# Rec

Pseudo-inverse and projection matrices Pseudo-inverse and projection matrices are also often used in recommendation systems, so I’ll make a note of them. github The file in jupyter notebook format is here . google colaboratory If you want to run it in google colaboratory here Author’s environment The author’s OS is macOS, and the options are different from Linux and Unix commands. !sw_vers ProductName: Mac OS X ProductVersion: 10.
Singular value decomposition and low-rank approximation I am going to summarize my knowledge of linear algebra, which is mainly needed to understand recommendation systems. The user-item matrices (preference matrices) used in recommendation systems are often discussed under the assumption that low-rank approximations hold. It is based on the implicit assumption that users can often be classified into a finite number of clusters. For example, even if there are one million users of all book e-commerce sites, it is possible to categorize them to some extent, such as users who often buy programming books, users who buy math books, users who buy medical books, and users who buy weekly magazines.
HHL algorithm I am going to study quantum algorithms in my own way using qiskit. Since this is a record of my personal study, I may have left out a lot of explanations. I am following the qiskit website. https://qiskit.org/textbook/ja/ch-applications/hhl_tutorial.html The reason why qiskit was categorized as a Rec (recommendation system) in my blog was all to understand HHL. Currently, I am interested in recommender systems and am developing them.
Grover’s algorithm I will be using qiskit to study quantum algorithms in my own way. Since this is a record of my personal study, I may have left out a lot of explanations. I am following the qiskit website. https://qiskit.org/textbook/ja/ch-algorithms/quantum-phase-estimation.html Grover’s algorithm is famous for its ability to perform search problems very fast. For the search problem of an array with a normal list structure, performing a sequential search requires a computation time of $O(1)$ in the best case and $O(N)$ in the worst case.
Shore’s algorithm I will be using qiskit to study quantum algorithms in my own way. Since this is a record of my personal study, I may have left out a lot of explanations. I am following the qiskit website. https://qiskit.org/textbook/ja/ch-algorithms/quantum-phase-estimation.html I would like to proceed to the Shore algorithm, which has the potential to break the RSA cipher, where quantum computers are expected to have the biggest impact. The RSA currently used in web systems is easy to calculate the product of two primes, but the inverse factorization takes $O(N)$ of computation, and nowadays, at 1000 bits (about 300 digits), it takes as much time as the history of the universe, even with a supercomputer, making it practically impossible This means that it is practically impossible.
Quantum phase estimation I am going to use qiskit to study quantum algorithms in my own way. This is a record of my personal study, so I may have left out a lot of explanations. I am following the qiskit website. https://qiskit.org/textbook/ja/ch-algorithms/quantum-phase-estimation.html Let’s study quantum phase estimation, which is the most important quantum algorithm. It is used in a variety of algorithms and understanding it is essential. It is a combination of phase kickback and quantum Fourier inversion, and estimates the eigenvalues of an eigenvector for a unitary operator (its phase).
Quantum Fourier transform I’m going to study quantum algorithms in my own way using qiskit. This is a record of my personal study, so I may have left out a lot of explanations. I am following the qiskit website. https://qiskit.org/textbook/ja/ch-algorithms/quantum-fourier-transform.html Next, let’s review the quantum Fourier transform. I thought I understood it when I was in school, but I’ve completely forgotten it, so I’m going to have to relearn it from scratch.
Simon’s algorithm I’m going to use qiskit to study quantum algorithms in my own way. Since this is a record of my personal study, I may have left out a lot of explanations. I am following the qiskit website. https://qiskit.org/textbook/ja/ch-algorithms/simon.html In this article, I will try to understand Simon’s algorithm by following the formula. The difference is that Simon’s algorithm determines whether the function $f(x)$ is a 1:1 function or a 2:1 function.
Dioichi-Josa’s algorithm I will be using qiskit to study quantum algorithms in my own way. Since this is a record of my personal study, I may have left out a lot of explanations. I am following the qiskit website. https://qiskit.org/textbook/ja/ch-algorithms/deutsch-jozsa.html In this article, I will try to deepen my understanding of the Doichi-Josa algorithm by following the formulas. It is my lack of study, but when I studied quantum information as a student, I did not know about the Doychi-Josa algorithm.
PageRank and Google matrix I recently had to look up PageRank and Google Matrices, so I’ll try to summarize them for your notes. The textbook is as follows, and the expressions of the formulas are also adapted from this. The Mathematics of Google PageRank - In Search of the Most Powerful Search Engine Ranking Method I actually bought this in 2013 (8 years ago), and it had been lying on