Using Quantum Computing to Classify Solar Flares

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Friedrich Doku, Urbas Ekka, Ricco Venterea

Problem Statement

Predicting solar flares has been a difficult task in the field of heliophysics. These eruptive events from the sun are usually accompanied by coronal mass ejections (CMEs). CMEs contain streams of energetic particles, which can have extreme terrestrial consequences, such as disruption of satellite communications and “electrical power blackout[s]” [3]. CMEs are difficult to predict due to the physical interactions that occur on the sun, such as magnetic reconnection. Predicting solar flares would save preparation time and money. Our algorithm classifies and predicts the strength of solar flares within a 24 hour period based on data from [4].

Solar Flare gif as recorded by NASA [8].

Classical vs Quantum

We used quantum computing phenomena to solve NP-Hard problems. In computer science, NP-Hard problems are problems that cannot be solved in polynomial time by a classical computer. They can only be solved with bruteforce solutions. For example, to find the global minimum of the graphs below [5] a classical computer would have to test every point on the graph. A quantum computer can do it much faster by traveling through hills.

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Classical vs Quantum

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A quantum computer exploits quantum annealing, which allows you to find the global minima based on energy states. Qubits are coupled together to create different energy states in the system and the lowest energy state is the answer (see figure below [6]).

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Classical vs Quantum

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Finally, this question comes down to Adaboost and Decision Trees vs Qboost. Decision Trees are a tree-like model of decisions and their consequences. This is the very foundation of classification. Adaboost is a machine-learning meta-algorithm that can, classically and much more efficiently than previously possible, perform classifications. It is generally thought to be the best “out of the box” classifier. QBoost on the other hand uses quantum annealing, which is generally more efficient. But the real difference lies in the training each algorithm performs. Adaboost utilized a richer set of weak classifiers in order to reach the minimal training error, while QBoost did so with a smaller set of classifiers [1]. On a small scale, this isn’t a big deal, but as the number of elements in a data set greatly increase, the Adaboost becomes less and less efficient and accurate.

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A shows data; B shows test data through saturation; C shows optimal classification; bottom row shows classification as number of iterations T increase [5].

Basis of Algorithm

Optimization via quantum computing relies on “training…to solv[e]…minimization problem[s]” [1].

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This equation seeks to minimize both overfitting of the training and the function in question.

Algorithm

Using data from [4], we created an algorithm [7] that reads in solar flare data and categorizes them into C-, M-, and X-class flares (in increasing energy). We can train our data set and compare it against our real data.

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Limitations

There are several limitations to this interpretation of quantum computing. The current biggest limitation of quantum is the lack of qubits, this results in general lack of memory, which requires projects to be scaled down in order to have algorithms such as QBoost to run efficiently. This is also why classification in quantum utilizes a hyper-cube lattice which is more compact. Another limitation is the size of the data set. Classical computing performs just as well as quantum on smaller data sets, as seen in our results, as quantum really differentiates itself on very large data sets. Yet another limitation is the sheer cost of usage. The only commercially available quantum computer is the system D-wave offers, which costs $2,000 per hour to use.

References

[1]H. Neven, V.S. Denchev, G. Rose, W.G. Macready, Training a Binary Classifier with the Quantum Adiabatic Algorithm, ArXiv:0811.0416 [Quant-Ph]. (2008). http://arxiv.org/abs/0811.0416 (accessed February 27, 2021).

[2]Q.W. Association, Quantum Annealing, Medium. (2018). https://medium.com/@quantum_wa/quantum-annealing-cdb129e96601 (accessed February 27, 2021).

[3]H. Zell, The Day the Sun Brought Darkness, NASA. (2015). http://www.nasa.gov/topics/earth/features/sun_darkness.html (accessed February 27, 2021).

[4]G. Bradshaw, OpenML, OpenML: Exploring Machine Learning Better, Together. (n.d.). https://www.openml.org/d/40687 (accessed February 27, 2021).

[5]V.N. Smelyanskiy, E.G. Rieffel, S.I. Knysh, C.P. Williams, M.W. Johnson, M.C. Thom, W.G. Macready, K.L. Pudenz, A Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration, ArXiv:1204.2821 [Quant-Ph]. (2012). http://arxiv.org/abs/1204.2821 (accessed February 28, 2021).

[6]What is Quantum Annealing? — D-Wave System Documentation documentation, (n.d.). https://docs.dwavesys.com/docs/latest/c_gs_2.html (accessed February 27, 2021).

[7]F. Doku, MutexUnlocked/boostgangx, Mutex, 2021. https://github.com/MutexUnlocked/boostgangx (accessed February 27, 2021).

[8]GIPHY, Flare GIF by NASA - Find & Share on GIPHY, n.d. https://media3.giphy.com/media/l2Sq7UcchYPqoR3vq/giphy.gif (accessed February 28, 2021).

[9]A. Neutron, العربية: نموذج داخل البروتون وبزوغ الكواركات للوجود والعدم فى أوقات قصيرة جداً لا تكاد تدرك, 2018. https://commons.wikimedia.org/wiki/File:Quantum_Fluctuations.gif (accessed February 28, 2021).

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Classification in Quantum

A Hyper-cube lattice, a collection of diagonal hyper-planes in N-dimensions, is utilized for classification in quantum computing. In classical computing, the exponential growth of the regions would result in a solution that would take non-polynomial time, or NP-hard, to achieve. But due to the quantum annealing, the quantum computing can rather easily solve combinatorial optimization problems in polynomial time [1].

Optimization

Whether looking for a maximum or minimum of a function, we can use optimization to achieve this. There are various numerical methods to achieve this, such as gradient descent or lagrange multipliers. From a classical perspective, optimization is time consuming and and computationally expensive. Quantum computing, on the other hand, relies on thermodynamic processes and quantum annealing, allowing for a superposition of states. For large sets of data, quantum tunneling saves time and produces reliable results.

Background Information

Quantum Annealing: A metaheuristic for finding the global minima of a given function over a set of candidate solutions (or candidate states) which is achieved through quantum fluctuations, which test certain regions by temporarily and randomly changing the amount of energy in certain points in space.

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Quadratic unconstrained binary optimization (QUBO): Our algorithm relies on this model, which allows us to classify data, based on datum characteristics, into two distinct sets and minimize a binary quadratic function.

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Animation of quantum fluctuation by Neutron [9].