⚡ Quantum computing

*Image: In the geometric representation of a two-level quantum state, a qubit such as a spin, can be represented by a point on a sphere. In this Bloch sphere, the first qubit (qubit 0) is in the 100% quantum state |1>, while the second qubit (qubit 1) is in the 100% quantum state |0>. The points on the surface of the sphere correspond to the pure states (described by a single vector) of the system, while the interior points correspond to the mixed states, 20% |0> + 80% |1> (described by its density matrix with lengths and angles). Credit: IBM Quantum Computer. *

### The qubit

At the microscopic scale, the quantum computer uses the quantum properties of matter, in particular the superposition of states.

The quantum computer or quantum processor works on qubits whose values 0 and 1 (notation for quantum states: |0 > or |1 >) are all superimposed unlike the classical computer whose values are either 0 or 1. In other words, with a classical computer 2 bits correspond to 2 pieces of information, with a quantum computer 2 qubits correspond to 4 pieces of information where each piece of information is probabilistic, 10% |00 > + 25% |01 > + 60% |10 > + 5% |11 >.

So 4 bits correspond to 4 information and 4 qubits to 16 probabilistic information. Each time we add 1 qubit we multiply by 2 the number of information (2^{N}) that the quantum computer can process at the same time, so it goes to 2^{N} times faster than a conventional computer.

N qubits represents a superposition of 2^{N} mixed quantum states, so the processing speed increases exponentially with the number of qubits (with 20 qubits the gain factor is 1 million).

An interesting metaphor allows us to compare classical computing and quantum computing. If you are looking for someone in a room of 1000 people who is six feet tall and speaks English, traditional computers must interview each participant one by one and noting the answers, which will take some time. For quantum computing, it is as if we were making a general call "Can people who are six feet tall and speak English raise their hands?" », The answer is almost instantaneous. In this case, the calculation is holistic and no longer sequential.

With a power of 40 qubits, we could reach the power of the largest existing computer in 2021 (IBM's Behold Summit). The advantage of a quantum computer is therefore to perform calculations much faster!

A quantum computer capable of handling 70 qubits (2 ^{70 }of information) in a controlled manner, could provide an immediate result on 10 billion terabytes of information.

This number is enormous, in fact each year on the internet users produce around 1 billion terabytes of information.

This hyper-powerful machine must work with specific algorithms (Glover, Shor, Brassard, Høyer and Tapp, Farhi, Goldstone, Gutmann algorithms, etc.). These quantum algorithms make it possible to perform certain "very particular" calculations extremely quickly, today beyond the reach of a conventional computer.

Warning, the quantum computer will not be able to be faster than the classical computer for consumer applications as an engine for word processing, video, music, etc.

Much less versatile quantum computers will therefore not be used like conventional computers, so they will not be for the general public.

*NB: A qubit is the physical carrier of quantum information. It is the quantum version of a bit, and its quantum state can take values of |0>, |1>, or the linear combination of both, which is a phenomenon known as superposition. *

### Quantum computer

*Image: Workflow consisting in submitting a job from a classical computer to an IBM quantum computer. Once the work is done, the quantum measurement result is returned to the conventional computer for analysis and storage. In order to minimize errors, in addition to the radiation shielding, the computer should be immersed in a tank of liquid helium at a temperature close to absolute zero (-273 °C). Image credit: Andi Sama *

In recent years, most research activities on the quantum computer have strived for quantum supremacy.

Unfortunately, its development since the 1990s is extremely complex because the phenomenon of decoherence (loss of quantum effects by going to the macroscopic scale) goes against the physical realization of the basic elements: the qubits. Even today, one of the biggest challenges in building quantum computers is controlling or removing quantum decoherence.

Many researchers have expressed skepticism about the possibility of building evolutionary quantum computers, usually due to the problem of maintaining consistency on a large scale.

In 1998, IBM presented a quantum calculator of 2 qubits, 5 qubits in 2000 then in 2017 systems equipped with 16 qubits. In 2017, IBM runs a 50-qubit calculator for 90 microseconds reaching the theoretical threshold of quantum supremacy.

In 2019, Google made Sycamore, a 53-qubit quantum processor with an assumed power of 10 trillion superimposed quantum states.

Google would have achieved quantum supremacy!

The article published by Google on October 23, 2019 in the scientific journal Nature, shows that for the first time since the 1990s, quantum computing is possible. This article has been submitted for evaluation by external researchers. IBM in competition with Google published an article saying that the calculation which would take 10,000 years according to Google with a conventional computer would be doable in just 3 days with another algorithm and by increasing the RAM memory to 250 million GB.

The quantum computer is very vulnerable to errors on qubits, which requires very sophisticated error correcting codes. To minimize errors, in addition to the radiation shielding, the computer should be immersed in a tank of liquid helium at a temperature close to absolute zero (-273 °C).

Indeed, it must be completely isolated from the outside world during the computation phase because it must not interact with other quantum objects.

The more qubits the system has, the more the time during which it remains coherent decreases, it even decreases exponentially. Beyond a certain number of atoms, the duration is zero.

In conclusion, quantum computers will probably not be dedicated to consumer applications but rather to analytical calculations (financial markets, climate models, particle physics simulations, intelligent vision, modeling of molecules, research in gigantic databases, cryptography, etc.). In addition they will be coupled with conventional computers in order to be controlled.

*NB: quantum supremacy (term introduced by physicist John Preskill) designates the number of qubits beyond which no classical supercomputer is able to reach the computing power of a quantum computer. Supercomputer can reach the computing power of a 40-qubit quantum computer, but from 50 qubits it becomes physically impossible, the computing time would be unacceptable (thousands of years). *