# Chasing a million cubits

(ORDO NEWS) — Over the past twenty years, the number of qubits in quantum processors has increased from one or two to hundreds (depending on the technology platform).

Despite this impressive progress, a full-fledged quantum computer that could run an arbitrary quantum algorithm has never been created. Why this is still a very difficult engineering task, comparable to landing a man on the moon, and how it is being solved all over the world (including Russia), Naked Science will tell in this third article of our “quantum cycle”.

Back in 1965, one of the founders of Intel, Gordon Moore, once noticed that the number of transistors on integrated circuits is doubling every year. In a slightly corrected form, this observation became known as “Moore’s Law” and predetermined the development of the entire semiconductor electronics industry, which regularly managed to produce chips with more and more basic elements, decreasing their size and increasing their density (approximately twice every two years).

This amazing trend has become the reason for the incredibly rapid development of the entire computer field, which completely changed the modern world. But does Moore’s Law also apply to quantum computers?

Simple calculations make it clear that, alas, not yet. If the number of qubits in quantum processors doubled every two years, then at the moment we should have devices with more than a thousand qubits. And we have – processors with several tens of qubits, which clearly does not reach the high bar of Gordon Moore. Maybe you can just combine a hundred or two of the available quantum processors and get the desired quantum computer with a thousand qubits? Not so simple.

The complexity of scaling multi-qubit systems once again shows the cardinal difference between our classical world and the quantum world. As we already wrote in the previous articles of the series ( links ), any classical interaction with a quantum system leads to the collapse of both its quantum state and its projection onto one of the classical (basic) states. An illustrative example is the collapse of the three-dimensional Bloch sphere ( link ), which describes the quantum state of one qubit, into one of the classical bit values (0 or 1).

In the general case, such a process of degradation of a quantum state is called decoherence – a gradual loss of quantum properties by the system due to interaction with the environment. At the same time, the interaction itself can be completely different – through an electric and magnetic field, vibration, temperature. The list of possible paths through which the macroscopic world affects quantum objects is enormous! After all, even high-energy particles arriving from the depths of space can destroy the quantum states of qubits here on Earth!

Thanks to decades of scientific research, physicists have learned to hold a given quantum state of qubits long enough to perform the necessary operations with them. This time, called the coherence time of a qubit, varies, depending on its specific physical implementation, from tens of microseconds to several seconds.

This coherence time allows performing several hundred quantum operations with a qubit until its quantum state collapses too much. After that, the qubit must be returned to its initial state (initialized) to perform subsequent operations. By analogy with classical computer circuits, quantum operations are often called quantum gates or quantum gates.

If, in the case of one qubit, decoherence can be considered practically defeated (at least at a sufficient level to perform an acceptable number of quantum computational operations), then when additional qubits are added to the system, the situation changes dramatically.

Due to the interaction with each other, the imperfections of the qubits begin to multiply, making the result of performing quantum operations unpredictable. For example, if the accuracy of performing quantum operations on one qubit is 99% (that is, in 99 cases out of 100 we get the correct calculation result), then on 10 qubits the correct result will be given only 9 out of 10 times, and on 100 qubits – and only a third of the results returned will make sense. The same problem of accumulating errors arises in the sequential execution of many quantum computational operations,

## These imperfect qubits

It is reasonable to ask, what is the reason for the initial imperfection of the qubits themselves? It is rather difficult to answer this question in the general case of a “spherical qubit in vacuum”, therefore, we will focus on two real, physical realizations of quantum bits: ions in traps and superconducting structures.

It is these two technologies that have shown the fastest progress in the last decade and are currently considered the leaders in the field of “hardware” for a quantum computer (eng. Quantum computing hardware).

With ions in traps, everything is quite simple – by themselves, all ions are identical and, in isolation from the external environment, can maintain their quantum state for an indefinitely long time. However, it is rather difficult to completely isolate them from the influence of the environment, especially considering the fact that they are trapped by the electromagnetic field.

Therefore, the main source of problems for this type of qubits is the imperfection of the electromagnetic trap itself, external electromagnetic noise, as well as laser radiation used to control the quantum state of ions. It is clear that the more ions are placed in a trap, the larger its physical dimensions must be, which leads to an increase in defects in such systems and to the complexity of manipulating it (for example, due to the physical limitations of optical elements used in experimental installations ).

This is what Naked Science answered when asked about the prospects for building a quantum computer, Kirill Lakhmansky, head of the laboratory for quantum computing on cold ions at the Russian Quantum Center: “At the multi-ion level, the main problems with ion qubits have now been resolved. The main problem is the scalability of such systems. Ions are charged particles trapped in electromagnetic traps, interacting with each other due to Coulomb repulsion.

Traditionally, large three-dimensional electrodes are used to create traps, to which a high voltage is applied. In such traps, the ions are “stretched” in a chain along the entire length of the electrodes (see the image below). The problem is that we cannot create such infinitely long traps for a large number of ions due to various technical limitations and side effects.

Therefore, at the moment it is possible to trap about a hundred ions as much as possible and work with 30-40 of them. But further scaling of quantum processors based on ions by banal lengthening of such ion chains is simply unattainable. You can organize chains into separate modules, or you can create a more complex organization of ions on a chip.

“With traditional three-dimensional traps,” continues Kirill Lakhmansky- it is rather difficult to do this, therefore, recently, scientists have focused on the so-called surface or two-dimensional traps on chips manufactured using microfabrication technologies. It turns out that it is possible to place separate electrodes on the surface of the chip, thus creating its own trap for each ion, with the possibility of individual control, and not one trap for all ions, as it is now.

This approach solves most of the traditional problems, but the quality of two-dimensional traps on chips (and, above all, their surfaces) still leaves much to be desired. The technologies for their manufacture are not yet so debugged and perfect. And, if in traditional traps it is clearly felt that we have hit a certain limit, then in two-dimensional there is now an obvious variety of approaches, designs, and implementations. I’m sure,

“The field of quantum computing on ions in Russia has only recently begun to develop. – Kirill Lakhmansky says in conclusion , – In fact, now there are only two laboratories in the RCC and FIAN, which are engaged in this topic. But now, thanks to the support of Rosatom, as well as the interest of the industry, the development of the region is accelerating.

We hope to quickly go through the necessary stage of fundamental research in order to open up an opportunity for further applied developments in the field of quantum computing, which will lead to the emergence of the first Russian companies in this area. I think this is, in a way, a natural process. ”

Several other problems plague the superconducting qubit region. As Naked Science discussed in a previous article , this type of qubit is based on artificially created objects on chips – superconducting chains. Such superconducting circuits are manufactured on silicon or sapphire wafers by a method similar to traditional microelectronics – using photo- and electron lithography and subsequent deposition of thin metal films (usually aluminum or niobium). The sizes of elements in superconducting circuits vary from hundreds of micrometers to tens of nanometers, which creates a whole range of problems associated with their manufacture.

On the one hand, the difficulty lies in obtaining special nanoscale overlaps (Josephson junctions), tunneling through which electron pairs in a superconductor create a quantum state. In an array of qubits, the geometric dimensions of such transitions must be as identical as possible for the system to work together (otherwise, it will be problematic to connect individual qubits with each other).

Current technologies of nano-lithography make it possible to achieve an accuracy of fabrication of circuit elements of the order of 10 nanometers, which in itself leads to variations in the parameters of individual qubits by 10% or more. An even deeper problem lies in the imperfection of the deposited metal films, which at the nanoscale consist of individual granules that are far from perfectly adjacent to each other, which serves as another source of noise.

On the other hand, with an increase in the number of qubits on a chip, its size increases proportionally, as does the complexity of the microwave lines used to control the qubits. This leads both to a greater likelihood of defects occurring due to imperfect manufacturing processes for elements of superconducting circuits, and to a more fundamental problem of bonding an array of qubits to each other.

Unlike a chain of ions, the connection between which is realized using laser pulses, it is not so easy to connect arbitrary superconducting qubits. This problem is solved using communication lines or resonators for a pair of neighboring qubits (English neighbor-to-neighbor coupling), however, creating an entangled state of an array of many qubits in this way is very problematic.

It would seem that the ability to operate on a complex quantum state of many coupled qubits underlies the speed of a quantum computer and is used in quantum algorithms. But in practice, it turns out that such a state is unstable or completely unattainable for a couple of tens of qubits. What to do in this case?

Fortunately, in the 1990s, the Russian theoretical physicist Aleksey Kitaev put forward and proved a theorem (Solovay-Kitaev theorem) that any multi-qubit operation can be decomposed into a sequence of one- and two-qubit gates (gates). And scientists have already learned how to carry out manipulations with two coupled qubits with very, very high accuracy.

Of course, quantum algorithms composed of two-qubit gates are many times longer than their multi-qubit versions, but this is not a fundamental problem. You just need to have quantum processors with a sufficiently long coherence time and sufficiently fast one- and two-qubit gates to perform hundreds of thousands of elementary quantum operations in one computational cycle.

**The error came out, sorry!**

The phrase “you just have to have quantum processors with the right specs” from the end of the last chapter sounds pretty good and is generally doable. But there is a nuance. The accuracy of performing quantum operations on two qubits on today’s best quantum processors is approximately 99% (according to the latest information, IBM has reached an accuracy of two-qubit operations of 99.9%, but these numbers have not yet been confirmed).

This means that, on average, there will be one error for every hundred correctly performed operations. In a full-blown quantum computer running a complex quantum algorithm, such errors will quickly accumulate, leading to erroneous computation results. At the same time, it is not yet possible to significantly improve the accuracy of two-qubit quantum gates in multi-qubit quantum processors.

Fortunately, many of the shortcomings of computer hardware can often be solved programmatically. For example, physical errors that occur in classical computers or data lines are detected and corrected using real-time error correction algorithms developed back in the mid-20th century. Similar algorithms were proposed a couple of decades ago for quantum systems.

For example, the aforementioned Aleksey Kitaev in 1998 proposed a so-called “surface code” capable of detecting errors occurring in a two-dimensional (hence its name) array of qubits. The general idea of this error correction approach is quite simple – neighboring physical qubits are combined into logical blocks, each of which is further used by the quantum algorithm as a “logical qubit”. Moreover, if each logical block contains a sufficiently large number of physical qubits, then, even in spite of the periodic physical errors in them, the error level of a logical qubit can be made arbitrarily low.

How many of these logical, error-free qubits does it take to run some full-blown quantum algorithm? Let’s take, for clarity, the same sensational Shor algorithm that promises to hack the Internet. Current methods of cryptographic data protection use encryption keys consisting of thousands of bits, which would require several thousand logical qubits to factorize it effectively (factorization).

Given the number of quantum operations required and the desired level of error occurrence, each such logical qubit should consist of about a thousand physical qubits. By multiplying these two numbers, we get an estimate of a million physical qubits that a quantum computer needs to run Shor’s algorithm.

## Mission Possible?

Considering that the most powerful quantum processors in existence operate with dozens of qubits, the desired million of qubits looks somewhat transcendental. However, if you look at the history of the development of the traditional semiconductor electronics industry, you can see an example of such an engineering miracle, which made it possible to increase the number of transistors on chips from a few hundred in the late 1960s to tens of millions in the late 1990s.

The technological leap required for such scaling, in terms of complexity and volume of investments, can only be compared with a manned space walk or landing on the moon.

By the way, the current “quantum race” can be compared to the space race of the 1950s-1960s in many ways. Only the number of participants differs significantly. Instead of two superpowers, not only most of the developed countries of the world (USA, Canada, Great Britain, Germany, France, China, Australia, Japan), but also an incredible number of private companies (IBM, Google, Microsoft, Amazon, Alibaba , Rigetti, IonQ), shaping the new quantum technology industry.

Many of the players in this high-tech market have presented and are regularly updating roadmaps for the development of their quantum platforms. For example, the company IonQ, which creates quantum processors based on trapped ions, plans to create a full-fledged quantum computer with a thousand logical qubits (necessary to run serious algorithms) by 2028.

Many government programs aimed at creating a quantum computer have similar ambitions. China can rightfully be considered the leader in terms of investment volume, having invested more than $ 10 billion in its national quantum program back in 2016-2017.

Now these investments are beginning to bring the first results, especially noticeable for breakthrough articles.from the Chinese University of Science and Technology in Hefei (University of Science and Technology of China, Hefei). Trying to catch up with China and the US national quantum initiative with a budget of just over a billion dollars, aimed at creating new federal laboratories.

Comparable budgets were allocated for the development of quantum technologies and individual European countries, and the European Union itself, back in 2018, launched a billion-dollar Quantum Flagship program aimed at supporting joint projects on quantum technologies throughout Europe. The total investment in this rapidly growing market is estimated at $ 25 billion, which is comparable to the budget of the American lunar program in the 1960s.

## A special way

And what about Russia? Despite the pioneering ideas of Yuri Manin in the 1980s and the invaluable contribution of Russian scientists in the field of quantum computing and quantum information, Russia is currently slightly behind the market leaders listed above. This situation is partly due to the late start, because the first applied projects on quantum technologies in Russia were launched only in the 2010s (for example, the Russian Quantum Center), 10-15 years after the creation of the first quantum processors.

The first one- and two-qubit systems in Russia were created in 2015-2016, and this year the first 5-qubit quantum processor was presented. Scaling up to existing world counterparts with dozens of qubits will require several more years of hard work by Russian laboratories, subject to a level of investment comparable to that of world leaders.

Point grant investments in Russian quantum technologies have been carried out at least over the past ten years, but their small, relatively world-class, volume, and weak interaction between grantees hindered the rapid development of this area in Russia.

The lack of a modern technological base for the creation of microelectronic circuits (nanofabrication centers) necessary for quantum processors, as well as difficulties with the supply of high-tech measuring equipment from abroad (cryogenics, microwave and optical systems) and the lack of specialists in the field of quantum technologies also played a role here.

To overcome these difficulties and accelerate the creation of a Russian quantum computer, a roadmap for the development of quantum computing in Russia was presented in 2019, and in 2020 the National Quantum Laboratory was formed under the leadership of ROSATOM.

It includes many Russian scientific groups with many years of expertise in the field of quantum technologies (MIPT, HSE, MISiS, FIAN, RCC, and others). The goal of this collaboration is to present by 2024 a working prototype of a quantum processor with 30-100 qubits, and in parallel 4 platforms will develop at once: on superconductors, on neutral atoms, on ions and on photons.

Time will tell who will be the winner in this quantum race, but it is important to remember that the competition is not only between individual countries, companies and technology platforms. The main challenge is posed to nature itself in an attempt to make the laws of the quantum world work for solving the most complex computational problems. Overcoming this milestone will become a significant milestone on the path of scientific and technological progress and will open up new horizons for further research and applied development.

In addition, as the history of the space race shows, such competitions give impetus to the development of a variety of related technologies that find a wide variety of applications in everyday life. For example, the American lunar program has created about 2,000 new high-tech products, including wireless chargers, solar panels and digital cameras, and more. Without a doubt, in the next 5-10 years, the quantum race will give no less interesting results and will present us with many more surprises!

## Scarcity and competition

The situation in Russia especially for Naked Science was commented on by Mikhail Nasibulin, director of the project “Development of Quantum Computing” of the State Atomic Energy Corporation “Rosatom” :

Quantum computing is at an early stage of technology availability today. In this regard, there is technological uncertainty in the choice of optimal solutions for the implementation of multi-qubit quantum computers, which requires further fundamental research in the physics of quantum systems and technologies for their creation. The evolution of future solutions will be determined by the development vector of the most promising quantum hardware and scientific and technological environment in Russia and in the world.

In accordance with the Agreement of Intent with the Government of Russia, ROSATOM is implementing a roadmap for the development of the high-tech area “Quantum Computing”. The action plan of the roadmap of which was formed taking into account the best world practices and with the participation of the scientific and business communities.

But the competitive advantage of the Russian quantum computing architecture being created is the presence in it of quantum processors built on various technological platforms, including four priority (based on superconductors, neutral atoms, ions in traps and photonic chips) and promising (based on magnons, polaritons, etc. spins). These platforms will be built within a single concept and will be compatible with the suite of tools for developing quantum applications and solving optimization problems.

There are specific difficulties associated with the manufacture, scaling and integration of quantum computing systems, both from the point of view of their technical implementation, and taking into account possible foreign sanctions and violations of procurement conditions.

The implementation of the set of measures provided for by the Quantum Computing roadmap aimed at creating the necessary material and technical base will ensure not only the implementation of the planned R&D, but also the further transition to the serial automated production of Russian equipment and components, including the element base of quantum processors, which are not inferior to world analogues.

The explosive growth in the popularity of quantum computing is accompanied by a global shortage of qualified personnel in this field. A rapid build-up of top-class competencies is required across the entire spectrum of applications – from physicists directly involved in the creation and improvement of quantum computers, quantum programmers, engineers and technologists, to potential consumers and end users of technology, for whom specialized knowledge in the operation and practical application of such systems will also be in demand.

A set of necessary measures, including work on the development of human resources, activities in the field of higher professional and general education, the development of additional education programs, the formation and development of professional communities in order to strengthen the necessary competencies is provided in the “Quantum Computing” Roadmap.

Work in this direction is carried out with active participation and in cooperation with Russian universities and research centers, both already possessing competencies in the field of quantum physics, quantum mechanics, and striving to develop these areas.

The shortage of personnel is naturally accompanied by the highest competition for talented scientists, who represent a unique potential that can provide a technological transition to a new level. It is necessary to create conditions for people to work in Russia, so that they do not go abroad, but implement their projects in our country. We also attract scientists and experts from other countries – today a number of Russian scientists have returned to Russia, having received the conditions here for the implementation of their quantum scientific projects.

As for the forecasts for the creation and use of a quantum computer in Russia and in the world, I would like to note that the quantum computers currently being developed as part of the implementation of the “Quantum Computing” roadmap are experimental and not intended for commercial sales. The implementation of fully functional prototypes of all flagship quantum computing products, which will form the basis of future commercial solutions, is planned in Russia by 2025.

Due to the high complexity of the systems currently being created and the low level of technology readiness, it is still premature to predict the emergence of a mass market for quantum computers.

To create a full-fledged market, it is advisable to actively involve technological, industrial and financial partners in the joint development of quantum computing. It is necessary to build critical developer relationships with potential customers from large industrial companies, seek seed funding, business and management consulting services for companies, and provide feedback and guidance on the technology itself.

Formation of such an ecosystem of partnerships with companies, incl. in the form of joint ventures, consortia, with the aim of applying solutions in the field of quantum computing with potential partners and customers, is provided for by the Roadmap.

The first step to achieve this result was the National Quantum Laboratory (NKL) – a scientific and technological consortium created in November 2020, which is the basis of the Russian quantum ecosystem, whose tasks include the development of human resources, the creation of educational programs and start-ups, interaction with technological and financial partners. …

In terms of stimulating demand, activities are planned to provide consulting services to clients to improve operational efficiency and create value, both through the provision of information and advice, and the provision of services for access to the cloud platform of quantum computing.

Computers built on quantum principles will be more efficient than classical computers in solving many computational problems due to an increase in the speed of computations and the use of previously unavailable phenomena of quantum mechanics. The effectiveness of the use of quantum computers is predicted in many areas: quantum chemistry and new materials, biomedicine, logistics optimization, big data and machine learning, banks and insurance, the financial sector, energy, retail.

According to forecasts of foreign analysts, in the next 3-5 years, the most powerful quantum computing systems will be able to solve practical optimization problems, such as transport and logistics routing, optimization of financial portfolios and trade settlements. The implementation of more complex tasks will take from 5-7 years (some problems of scenario modeling and machine learning) to 10-20 years (modeling complex molecules, searching in disordered databases, cryptanalysis).

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