Current breakthroughs in Quantum computing and their practical applications

Current breakthroughs in Quantum computing and their practical applications

Quantum computing is an extremely interesting and popular topic. Even though it is still in its infancy, it promises to change the computing landscape and even usher another stage to our civilizational development. This is all due to an exponential increase in computing power that it will inevitably bring. It will make all of the tasks that previously took months and years to complete easily solvable within days, hours and even minutes. The wide spectrum of its potential applications ranges from medicine to finance. It will solve tasks that were previously unachievable and revolutionize every sphere where it is applied. The potential changes that it will bring being groundbreaking, to say the least. Recent achievements in quantum computing and their practical applications will be described in the paragraphs below.

General overview

First of all, it is important to understand the fundamentals of quantum computing in order to see how it differentiates from classical computing and how is it capable of exceeding it. Its basis lies in a completely new approach to computing and to matter itself. It draws on the principals of quantum physics and operates on a completely new worldview of the universe. The quantum bits, unlike classical bits that are either 1 or 0, combine both in themselves. Allowing them to simultaneously exist in multiple states at once. This allows for multiple computations to happen simultaneously and is generally known as superposition. The best example to illustrate it would be the widely-known Schrodinger’s cat, which is in two states at once.

Moreover, those qubits can be anything that exhibits quantum behavior: molecules, atoms, electrons, etc. Making them far more accurate if compared to classical computers that are sodium-based. In comparison, classical computers are 70 to 200 percent off in their computations, compared to quantum computers. All due to the limitations imposed by the materials that are used in their hardware. On top of that, the more electrons there are in a molecule, the more possible states there is for it. For example, a molecule with 10 electrons has 1000 possible states, while a molecule with 20 electrons has over 1 million possible states. This contributes to the number of calculations in quantum computers, increasing their computing capabilities exponentially.

Another important concept is quantum entanglement. It interlinks the qubits and allows them to operate together. Combined with superposition this gives the quantum computers its most prominent feature. An ability to process vast quantities of information, much greater than what classical computers are capable of. In addition to this, quantum computers can calculate infinite possibilities for their inputs. Allowing them to model algorithms that are more complex and develop far more intricate and sophisticated models. This is useful in processing vast amounts of market data of the stock exchange, modeling molecules with all of their details for pharmacological substances, creating unbreakable codes for encryption and many more.

There are two main types of quantum computers that currently exist. First are based on the quantum gate model and quantum circuits, being the most similar to current computers. A good example of such would be the IBM Q System One. The first full-fledged quantum computer that was introduced earlier this year. Second are the superconducting quantum computers. With the largest ones, having over 2000 qubits, produced by D-Wave Systems. They rely on quantum annealing (finding a global minimum of a given function over a given set of candidate solutions) and will be explicitly featured in financial application examples below. Both types of computers are developed by large companies, such as IBM, Google, D-Wave, Intel and others. As we can see, the shift is already happening, even though on a more of a Research and Development, and initial testing stages.

Current examples and recent developments

To get a better understanding of how such computers work let us take a look at IBM Q. In order to achieve the necessary working environment for the quantum chip, there are two main conditions to be met. First is the necessity of achieving an absolute zero temperature (–273.15 degrees Celsius). Second is the absolute vacuum. Both are not easy to achieve and maintain but have been attained in IBM Q System One and its previous iterations. On top of that, there is a good reason for the entire computer to be encased in a protective metal cylinder and placed in a hardened glass box. Quantum chips are extremely fragile and even the slightest interference will be damaging for them.

IBM Q System One is a 20-qubit, circuit-based quantum computer. It has doubled its QV network volume from 8 to 16 in comparison to its predecessor. This computing power opens great potential for practical applications: “the higher the Quantum Volume, the more real-world, complex problems quantum computers can potentially solve, such as simulating chemistry, modeling financial risk, and supply chain optimization.”[1]. In addition to considerable computing power, it has the lowest error rates (1–2%): “some of the lowest error rates IBM has ever measured, with an average 2-qubit gate error less than 2 percent, and its best gate achieving less than 1 percent error rate.”[2]

While not the largest quantum computer to date, it is the first commercially available one that is ‘quantum ready’. Meaning that it can perform all of the tasks of a large classical computer. IBM promises to achieve a quantum advantage over traditional computers in 3–5 years. However, there are bigger machines that already exist. A quantum computer used and developed by Google is a great example of how far quantum computing already went. It already has 72 qubits and Google estimates that they will reach quantum superiority over classical computers this year. Another, even more interesting example is the machine being built by Rigetti Computing. They aim to build a 128-qubit computer that will be unveiled this year: “Our 128-qubit chip is developed on a new form factor that lends itself to rapid scaling. Because our in-house design, fab, software, and applications teams work closely together, we’re able to iterate and deploy new systems quickly.”[3]. Thus, we can see that the information technology companies put significant effort into developing quantum computers that will outperform current computers rather sooner than later.

It’s important to mention that Quantum computers are a new valid application of Moore’s Law, which states that computer transistors will double in performance every year. This would culminate into one of the goals of quantum computing — creating a big enough quantum computer that will be infinitely more powerful than any classical computer. Let’s also look at some of the most interesting uses of such quantum computers.

Practical applications

One of the most important applications that would impact everyone is the ability to create simulations of biological molecules. This will allow to significantly improve drug design and better determine positive treatment effects as well as negative side effects. Another example would be the quantum internet. This will have two important features. First of all, it will be possible to encode far more information in a qubit than in a conventional bit. Second, it will make all of the messages completely secure. In addition to quantum encoding, it will be possible to detect any attempts to intercept messages due to the nature of qubits that react when they were influenced by any third party intruder. Switching to quantum internet will be possible if current broadband technologies are improved. Photons can be used as qubits, which makes fiber-optic cables applicable for such purpose. Moreover, a recent breakthrough by Australian scientists can make Erbium the prime substance for enabling it in existing networks: ‘Recently, we found that applying a large magnetic field can greatly improve the quantum storage time of certain erbium crystals. This field, which is similar to that inside a hospital MRI machine, quiets the magnetic field fluctuations. The erbium storage time can then improve by a factor of 10,000 to more than 1 second.’[4] Other utilizations that are already in testing include improving the logistics through better route calculation, improving rates of machine learning, and bettering the cybersecurity. With the last completely transforming the world of online protection.

To understand how quantum computing will impact cybersecurity it’s important to understand the main algorithm used for this purpose. The main principle of encryption has to do with numerical factors for very large numbers that are used to secure the data transfer. If some hacker attempts to break into encrypted information, he would have to find the right prime number to crack the big number securing it. Current methods usually employ guesswork and repeated attempts to find the right number. With quantum computers, on the other hand, it will be possible to factor in a prime number and by the end of the computation have all of the wrong answers eliminated with only a single right one remaining. That is exactly the function of Shor’s algorithm. It uses a product of two large prime numbers that it then factors in to get the right answer. It will give that right value with a high probability, and in case it will not work from the first attempt it will give the answer with even a greater chance of being correct once it’s used again. Quantum computers enable this algorithm simply due to the large number of simultaneous computations that they can run. Thus, the current RSA encryption will become negligible for any sufficiently large quantum computer. However, it is not all about the vulnerability that quantum computers can exploit. They are also capable of creating secure encrypted keys that would offer a greater degree of data protection. Those algorithms are currently being developed by mathematicians in academia together with governmental institutions. With all likelihood, they will rely upon quantum cryptography as well, which is also gaining popularity. It is a branch of science that relies on quantum mechanical properties to perform cryptographic tasks. However, it is not a part of the current subject and we will not go far into it.

Quantum computing in finance

There are multiple practical applications for quantum computers in the field of finance. First of all, the entire financial market can be modeled as a quantum process, where quantities that are usable for quantum computing, such as covariance matrix, emerge naturally. In addition to that, some well-known financial problems can be directly expressed in a quantum-mechanical form. Potential uses of quantum computers coupled with the exponential growth of their computing power would provide financial firms with a humongous advantage over their competitors and will change the financial field forever. In a recently published paper, deep research was done into the possible applications of quantum computers and related financial algorithms. The below examples are drawn directly from it. Thay will show in detail how current and upcoming developments of quantum computers can be applied, and what applications already exist. Also note that from this point, we will get into very detailed and technical financial and computing terms and practices in order to show the exact practicality of quantum computers. The subjects mentioned below, such as credit scoring, market projections, and evaluations directly or indirectly impact everyone. Either through influencing the capacity to gain finances for an individual business or a firm where a person is employed or through the global state of the economy which has much to do with the stock markets.

The numerous problems in finance have to do with optimization. And they can be addressed with quantum annealers that were mentioned earlier. A valid application would be searching for patterns in the past data in order to predict future market patterns and fluctuations. That is the core of technical analysis that is commonly used in finance. It can be addressed with improved machine learning that quantum computers provide. Which in this case would be both faster and more affordable. Being able to go over greater data amounts much faster than classical counterparts.

Finance also deals with the uncertainty of future behavior of assets and their projected returns. Risk in financial terms is the possibility of the difference between actual and expected returns. The risk can be purposefully mitigated. Particularly in case of high return, risky assets, by selecting additional assets and creating a portfolio. Both portfolios and assets are intrinsically random systems due to inherently incomplete knowledge of the market. This randomness is a risk that is very difficult to estimate. However, numerical simulation methods (Monte Carlo for example) can be used to estimate what an option is worth. And quantum computers can be applied to solve related computational issues in such calculations. In this case, portfolio optimization can be done using a model that is trained to identify the important data. Then it can be used to predict the behavior of new data points. Which is basically the process of machine learning. The particular improvement that quantum computers provide would be in speeding up the training of such a model.

Monte Carlo methods (statistical sampling) can usually be implemented efficiently. They would, however, require many runs to provide an accurate estimation of the expected return and its distribution. Its accuracy can be further improved by modeling the parameters as stochastic functions. Yet there is a colossal computational power required to accurately describe the system. This only gets higher as the amount of data gathered increases. Which is an issue that quantum computers are best suited to solve. And the faster the required algorithms can be run, the greater the advantage it will provide.

Grover’s algorithm is another important application of quantum algorithms. Its function is finding a particular register in an unordered database, at a significantly greater efficiency than typical algorithms. It can be adapted to solve optimization problems, help to find flow-like variables, and implement Monte Carlo Methods. There are other quantum algorithms that prove to be more efficient than classical ones: Quantum Approximate Optimization Algorithm (QAOA), Quantum Fourier Transforms (QFT), Quantum Principal Component Analysis (PCA), Quantum Support Vector Machines (SVM) and Harrow, Hassidim, and Lloyd (HHL) algorithm.

Here is an example of dynamic portfolio optimization, with a discrete multiperiod version amenable to quantum annealers and implementable on D-Wave quantum processors. An optimized cost function would look like this:

(μ –forecast returns, w — holdings, Σ — forecast covariance tensor, γ — risk aversion)

Overall return to be optimized under the sum of holdings equal to K

And the sum of the maximum allowed holding of each asset to be at most K′

The above dynamic portfolio optimization was successfully done on D-Wave chips, proving that it can be solved with a high success rate on quantum computers. In the previously mentioned research paper, there are other formulas that demonstrate the exact workings of the quantum algorithms listed in this article. If one desires to get a deeper understanding of its workings I would advise the reader to follow the previously given link to that research document.

Let’s take another financial practice that can be better solved using quantum algorithms. Arbitrage — the practice of making a profit from differing prices on the same asset in different markets. The problems of this subject are NP-hard (non-deterministic polynomial-time hardness), which makes them perfect for quantum algorithms to handle, particularly for quantum annealers. Moreover, there are practical instances of arbitrage problems that were converted into quadratic unconstrained binary optimization (QUBO). That was then implemented on the D-Wave quantum annealers that have produced the same optimal solutions as an exhaustive classical solver.

Another important financial issue that quantum computers can successfully tackle is credit scoring. Being the basis for determining the risk of a loan and a likelihood of the borrower defaulting on payments. It can be translated to a QUBO problem that can be run on a quantum annealer as well. Apart from that, the problems that arise from the lack of data or from having to deal with large quantities of data are a prime subject for quantum computers to deal with. In this case, it was implemented as a proof-of-principle on 1Qbit SDK toolkit and the results have shown that future quantum annealers can be used to find optimal features in credit analysis.

It is also important to elaborate on the prospects of machine learning with quantum computers. As was previously mentioned, the entire process can be made more efficient and less time-consuming. On top of that, the produced algorithms can tackle a large diversity of tasks. Those would include pattern recognition, data classification, and others. The training of AI to perform those tasks can be significantly improved. Let’s take a look at classification algorithms. In our example, each data point (customer) can be expressed as a vector, with vector space of all considered attributes. Each vector, in turn, would belong to a class, a certain loan risk. Such a classification algorithm would be an essential tool for financial predictions. And the methods for running classification algorithms on a quantum computer would generally focus on efficiently performing projection operations.

A ̈ımeur, Brassard and Gambs were the pioneers of the idea of recasting the above problem on a quantum computer by expressing each data point as a quantum state. They developed the idea of Buhrman to efficiently estimate the classical distance between states by repeatedly performing swap tests. Lloyd also suggested an alternative method for encoding classical data in a quantum state. While also relying on swap tests, it boasts efficiency that is greater than classical algorithms. There are also early suggestions for the application of quantum classification algorithms to pattern recognition problems.

Financial supply chain management is an important subject as well. It has to do with meeting customer demand while avoiding unwanted stock. Same as classification algorithms, it requires taking a significant number of factors into account that relate to every specific problem. It requires to learn a numeric function from the training data set and employs regression — core tool for economic forecasting. It is used to gain an understanding of how the typical value of a response variable changes as an attribute is varied. The optimal parameters are found by minimizing the least-squares error between the training data and the values predicted by the model. Done by finding the (pseudo)inverse of the training data matrix. This can be computationally expensive for classical data sets, but not for the quantum ones. Also, Wiebe, Braun, and Lloyd managed to apply a powerful mathematical toolbox to perform regression on a quantum computer. In their example, a sparse training data matrix was used to encode the model’s optimal fit parameters into the amplitudes of a quantum state, which is far faster than the fastest classical algorithm. Wang has managed to improve on it by applying the modern methods for matrix inversion and generalizing the algorithm to non-sparse training data matrices. Another method applicable to this kind of task was a Gaussian process regression. The last development on the subject was done by Schuld, Sinayskiy, and Petruccione who managed to solve the expansive data size problem by encoding their regression model into a quantum state. However, that solution is rather inconvenient in its current state.

In terms of portfolio optimization, it is very important to have a global vision of interest rate paths, even when dealing with hundreds of swap instruments. A standard machine learning tool for this is Principal Component Analysis (PCA). It amounts to finding dominant eigenvalues and eigenvectors of a very large matrix. However, when the number of stocks reaches over millions the cost becomes astronomical. The PCA algorithm can be run exponentially faster on a quantum processor. It allows us to find approximations to the principal components of a correlation matrix as well as estimate risk and maximize profit in situations not feasible using classical methods.

Neural networks have proved to be extremely successful at predicting markets and analyzing credit risk. The key to their success lies in the ability to tackle tasks that require intuitive judgment for incomplete data sets. This makes them essential for financial prediction. They too can be accelerated through quantum computing. Quantum annealers can significantly reduce the computational cost of machine learning. Moreover, once trained the algorithm can be used on any classical computer. The previously mentioned PCA can be used to speed up the process exponentially and fully new quantum neural network algorithms can be designed for that purpose. Altogether allowing the network to learn much more complex data patterns.

Coming back to Monte Carlo methods, they perform best when dealing with extremely large or complex systems that can’t be handled otherwise. The stochastic approach is usually used to simulate the effect of uncertainties affecting the given financial object (stock, portfolio, option). Which makes Monte Carlo methods applicable to portfolio evaluation, personal finance planning, risk evaluation, and derivatives pricing. In order to obtain the most probable outcome of wide distribution, or to get a result with a very small associated error, the necessary number of Monte Carlo simulations can become gigantic. For example stock market simulations, that are usually day-long simulations. A quantum speedup would bring a huge change, greatly speeding up the process.

The first steps for it were done by Brassard, Hoyer, Mosca, and Tapp. In the first part, documented in their research paper, they extend Grover’s search algorithm to construct the Quantum Amplitude Estimation (QAE) algorithm. Which can be used to get a quadratic speed-up in the calculation of expectation values by Monte Carlo sampling. It applies a series of QAA operations, followed by a QFT from Shor’s quantum factoring algorithm to measure the approximate amplitude of any given state. Developing from the obtained results, Montanaro showed that Monte Carlo simulations can run on a quantum computer with the same accuracy as classical machines and with quadratically fewer samples required. QAE algorithm serving as a source of this speedup. Additionally, if random sampling is performed through a quantum algorithm this can provide another speed increase.

Building upon Montanaro’s work, Rebentrost, Gupt, and Bromley suggested using quantum-accelerated Monte Carlo to obtain quadratic speedup in pricing financial derivatives. While Woerner and Egger pioneer the idea of adapting the core principles of such to efficiently estimate VaR and CVaR for financial risk analysis. By applying QAE algorithm they determined VaR (value at risk) and CVaR (conditional value at risk) with a quadratic speed up as well. And it was actually tested on IBM Experience.

Thus, we can see that quantum computers already have several applications in the field of finance. Moreover, some of those applications were tested and yielded great results. That’s considering the current initial stage of the quantum computers. Therefore it can be concluded that the greater the increase of their computing power will be, the greater will be the speed ups and the more tasks they will be able to handle. It is quite certain that at one point they will become powerful enough to become disruptive in the field of finance. Meaning that whoever would own a powerful quantum computing machine would have a tremendous advantage over others.

To conclude this article, it is important to note that the above are only a few of the possible applications. And such fields as quantum teleportation have not even been mentioned. By now it is evident that quantum computers are growing in their computing power at an increasing rate. The greatest example would be the Rigetti machine that will have 128 qubits, which is far above 20 qubits of IBM Q System One that was just released on January 2019. And the farther the development goes, the more institutions and companies will be drawn to it. Which will bring a greater development speed, with everyone contributing their part to this grandiose technological development.

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References:

[1] https://interestingengineering.com/ibm-reveals-major-performance-gain-for-ibm-q-system-one — IBM Reveals Major Performance Gain For IBM Q System One’

[2] https://interestingengineering.com/ibm-reveals-major-performance-gain-for-ibm-q-system-one — ‘IBM Reveals Major Performance Gain For IBM Q System One’

[3] https://medium.com/rigetti/the-rigetti-128-qubit-chip-and-what-it-means-for-quantum-df757d1b71ea — ‘The Rigetti 128-qubit chip and what it means for quantum’

[4] https://theconversation.com/heard-of-the-element-erbium-it-could-pave-the-way-to-a-quantum-internet-84123 — ‘Heard of the element erbium? It could pave the way to a quantum internet’

https://arxiv.org/abs/1807.03890 — ‘Quantum computing for finance: overview and prospects’

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