## Quantum Computing for Everyone – The Startup – Medium

Posted: March 19, 2020 at 1:52 pm

Qubits are exponentially faster than bits in several computing problems, such as database searches and factoring (which, as we will discuss soon, may break your Internet encryption).

An important thing to realize is that qubits can hold much more information than a bit can. One bit holds the same amount of information as one qubit they can both only hold one value. However, four bits must be used to store the same amount of information as two qubits. A two-qubit system in equal superposition holds values for four states, which on a classical computer, would need at least four bits to hold. Eight bits are needed to store the same amount of information as three qubits, since a three-qubit system can store eight states 000, 001, 010, 011, 100, 101, 110, and 111. This pattern continues.

The below graph provides a visual for the computing power of qubits. The x-axis represents the number of qubits used to hold a certain amount of information. The blue lines y represents the number of bits needed to hold the same amount of information as the number of qubits (x-axis), or 2 to the power of x. The red lines y represents the number of qubits needed to hold the same amount of information as the number of qubits in the x-axis (y=x).

Imagine the exponential speedup quantum computing can provide! A gigabyte (8E+09 bits) worth of information can be represented with log(8E+09)/log(2) = 33 (rounded up from 32.9) qubits.

Quantum computers are also great at factoring numbers which leads us to RSA encryption. The security protocol that secures Medium and probably any other website youve been on is known as RSA encryption. It relies on the fact that with current computing resources, it would take a very, very long time to factor a 30+-digit number m that has only one solution namely, p times q, where both p and q are large prime numbers. However, dividing m by p or q is computationally much easier, and since m divided by q returns p and vice versa, it provides a quick key verification system.

A quantum algorithm called Shors algorithm has shown exponential speedup in factoring numbers, which could one day break RSA encryption. But dont buy into the hype yet as of this writing, the largest number factored by quantum computers is 21 (into 3 and 7). The hardware has not been developed yet for quantum computers to factor 30-digit numbers or even 10-digit numbers. Even if quantum computers one day do break RSA encryption, a new security protocol called BB84 that relies on quantum properties is verified safe from quantum computers.

So will quantum computers ever completely replace the classical PC? Not in the forseeable future.

Quantum computing, while developing very rapidly, is still in an infantile stage, with research only being conducted semi-competitively by large corporations like Google, Microsoft, and IBM. Much of the hardware to accelerate quantum computing is not currently available. There are several obstacles to a quantum future, of which a major one is addressing gate errors and maintaining integrity of a qubits state.

However, given the amount of innovation that has happened in the past few years, it seems inevitable during our lifetimes that quantum computing will make huge strides. In addition, complexity theory has shown that there are several cases where classical computers perform better than quantum computers. IBM quantum computer developers state that quantum computing will probably never completely eliminate classical computers. Instead, in the future we may see a hybrid chip that relies on quantum transistors for certain tasks and classical transistors for others, depending on which one is more appropriate.

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Quantum Computing for Everyone - The Startup - Medium

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