A lot of research on the fundamentals of quantum computing has been devoted to error correction. Part of the difficulty stems from another of the key properties of quantum systems: Superpositions can only be sustained as long as you dont measure the qubits value. If you make a measurement, the superposition collapses to a definite value: 1 or 0. So how can you find out if a qubit has an error if you dont know what state it is in?

One ingenious scheme involves looking indirectly, by coupling the qubit to another ancilla qubit that doesnt take part in the calculation but that can be probed without collapsing the state of the main qubit itself. Its complicated to implement, though. Such solutions mean that, to construct a genuine logical qubit on which computation with error correction can be performed, you need many physical qubits.

How many? Quantum theorist Aln Aspuru-Guzik of Harvard University estimates that around 10,000 of todays physical qubits would be needed to make a single logical qubit a totally impractical number. If the qubits get much better, he said, this number could come down to a few thousand or even hundreds. Eisert is less pessimistic, saying that on the order of 800 physical qubits might already be enough, but even so he agrees that the overhead is heavy, and for the moment we need to find ways of coping with error-prone qubits.

An alternative to correcting errors is avoiding them or canceling out their influence: so-called error mitigation. Researchers at IBM, for example, are developing schemes for figuring out mathematically how much error is likely to have been incurred in a computation and then extrapolating the output of a computation to the zero noise limit.

Some researchers think that the problem of error correction will prove intractable and will prevent quantum computers from achieving the grand goals predicted for them. The task of creating quantum error-correcting codes is harder than the task of demonstrating quantum supremacy, said mathematician Gil Kalai of the Hebrew University of Jerusalem in Israel. And he adds that devices without error correction are computationally very primitive, and primitive-based supremacy is not possible. In other words, youll never do better than classical computers while youve still got errors.

Others believe the problem will be cracked eventually. According to Jay Gambetta, a quantum information scientist at IBMs Thomas J. Watson Research Center, Our recent experiments at IBM have demonstrated the basicelementsof quantum error correction onsmalldevices, paving the way towards larger-scaledevices where qubits canreliablystorequantum informationfor a long period of time inthepresence of noise. Even so, he admits that a universal fault-tolerant quantum computer, which has to use logical qubits, is still along way off. Such developments make Childs cautiously optimistic. Im sure well see improved experimental demonstrations of [error correction], but I think it will be quite a while before we see it used for a real computation, he said.

For the time being, quantum computers are going to be error-prone, and the question is how to live with that. At IBM, researchers are talking about approximate quantum computing as the way the field will look in the near term: finding ways of accommodating the noise.

This calls for algorithms that tolerate errors, getting the correct result despite them. Its a bit like working out the outcome of an election regardless of a few wrongly counted ballot papers. A sufficiently large and high-fidelity quantum computation should have some advantage [over a classical computation] even if it is not fully fault-tolerant, said Gambetta.

One of the most immediate error-tolerant applications seems likely to be of more value to scientists than to the world at large: to simulate stuff at the atomic level. (This, in fact, was the motivation that led Feynman to propose quantum computing in the first place.) The equations of quantum mechanics prescribe a way to calculate the properties such as stability and chemical reactivity of a molecule such as a drug. But they cant be solved classically without making lots of simplifications.

In contrast, the quantum behavior of electrons and atoms, said Childs, is relatively close to the native behavior of a quantum computer. So one could then construct an exact computer model of such a molecule. Many in the community, including me, believe that quantum chemistry and materials science will be one of the first usefulapplications of such devices, said Aspuru-Guzik, who has been at the forefront of efforts to push quantum computing in this direction.

Quantum simulations are proving their worth even on the very small quantum computers available so far. A team of researchers including Aspuru-Guzik has developed an algorithm that they call the variational quantum eigensolver (VQE), which can efficiently find the lowest-energy states of molecules even with noisy qubits. So far it can only handle very small molecules with few electrons, which classical computers can already simulate accurately. But the capabilities are getting better, as Gambetta and coworkers showed last September when they used a 6-qubit device at IBM to calculate the electronic structures of molecules, including lithium hydride and beryllium hydride. The work was a significant leap forward for the quantum regime, according to physical chemist Markus Reiher of the Swiss Federal Institute of Technology in Zurich, Switzerland. The use of the VQE for the simulation of small molecules is a great example of the possibility of near-term heuristic algorithms, said Gambetta.

But even for this application, Aspuru-Guzik confesses that logical qubits with error correction will probably be needed before quantum computers truly begin to surpass classical devices. I would be really excited when error-corrected quantum computing begins to become a reality, he said.

If we had more than 200 logical qubits, we could do things in quantum chemistry beyond standard approaches, Reiher adds. And if we had about 5,000 such qubits, then the quantum computer would be transformative in this field.

Despite the challenges of reaching those goals, the fast growth of quantum computers from 5 to 50 qubits in barely more than a year has raised hopes. But we shouldnt get too fixated on these numbers, because they tell only part of the story. What matters is not just or even mainly how many qubits you have, but how good they are, and how efficient your algorithms are.

Any quantum computation has to be completed before decoherence kicks in and scrambles the qubits. Typically, the groups of qubits assembled so far have decoherence times of a few microseconds. The number of logic operations you can carry out during that fleeting moment depends on how quickly the quantum gates can be switched if this time is too slow, it really doesnt matter how many qubits you have at your disposal. The number of gate operations needed for a calculation is called its depth: Low-depth (shallow) algorithms are more feasible than high-depth ones, but the question is whether they can be used to perform useful calculations.

Whats more, not all qubits are equally noisy. In theory it should be possible to make very low-noise qubits from so-called topological electronic states of certain materials, in which the shape of the electron states used for encoding binary information confers a kind of protection against random noise. Researchers at Microsoft, most prominently, are seeking such topological states in exotic quantum materials, but theres no guarantee that theyll be found or will be controllable.

Researchers at IBM have suggested that the power of a quantum computation on a given device be expressed as a number called the quantum volume, which bundles up all the relevant factors: number and connectivity of qubits, depth of algorithm, and other measures of the gate quality, such as noisiness. Its really this quantum volume that characterizes the power of a quantum computation, and Gambetta said that the best way forward right now is to develop quantum-computational hardware that increases the available quantum volume.

This is one reason why the much vaunted notion of quantum supremacy is more slippery than it seems. The image of a 50-qubit (or so) quantum computer outperforming a state-of-the-art supercomputer sounds alluring, but it leaves a lot of questions hanging. Outperforming for which problem? How do you know the quantum computer has got the right answer if you cant check it with a tried-and-tested classical device? And how can you be sure that the classical machine wouldnt do better if you could find the right algorithm?

So quantum supremacy is a concept to handle with care. Some researchers prefer now to talk about quantum advantage, which refers to the speedup that quantum devices offer without making definitive claims about what is best. An aversion to the word supremacy has also arisen because of the racial and political implications.

Whatever you choose to call it, a demonstration that quantum computers can do things beyond current classical means would be psychologically significant for the field. Demonstrating an unambiguous quantum advantage will be an important milestone, said Eisert it would prove that quantum computers really can extend what is technologically possible.

That might still be more of a symbolic gesture than a transformation in useful computing resources. But such things may matter, because if quantum computing is going to succeed, it wont be simply by the likes of IBM and Google suddenly offering their classy new machines for sale. Rather, itll happen through an interactive and perhaps messy collaboration between developers and users, and the skill set will evolve in the latter only if they have sufficient faith that the effort is worth it. This is why both IBM and Google are keen to make their devices available as soon as theyre ready. As well as a 16-qubit IBM Q experience offered to anyone who registers online, IBM now has a 20-qubit version for corporate clients, including JP Morgan Chase, Daimler, Honda, Samsung and the University of Oxford. Not only will that help clients discover whats in it for them; it should create a quantum-literate community of programmers who will devise resources and solve problems beyond what any individual company could muster.

For quantum computing to take traction and blossom, we must enable the world to use and to learn it, said Gambetta. This period is for the world of scientists and industry to focus on getting quantum-ready.

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