# New Quantum linear Algorithm is not limited to Sparse Data

A recent study published in American journal Physical Review Letters proposed an enhanced version of the “Quantum Linear Algorithm”. New Algorithm could crunch numbers on problems such as commodities pricing, social networks and chemical structures.

Initially the linear system algorithm introduced in 2009 which works on gigantic matrix. This algorithm initially used to head start research into quantum computing in terms of machine learning and artificial intelligence. Later on a re-classified algorithm introduced which is nowadays used to process the various data in AI and ML.

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Basically there are millions of computation involved in order to analyze the matrix. When a matrix gets beyond 10,000 by 10,000 entries it became harder to resolve for general computer. And every doubling of the matrix size increases the length of the calculation eight-fold. Even all Google’s server centers together will not be capable of coming up with the best solution to this optimization problem in a such a short time.

### Optimization Problem:

You want to do a trip through South America and you want to visit a number of cities. And then you ask what is the cheapest ticket I can get to visit 20 cities? Then it consider different routes, airlines, available seats, non-stop flight, connecting flights, layover, standby, weather, ratings, time tables, window seat, entertainment, connection, arrival times, departure times. meals, business class, baggage fees, punctuality, Wi-Fi and more…! This generate vast amounts of data. And to finding the best solution for such problem is called optimization problems.

Quantum Linear Algorithm can analyze relationships within large sets of data faster, for a wider array of data types than previously expected. Zhao Zhikuan, the paper’s corresponding author from Singapore University of Technology and Design explained that previous quantum algorithm of this kind can be applied to a very specific type of problem. This is because the number of computational steps goes up rapidly with the number of elements in the matrix.

Quantum linear Algorithm relies on a quantum singular value estimation and can cope with data not limited to sparse data. The algorithm calculates how strongly each element is is correlated with another by “inverting” the matrix. But as I mentioned above in order to get the best performance of this algorithm it will require bigger quantum computers. Zhao expects that it still need about 3-5 years when they can actually use the hardware to do meaningful quantum computation.