# Which subatomic particle does each company use in quantum computing?

Probably each company (Google, Amazon, Intel, IBM, Microsoft, D-Wave and so on) uses a mix of subatomic particles and technologies. I would like to know which particles/technologies are used by each company.

Are there specific reasons to choose a particular technology?

Google, IBM and Rigetti use transmon qubits; these are basically fancy LC circuits where a Josephson junction and capacitor connect two superconducting islands. Because of this, they are also often referred to as superconducting qubits. The qubit states are the various charge levels that can exist on the circuit; since the lowest two levels are separated in energy with respect to the higher levels, a two-level system arises. There are also other designs that encode the qubit in the charge levels, collectively they're therefore also known as the charge qubits.

Intel also used superconducting qubits, but lately has also been interested in quantum dot qubits. A quantum dot is like a $$0$$-dimensional island on which a single electron can be placed; since the electron is a fermion it has only two natural states (and therefore makes a good qubit). The encoding can also be different, by encoding the qubit into two rather than one electron in the quantum dot (making use of the orthogonality of the singlet and triplet states). The go-to method of building a quantum dot is by using semiconductors (like silicium, known as the go-to material in classical computing); therefore they are also known as semiconducting qubits. Note that due to their extensive usage in classical computing, the engineering field of semiconductors is (at least relatively) very well developed.

Microsoft is trying a different route: they are trying to built a topological quantum computer. This is a different type of quantum computer where the qubits are encoded in topological states of matter, using quasi-particles known as (non-Abelian) anyons. A likely candidate for a physical implementation is a Majorana fermion, which can act as an anyon. Such a Majorana fermion is its own anti-particle; no physical Majorana fermion (as opposed to the 'normal' Dirac fermion, e.g. electrons) has ever been found, but it could be realized as a quasi particle; a delocalized pair of electrons on a super-conducting bridge. It is worth noting that this is a considerably harder design than your 'run of the mill' transmons etc, but these topological states are intrinsically protected to many types of noise, thereby reducing or even omitting the need for quantum error correction. They live in the middle of the conductance-free gap of this superconductor, so that relatively small excitations (i.e. not pushing them out of that gap) are not 'allowed'.

D-Wave's systems is based on a yet more different method of quantum computing: the adiabatic quantum computer or quantum annealer. The way computations are performed on these computers are not alike the circuit model (which is the most used model, exploited by transmons, super-conducting and semi-conducting qubits and the like). Moreover, the qubits themselves act very differently, and the comparison of 'adiabatic-syle' qubits and 'circuit-type' qubits is not a good or well-defined comparison. An adiabatic quantum computer needs many more qubits to have the same computational power as a circuit-based quantum computer, but they are (at least on paper) equally powerful (in terms of complexity classes). That means that the overhead is on paper is at most always polynomic. In an adiabatic quantum computer, the calculation's answer is encoded into the ground state of the entire system. It might therefore feel intuitive that these machines are particularly suited for optimization problems. It is also notable that there is still open discussion on whether the D-Wave-machines are 'universal' quantum computers, in the sense that they can do everything that an adiabatic QC needs to be able to do to be equivalent to a gate-based quantum computer. If you are familiar with the Ising model (basically a quantum annealer can calculate (the value of) the ground state of any Ising interaction): D-Wave's machines are not (yet) able to have any possible interaction term between qubits - they are able to do $$\sigma_{z}\sigma_{z}$$ interactions, but they also need either $$\sigma_{x}\sigma_{x}$$ or $$\sigma_{y}\sigma_{y}$$ interactions.

There are also other types of qubits (that are not used by any of the companies you listed). Two to look out for are:

• Trapped-ion qubits. Qubits are encoded into states of ions; these ions are trapped by optical tweezers (light) and therefore localized and isolated. They (more or less) make use of the gate-based model of quantum computation; some restrictions apply because generally they can only be realized in a one-dimensional fashion. A big advantage is that the cooling requirements of this design is considerably less severe; room-temperature realizations are as far as I understand it not out of the question.

• Photonic quantum computation. Qubits are encoded into degrees of freedom of photons (=light), most often the polarization; time-bin encoding is also often used, especially when considering flying qubits. These photonic machines normally use the computation model of measurement based or one-way quantum computation, which is comparable to the circuit model but creates all entanglement in the beginning of the computation. This design also has the added benefit of not needing to cool the system. However, to be able to scale one needs many coherent photon-resources (where a laser won't do), which is a tough resource.

There is no clear best implementation (yet). Transmon qubits are the most mature by most standards, but they are relatively big which will give big implications and problems when these devices will be scaled to include millions of qubits. Semiconducting qubits are a very interesting candidate because they are much smaller and implemented on (the very well developed technology of) semiconductors, but not much has been developed. Trapped ions are promising as well, but they can only be manufactured in a line (as a one-dimensional array of qubits). I'm interested to see what will happen with photonic quantum computers; they can be very promising but not many large companies are working on them; the measurement based model of QC is less popular. A topological quantum computer is the dream of many, but for now it seems out of reach in the near future, due to the exceedingly exotic nature of its design.