**Quantum Computers**

## Quantum mechanical principles

A *quantum computer* operates on the basis of the *quantum mechanical principles*
superposition and quantum entanglement.
The unit of information in a quantum computer is called *qubit*. In contrast to classical bits,
which either have the value 1 or 0 and are therefore in one state or the other, a qubit is a
superposition of these states. This means that it is both 0 and 1 at the same time and assumes both
states. The phenomenon of quantum entanglement is the second principle of quantum mechanics that applies
to qubits. This principle allows qubits to interact and influence one another regardless of the distance
and medium between them.

Combined with other properties of quantum computers, these principles make it possible to calculate specific problems much more efficiently than with conventional computers. The main advantage of a quantum computer is its ability to simulate the physical micro-world much more accurately. As our world is governed by quantum mechanics at atomic level, a computer that understands and uses these same phenomena can much better approximate quantum behaviours than a traditional computer. Research on quantum computers has gained much traction in recent years. With a quantum computer, it is much faster to run simulations and perform certain calculations. Therefore, it can be used to optimize various applications and products in the pharmaceutical, chemical, and other industries. A rather negative side effect of quantum computers is their ability to solve the mathematical problems on which today's cryptography is based very efficiently.

## Quantum Computers and Cryptography

Small-scale quantum computers have already been created by large companies and organisations around the
world. These computers are expanding rapidly, and the goal of a large-scale quantum computer seems
within reach in the not-too-distant future. When these computers become available, current *public-key
cryptosystems* like RSA or elliptic curves will become insecure. Shor’s algorithm **[Shor94]**
shows how, using a quantum computer, the prime factorisation of a large number and the calculation of
discrete logarithms can be done in polynomial time.

Additionally, *symmetric encryption algorithms* and hash functions that are not directly tied to
a
mathematical problem are also at risk, as Grover’s algorithm
**[Grover96]** shows. In this case, the impact is
not
as devastating as in *public-key cryptography*, but the time it takes to break a symmetric scheme
or a
hash
function through a brute-force attack or an exhaustive search is reduced by almost half.

The
solution to the latter problem is considered easy, since the security parameters of the cryptographic
functions can be increased with relatively little effort. To solve the first problem however, it is
necessary to select new mathematical problems that are not vulnerable to quantum computers and to
design,
analyse, and implement new cryptographic schemes based on these mathematical problems.