Quantum computers sound exotic but their power may lie in solving mundane equations – fast.
Until now these systems have been geared towards tasks such as factorising huge numbers, which would not be much use outside cryptography.
In 2009, Seth Lloyd at the Massachusetts Institute of Technology and colleagues devised a quantum algorithm for solving systems of linear equations, such as determining two unknown variables that appear in two separate equations. This example is classroom algebra, but scale it up to millions of variables and the same mathematics drives weather forecasting, image processing and traffic analysis.
Lloyd's team showed that while the number of steps in the classical algorithm scales with the number of equations, for the quantum version, it scales with the logarithm of that number – equivalent to solving a trillion equations in a few hundred steps.
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