The Possibilities of Quantum Computing

There are problems in the World that we know how to solve, but they just take too much time. These are known as intractable problems, and a perfect illustration of this concept is the task of factorizing very large numbers, a fundamental problem in the field of cryptography. But a breakthrough in the 1990s would shake this particular problem to its core.

Factorization involves breaking down a number into a product of smaller numbers or factors. For small numbers, this is a straightforward process. However, as numbers grow larger, factorization can quickly become exceedingly difficult. This principle underpins RSA encryption, a widely used secure data transmission method, on payments and other infrastructure. The encrypted data remains secure as long as these numbers remain intractable and can be factored with existing technology and algorithms.

Shor's Algorithm, developed by mathematician Peter Shor in 1994, proved that this could be broken using quantum computing, a new technology. For example, the most significant numbers factorized by classical computers involve hundreds of digits. In contrast, quantum computers leveraging Shor’s Algorithm could potentially factor numbers much larger—numbers so large that they are beyond everyday comprehension and beyond the computational reach of all the classical computing power theoretically available in the visible universe. To give a sense, this could do calculations in a few hours of what a conventional computer could do in a human lifetime.

Shor’s Algorithm exploits the principles of quantum mechanics, such as superposition and entanglement, to perform computations on many different inputs simultaneously. Despite Shor's Algorithm's theoretical capabilities, the practical realization of quantum computers capable of executing it on a scale large enough to challenge current cryptographic systems is still in the developmental stage. But it shows the way of what can be possible, and how Humans can keep breaking impossible barriers.

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