Quantum Computing (part 2)

Some practical implications

 As it was outlined in the previous entry in this series, which was an introduction, I am going to continue here with presenting some practical endeavors on this field. From a theoretical perspective, the field of quantum computing has been active since about 1994 when the seminal Schor algorithm has been put forward. Despite tremendous theoretical advancements, from my point of view the practical advancements in this field have been painfully slow so far. We do stand though on the verge of an extraordinary explosion in this matter that I think will change in fundamental ways the way we interact with technology. So far there have been following 3 different paths towards reaching quantum supremacy and for the rest of this essay, I am going to go describe each one of them in a little more detail including their theoretical grounds, prerogatives and practical hurdles that need to be overcome.

Trapped ions

As most of the pioneering Quantum Physics principles had been showcased using individual atom interactions and effects (electron diffraction, Heisenberg uncertainty, electronic orbitals, Bell inequalities, etc....), this mindset had been prevalent and it was very natural for most of the early endeavors. There are a couple of ways to perform the trapping, one being the Paul trap that uses a complex electromagnetic field configuration to capture and trap the ion in mid-vacuum and maintain it there. This method of trapping has been in use since the 1950s.

The second method of trapping, which has a better potential for scalability, but poses other challenges is to trap the ions on semiconductor chips. Given the extensive practicalknowledge we already posses in building semiconductors, as well with the natural connectivity with classical computing methods that this offers, this method is attracting more research.

Some practical advantages of trapped ions include their spatial flexibility (because each ion is not necessarily attached in a fixed micro-frame to others). Also, hyperfine qubits are extremely long lived and this can allow for some interesting novel applications of this technology.

The main commercial player using this method of achieving quantum computing is IonQ that was incubated at the University of Maryland.

Emergent quantum states

Despite the early start that trapped ion quantum coherence had, the condensed matter physics offered a different avenue of achieving quantum computing using the crystalline lattices interactions that lead to emergence of quantum states that are not eigenstates of fundamental particles, but for which the principles of quantum mechanics apply equally well. There were 2 technological breakthroughs that allowed for this field to take off and presently to be the most beaten path towards achieving quantum supremacy.

The first one was the BCS theory of superconductivity, along with the discovery of study of superconductors. In certain materials, the electrostatic interaction between the phonon states in the crystalline lattice and the Fermi electron gas leads to an electronic level that is separated by a gap from the Fermi gas and has a lower energy than the Fermi ground state. Because this is a phonon level it offers a scatter free interaction between electrons and the lattice and if the time to cross the gap to the Fermi cloud is less than the coherence time on this level (true at low enough temperatures), one can form a coherent, scatterless electronic wave-function on this level which we know as superconductivity.

This way to achieve an emergent coherent quantum state was not enough to do quantum computing, as this state can not be easily controlled and measured. Another technological breakthrough that allowed for the control of these emergent states was the Josephson effect. This describes mathematically the tunneling of the BCS phonon electronic state across non superconducting (or weekly superconducting) barriers. It was observed accidentally in experiments in the late 1950s, it was predicted in 1962 and it has been experimentally confirmed a year later by Phil Anderson, whom I had the pleasure to meet. The Josephson gate allows one to control the superconducting quantum state and this opens the door for quantum computing applications that use these emergent states.

This can get even more interesting when the superconducting state is not just the basic BCS state. Doping a semiconductor and taking it to superconducting temperatures can lead to the presence of a split super-conducting state obtained using the Quantum Hall effect, akin to the hyperfine splitting in the single atom systems. This theory has been developed in the Russian school, with important contributions being made by Lev Landau, Nikolay Bogoliubov and Alexei Kitaev. One can generate a fractal structure in this splitting, opening the opportunity for controlling multiple concurrent fermionic states on the same substrate. The fermionic nature of the states also hypothetically allows for more stability, scalability and exotic interactions between the states that can not be achieved with just plain BCS states.

The most advanced quantum processors are made by DWave and they have the largest achieved number of quantum qubits, albeit using them in the most basic BCS configuration which allows only for quantum annealing algorithms.

Photonic quantum computing

Photons are bosons that are always on the go with a tremendous speed. This makes then a hard to tame medium for normal operations of quantum computing, but they are better than other applications for other quantum applications, like encryption, and quantum communication and security, or establishing de-localized entanglement.

In order not to make this entry way too long, I won't stress much on this method in this installment of the series, but I will tangentially get back to it in future entries. The Knill, Laflamme, and Milburn theorem from 2001 revealed quantum photonics to be a legit candidate for achieving quantum supremacy.

The most established commercial player in quantum photonics is ID Quantique in Switzerland.

Note: Because of the length of this entry, it took a little more than 1 week to get it ready and even so I only grazed over the last part. Expect the next one in about a week from now.