From Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH): “Early endeavours on the path to reliable quantum machine learning”

From Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH)

Florian Meyer

The future quantum computers should be capable of super-​fast and reliable computation. Today, this is still a major challenge. Now, computer scientists led by ETH Zürich conduct an early exploration for reliable quantum machine learning.

Building on concepts such as quantum entanglement, quantum computers promise a wealth of machine learning applications. (Photo: Keystone/Science Photo Library)

Anyone who collects mushrooms knows that it is better to keep the poisonous and the non-​poisonous ones apart. Not to mention what would happen if someone ate the poisonous ones. In such “classification problems”, which require us to distinguish certain objects from one another and to assign the objects we are looking for to certain classes by means of characteristics, computers can already provide useful support to humans.

Intelligent machine learning methods can recognise patterns or objects and automatically pick them out of data sets. For example, they could pick out those pictures from a photo database that show non-​toxic mushrooms. Particularly with very large and complex data sets, machine learning can deliver valuable results that humans would not be able to find out, or only with much more time. However, for certain computational tasks, even the fastest computers available today reach their limits. This is where the great promise of quantum computers comes into play: that one day they will also perform super-​fast calculations that classical computers cannot solve in a useful period of time.

The reason for this “quantum supremacy” lies in physics: quantum computers calculate and process information by exploiting certain states and interactions that occur within atoms or molecules or between elementary particles.

The fact that quantum states can superpose and entangle creates a basis that allows quantum computers the access to a fundamentally richer set of processing logic. For instance, unlike classical computers, quantum computers do not calculate with binary codes or bits, which process information only as 0 or 1, but with quantum bits or qubits, which correspond to the quantum states of particles. The crucial difference is that qubits can realise not only one state – 0 or 1 – per computational step, but also a state in which both superpose. These more general manners of information processing in turn allow for a drastic computational speed-​up in certain problems.

A reliable quantum classification algorithm correctly classifies a toxic mushroom as “poisonous” while a noisy, perturbed one classifies it faultily as “edible”. (Image: npj Quantum Information / DS3Lab ETH Zürich.)

Translating classical wisdom into the quantum realm.

These speed advantages of quantum computing are also an opportunity for machine learning applications – after all, quantum computers could compute the huge amounts of data that machine learning methods need to improve the accuracy of their results much faster than classical computers.

However, to really exploit the potential of quantum computing, one has to adapt the classical machine learning methods to the peculiarities of quantum computers. For example, the algorithms, i.e. the mathematical calculation rules that describe how a classical computer solves a certain problem, must be formulated differently for quantum computers. Developing well-​functioning “quantum algorithms” for machine learning is not entirely trivial, because there are still a few hurdles to overcome along the way.

On the one hand, this is due to the quantum hardware. At ETH Zürich, researchers currently have quantum computers that work with up to 17 qubits (see “ETH Zürich and PSI found Quantum Computing Hub” of 3 May 2021). However, if quantum computers are to realise their full potential one day, they might need thousands to hundreds of thousands of qubits.

Quantum noise and the inevitability of errors

One challenge that quantum computers face concerns their vulnerability to error. Today’s quantum computers operate with a very high level of “noise”, as errors or disturbances are known in technical jargon. For the American Physical Society (US), this noise is “the major obstacle to scaling up quantum computers”. No comprehensive solution exists for both correcting and mitigating errors. No way has yet been found to produce error-​free quantum hardware, and quantum computers with 50 to 100 qubits are too small to implement correction software or algorithms.

To a certain extent, one has to live with the fact that errors in quantum computing are in principle unavoidable, because the quantum states on which the concrete computational steps are based can only be distinguished and quantified with probabilities. What can be achieved, on the other hand, are procedures that limit the extent of noise and perturbations to such an extent that the calculations nevertheless deliver reliable results. Computer scientists refer to a reliably functioning calculation method as “robust” and in this context also speak of the necessary “error tolerance”.

This is exactly what the research group led by Ce Zhang, ETH computer science professor and member of the ETH AI Center, has has recently explored, somehow “accidentally” during an endeavor to reason about the robustness of classical distributions for the purpose of building better machine learning systems and platforms. Together with Professor Nana Liu from Shanghai Jiao Tong University [海交通大学](CN) and with Professor Bo Li from the University of Illinois Urbana-Champaign(US), they have developed a new approach. This allows them to prove the robustness conditions of certain quantum-​based machine learning models, for which the quantum computation is guaranteed to be reliable and the result to be correct. The researchers have published their approach, which is one of the first of its kind, in the scientific journal npj Quantum Information.

Protection against errors and hackers

“When we realised that quantum algorithms, like classical algorithms, are prone to errors and perturbations, we asked ourselves how we can estimate these sources of errors and perturbations for certain machine learning tasks, and how we can guarantee the robustness and reliability of the chosen method,” says Zhikuan Zhao, a postdoc in Ce Zhang’s group. “If we know this, we can trust the computational results, even if they are noisy.”

The researchers investigated this question using quantum classification algorithms as an example – after all, errors in classification tasks are tricky because they can affect the real world, for example if poisonous mushrooms were classified as non-​toxic. Perhaps most importantly, using the theory of quantum hypothesis testing – inspired by other researchers’ recent work in applying hypothesis testing in the classical setting – which allows quantum states to be distinguished, the ETH researchers determined a threshold above which the assignments of the quantum classification algorithm are guaranteed to be correct and its predictions robust.

With their robustness method, the researchers can even verify whether the classification of an erroneous, noisy input yields the same result as a clean, noiseless input. From their findings, the researchers have also developed a protection scheme that can be used to specify the error tolerance of a computation, regardless of whether an error has a natural cause or is the result of manipulation from a hacking attack. Their robustness concept works for both hacking attacks and natural errors.

“The method can also be applied to a broader class of quantum algorithms,” says Maurice Weber, a doctoral student with Ce Zhang and the first author of the publication. Since the impact of error in quantum computing increases as the system size rises, he and Zhao are now conducting research on this problem. “We are optimistic that our robustness conditions will prove useful, for example, in conjunction with quantum algorithms designed to better understand the electronic structure of molecules.”

See the full article here .


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Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH) is a public research university in the city of Zürich, Switzerland. Founded by the Swiss Federal Government in 1854 with the stated mission to educate engineers and scientists, the school focuses exclusively on science, technology, engineering and mathematics. Like its sister institution Swiss Federal Institute of Technology in Lausanne [EPFL-École Polytechnique Fédérale de Lausanne](CH) , it is part of the Swiss Federal Institutes of Technology Domain (ETH Domain)) , part of the Swiss Federal Department of Economic Affairs, Education and Research.

The university is an attractive destination for international students thanks to low tuition fees of 809 CHF per semester, PhD and graduate salaries that are amongst the world’s highest, and a world-class reputation in academia and industry. There are currently 22,200 students from over 120 countries, of which 4,180 are pursuing doctoral degrees. In the 2021 edition of the QS World University Rankings ETH Zürich is ranked 6th in the world and 8th by the Times Higher Education World Rankings 2020. In the 2020 QS World University Rankings by subject it is ranked 4th in the world for engineering and technology (2nd in Europe) and 1st for earth & marine science.

As of November 2019, 21 Nobel laureates, 2 Fields Medalists, 2 Pritzker Prize winners, and 1 Turing Award winner have been affiliated with the Institute, including Albert Einstein. Other notable alumni include John von Neumann and Santiago Calatrava. It is a founding member of the IDEA League and the International Alliance of Research Universities (IARU) and a member of the CESAER network.

ETH Zürich was founded on 7 February 1854 by the Swiss Confederation and began giving its first lectures on 16 October 1855 as a polytechnic institute (eidgenössische polytechnische Schule) at various sites throughout the city of Zurich. It was initially composed of six faculties: architecture, civil engineering, mechanical engineering, chemistry, forestry, and an integrated department for the fields of mathematics, natural sciences, literature, and social and political sciences.

It is locally still known as Polytechnikum, or simply as Poly, derived from the original name eidgenössische polytechnische Schule, which translates to “federal polytechnic school”.

ETH Zürich is a federal institute (i.e., under direct administration by the Swiss government), whereas the University of Zürich [Universität Zürich ] (CH) is a cantonal institution. The decision for a new federal university was heavily disputed at the time; the liberals pressed for a “federal university”, while the conservative forces wanted all universities to remain under cantonal control, worried that the liberals would gain more political power than they already had. In the beginning, both universities were co-located in the buildings of the University of Zürich.

From 1905 to 1908, under the presidency of Jérôme Franel, the course program of ETH Zürich was restructured to that of a real university and ETH Zürich was granted the right to award doctorates. In 1909 the first doctorates were awarded. In 1911, it was given its current name, Eidgenössische Technische Hochschule. In 1924, another reorganization structured the university in 12 departments. However, it now has 16 departments.

ETH Zürich, EPFL (Swiss Federal Institute of Technology in Lausanne) [École polytechnique fédérale de Lausanne](CH), and four associated research institutes form the Domain of the Swiss Federal Institutes of Technology (ETH Domain) [ETH-Bereich; Domaine des Écoles polytechniques fédérales] (CH) with the aim of collaborating on scientific projects.

Reputation and ranking

ETH Zürich is ranked among the top universities in the world. Typically, popular rankings place the institution as the best university in continental Europe and ETH Zürich is consistently ranked among the top 1-5 universities in Europe, and among the top 3-10 best universities of the world.

Historically, ETH Zürich has achieved its reputation particularly in the fields of chemistry, mathematics and physics. There are 32 Nobel laureates who are associated with ETH Zürich, the most recent of whom is Richard F. Heck, awarded the Nobel Prize in chemistry in 2010. Albert Einstein is perhaps its most famous alumnus.

In 2018, the QS World University Rankings placed ETH Zürich at 7th overall in the world. In 2015, ETH Zürich was ranked 5th in the world in Engineering, Science and Technology, just behind the Massachusetts Institute of Technology(US), Stanford University(US) and University of Cambridge(UK). In 2015, ETH Zürich also ranked 6th in the world in Natural Sciences, and in 2016 ranked 1st in the world for Earth & Marine Sciences for the second consecutive year.

In 2016, Times Higher Education WorldUniversity Rankings ranked ETH Zürich 9th overall in the world and 8th in the world in the field of Engineering & Technology, just behind the Massachusetts Institute of Technology(US), Stanford University(US), California Institute of Technology(US), Princeton University(US), University of Cambridge(UK), Imperial College London(UK) and University of Oxford(UK).

In a comparison of Swiss universities by swissUP Ranking and in rankings published by CHE comparing the universities of German-speaking countries, ETH Zürich traditionally is ranked first in natural sciences, computer science and engineering sciences.

In the survey CHE ExcellenceRanking on the quality of Western European graduate school programs in the fields of biology, chemistry, physics and mathematics, ETH Zürich was assessed as one of the three institutions to have excellent programs in all the considered fields, the other two being Imperial College London(UK) and the University of Cambridge(UK), respectively.