The future of quantum computing is being defined by a handful of companies, each with its own approach to creating and controlling qubits that are based on different phenomena within physics.

Take Google and IBM for example. They are focusing on __superconducting__ along with quantum startups IQM, Oxford Quantum Circuits and SeeQC. __Ion traps__ are being pioneered by Quantinuum, IonQ and Oxford Ionics, while Quantum Brilliance, SaxonQ and XeedQ are developing __NV-Centers__ in diamonds.

Elsewhere, Intel, QuTech, Diraq, Quantum Motion and Siquance are leading the charge on __silicon spin__ technology. __Photonic__ quantum computing is pursued by Psi Quantum and Xanadu or Quandela.

Another direction is __neutral atoms__, which counts Quera, Atom Computing, Cold Quanta, Planqc and Pasqal whose co-founder recently won the Nobel prize for physics.

These six platforms have their advantages, promises and challenges, and to make it even more complex there are another dozen approaches to quantum computing pursued by scientists in academia.

At Runa Capital, we have been tracking the quantum space for a few years, and our first quantum computing bet was on Pasqal.

When we participated in Pasqal’s Series A round in early 2021, we had little idea that its co-founder Alain Aspect would be awarded the Nobel Prize in Physics just 18 months later.

Professor Dr Aspect’s award-winning research with John Clauser and Anton Zeillinger explored “experiments with entangled photons, establishing the violation of Bell’s inequalities and pioneering quantum information science”.

The Nobel prize underscores the tremendous acceleration that quantum computing has enjoyed in recent years. However, there are still many challenges on the pathway towards developing and commercializing a universal quantum computer.

__Universal Quantum Computer.__

The majority of algorithms that have inspired the quantum computing industry assume there’s an environment of perfect qubits with 100% fidelity or resistance to errors. These algorithms are made of a succession of quantum logic gates acting on qubits, which is a basic quantum circuit operating on a small number of qubits. Theoretically, one- and two-qubit gates are all that is needed for a universal gate set (read: build a universal quantum computer).

This assumption of a perfect quantum qubit does not hold true for a physical qubit. In reality, Qubits interact with the environment and, as a result, are never perfect, so those inspirational algorithms just simply don’t work on today’s architecture. The current state of affairs is why quantum computing is often referred to as the Noisy Intermediate-Scale Quantum (NISQ) era.

The brightest minds among us have been dedicated to improving qubits through procedures known as quantum error correction. This allows for a so-called error-corrected logical qubit and such recalibrations are common in science.

In principle a perfect, albeit error-corrected, logical qubit is possible, but it requires an enormous amount of resources. One logical qubit typically requires an overhead of 100 to 1,000 physical qubits and these must have an error rate below 0.3% to make possible an exponential suppression of errors. That’s a fidelity of more than 99.7%.

A lack of pure perfection and scale is just one of the challenges of universal quantum computers and has therefore spurred innovation into a different area of the space.

__Digital Computing vs Analog Simulations__

Qubits currently have restrictions as they are not perfect and their number is limited. So, can these quantum machines actually be useful?

As always, the answer is yes.

The analog control allows for better hardware optimisation, which can help solve specific problems. We are familiar with analog computations as they have been the predominant form of high-performance classical computing since the 1970s.

Historically, quantum simulations have been produced in analog mode. It is the use of a quantum processor to simulate a quantum system of interest, like in materials science or chemistry. Analog control is the mode of computation through the dynamical programmation of the Hamiltonian of the system (a function used to determine its time evolution).

Neutral atoms naturally implement some instances of many-body Hamiltonians. But there has been also a significant effort to extend the capabilities to simulate Hamiltonians beyond those that are naturally implemented, e.g. by applying a periodic microwave drive.

Interestingly with analog computation, we don’t deconstruct a computational problem to gates. We build an artificial quantum system with atoms that are individually controlled and resemble the problem at hand.

This approach could be applied to the following areas:

- Simulating quantum effects in molecules, materials and nuclear physics. These systems are quantum by nature, and quantum computers are intrinsically better fit to simulate them compared to classical ones.
- Solving combinatorial optimization problems more rapidly and more efficiently than classical approaches. One example would be a Maximum Independent Set, or MIS problem. This is where the issue of finding the maximum set of vertices on a graph that is not connected directly by an edge. A real-world example would be finding a set of mobile base stations which can operate on the same radio frequency and not interfere with each other.
- Machine learning applications, such as machine learning on graphs, which is a challenging problem for classical computers due to high memory requirements.

These are just a handful of uses from an array of possible applications which can be explored using for example Pasqal’s open source Pulser library or its brand new NoCode Graphical UI.

__So why neutral atoms?__

The analog approach is essentially low-hanging fruit for quantum computers and is best suited for neutral atoms given a combination of fidelity, scale and connectivity that this platform demonstrates.

- Fidelity is arguably the most important parameter of qubits. The superconducting and the ion traps platforms were the first to reach 99.9% levels of fidelity and this is why there has been so much attention to these two platforms historically. That said, the neutral atoms, which are the new entrants with significantly fewer research years and funding, are already demonstrating fidelity as high as 99.1%. You can understand more from this Caltech report.
- The scale that quantum processors can achieve is largely determined by the coherence time of its qubits. The team at Universite Paris-Saclay behind Pasqal has recently demonstrated that the lifetime of a trapped 87Rb atom can reach 100 minutes. It also showed the efficient assembly of qubit arrays up to 324 atoms, which beat the previous record of 256 qubits. This opens the way to neutral atoms computers combining thousands of qubits.

- Connectivity is another important hurdle to overcome when building powerful quantum computers: the connectivity between qubits. We are still working with noisy qubits so the transfer of quantum state between remote positions on a quantum circuit adds to the accumulation of errors.For most platforms we’ve covered, the connectivity is restricted to the nearest neighbour. However, the ion trap and neutral atom approaches have an advantage when it comes to connectivity. In particular, the neutral can be excited to a so-called Rydberg state and interact within a Rydberg radius. In practice, this amounts to a couple of dozen interacting qubits.Recently researchers from Harvard University behind a quantum computing startup QuERA demonstrated a coherent transfer of qubit arrays while preserving their quantum states. This essentially opens the path towards all-to-all connectivity of qubits on the neutral atoms platform.
- In addition, the Rydberg neutral atoms platform is capable of forming unconventional quantum many-body states of matter, such as symmetry-protected topological band or topological surface code or toric code.

__Quantum Error Correction with Neutral Atoms__

The latter observed property of Rydberg atoms to form symmetry-protected topological states may be an important milestone in reaching quantum error correction, or QEC.

In fact, researchers at Harvard have reported a 7-qubit Steane code, a topological 19-qubit surface code and 24-qubit toric code cluster-states. The measured fidelities of these cluster-states indicate that the main source of their errors is in the underlying two-qubit CZ gates which are currently operating with a fidelity of about 97.5%.

They project that with a further 10 times increase in the intensity of a 1,013-nm laser, the atoms could be further laser-cooled to a temperature of 2 uK, which potentially improves the CZ gate fidelity to 99.7%, i.e. beyond the surface code threshold.

This would allow an exponential error suppression and realization of error-corrected logical qubits with the neutral atoms platform and open up the quantum computing era beyond NISQ.

Staying tuned!

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*Dmitry Galperin is the General Partner, Runa Capital*