it. In the case of 1, there is no need to do anything, so we can simply apply CRY as it is. The overall circuit is as follows, with RY represented by U3 and CCX. The last part of the circuit seems to be a bit more complicated, but it looks like conditional probability is implemented one by one. The circuit structure is straightforward and I feel like I understand how a Bayesian network is implemented in this way. <img src="https://assets.blueqat.com/public/uploads/us-east-2:4805ff4b-c3cc-4344-b165-86544c34d0bf/2022/09/29/2005-12474-pdf3.png"/><a href="https://arxiv.org/pdf/2005.12474.pdf" rel="noopener noreferrer" target="_blank" style="color: var(--chakra-colors-blue-500); background-color: rgb(255, 255, 255);">https://arxiv.org/pdf/2005.12474.pdf </a> I think the highlight of the paper is the RY+CRY implementation of conditional probability for Bayesian networks. In practice, they still had a lot of trouble with errors, and the conclusion was that error correction was necessary, so I thought it might not be usable for a while as it is. That is all.

[paper review] Quantum computation of oil company stock prices using IBM's quantum computer in a Bayesian network.

Yuichiro Minato