In recent years, quantum computers and Shor quantum algorithm have posed a threat to current mainstream asymmetric cryptography methods (e.g. RSA and Elliptic Curve Cryptography (ECC)). Therefore, it is necessary to construct a Post-Quantum Cryptography (PQC) method to resist quantum computing attacks. Therefore, this study proposes a PQC-based neural network that maps a code-based PQC method to a neural network structure and enhances the security of ciphertexts with non-linear activation functions, random perturbation of ciphertexts, and uniform distribution of ciphertexts. In practical experiments, this study uses cellular network signals as a case study to demonstrate that encryption and decryption can be performed by the proposed PQC-based neural network with the uniform distribution of ciphertexts. In the future, the proposed PQC-based neural network could be applied to various applications.

An overarching milestone of quantum machine learning (QML) is to demonstrate the advantage of QML over all possible classical learning methods in accelerating a common type of learning task as represented by supervised learning with classical data. However, the provable advantages of QML in supervised learning have been known so far only for the learning tasks designed for using the advantage of specific quantum algorithms, i.e., Shor's algorithms. Here we explicitly construct an unprecedentedly broader family of supervised learning tasks with classical data to offer the provable advantage of QML based on general quantum computational advantages, progressing beyond Shor's algorithms. Our learning task is feasibly achievable by executing a general class of functions that can be computed efficiently in polynomial time for a large fraction of inputs by arbitrary quantum algorithms but not by any classical algorithm. We prove the hardness of achieving this learning task for any possible polynomial-time classical learning method. We also clarify protocols for preparing the classical data to demonstrate this learning task in experiments. These results open routes to exploit a variety of quantum advantages in computing functions for the experimental demonstration of the advantage of QML.

There are important algorithms built upon a mixture of basic techniques described; for example, the Fast Fourier Transform (FFT) employs both Divide - and - Conquer and Transform - and - Conquer techniques. In this article, the evolution of a quantum algorithm (QA) is examined from a n information theory viewpoint. The complex vector entering the quantum algorithmic gate - QAG is considered as an information source both from the classical and the quantum level. The analysis of the classical and quantum information flow in Deutsch - Jozsa, Shor and Grover algorithm s is used. It is shown that QAG, based on superposition of states, quantum entanglement and interference, when acting on the input vector, stores information into the system state, minimizing the gap between classical Shannon ent ropy and quantum von Neumann entropy. Minimizing of the gap between Shannon and von Neumann entropies is considered as a termination criterion of QA computational intelligence measure. Let us discuss the main properties of classical and quantum information that in dynamic analysis of quantum algorithms are used. Additional necessary detail description of general properties of information amounts in Appendix 1 to this article is given. Any c omputation (both classical and quantum) is formally identical to a communication in time. By considering quantum computation as a communication process, it is possible to relate its efficiency to its classical communication capacity. At time, the programmer sets the computer to accomplish any one of several possible tasks. Each of these tasks can be regarded as embodying a different message. Another programmer can obtain this message by looking at the output of the computer when th e computation is finished at time . Computation based on quantum principles allows for more efficient algorithms for solving certain problems than algorithms based on pure classical principles [ 1 ]. The sender conveys the maximum information when all the message states have equal a priori probability (which also maximizes the channel capacity). In that case the mutual information (channel capacity) at the end of the computation is . Let us consider any peculiarities of information axioms and information capability of quantum computing as the dynamic evolution of QAs. If one breaks down the general unitary transformation of a QA into a number of successive unitary blocks, then the maximum capacity may be achieved only after the number of applications of the blocks. When its total value reaches the maximum possible value consistent with a given initial state o f the quantum computing, the computation is regarded as being complete (see, in details [ 2,3 ]). The classical capacity of a quantum communication channel is connected with the efficiency of quantum computing using entropic arguments [ 1 - 9 ]. This formalism allows us to derive lower bounds on the computational complexity of QA's in the most general context.

This content can also be viewed on the site it originates from. On the outskirts of Santa Barbara, California, between the orchards and the ocean, sits an inconspicuous warehouse, its windows tinted brown and its exterior painted a dull gray. The facility has almost no signage, and its name doesn't appear on Google Maps. A small label on the door reads "Google AI Quantum." Inside, the computer is being reinvented from scratch.

In 1994, a mathematician figured out how to make a quantum computer do something that no ordinary classical computer could. The work revealed that, in principle, a machine based on the rules of quantum mechanics could efficiently break a large number into its prime factors -- a task so difficult for a classical computer that it forms the basis for much of today's internet security. A surge of optimism followed. Perhaps, researchers thought, we'll be able to invent quantum algorithms that can solve a huge range of different problems. "It's been a bit of a bummer trajectory," said Ryan O'Donnell of Carnegie Mellon University.

In 1994, a Bell Labs mathematician named Peter Shor cooked up an algorithm with frightening potential. By vastly reducing the computing resources required to factor large numbers--to break them down into their multiples, like reducing 15 to 5 and 3--Shor's algorithm threatened to upend many of our most popular methods of encryption. Fortunately for the thousands of email providers, websites, and other secure services using factor-based encryption methods such as RSA or elliptic curve cryptography, the computer needed to run Shor's algorithm didn't exist yet. Shor wrote it to run on quantum computers which, back in the mid-1990s, were largely theoretical devices that scientists hoped might one day outperform classical computers on a subset of complex problems. In the decades since, huge strides have been made toward building practical quantum computers, and government and private researchers have been racing to develop new quantum-proof algorithms that will be resistant to the power of these new machines.

Quantum computing has a significant and game-changing impact on cybersecurity. Quantum computing holds immense promise in a range of sectors, including AI technology, health research, and weather prediction, to name a few. It does, however, pose a severe threat to cybersecurity, mandating a shift in how we protect our data. Regardless of the fact that quantum computers cannot yet crack most types of security, we must stay ahead of the curve and build quantum-proof technologies as quickly as possible. If we wait for those powerful quantum computers to breach our security, it will be too late.

A team of mathematicians has finally finished off Keller's conjecture, but not by working it out themselves. Instead, they taught a fleet of computers to do it for them. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research develop ments and trends in mathe matics and the physical and life sciences. Keller's conjecture, posed 90 years ago by Ott-Heinrich Keller, is a problem about covering spaces with identical tiles. It asserts that if you cover a two-dimensional space with two-dimensional square tiles, at least two of the tiles must share an edge.