A quantum algorithm that uses the solution to a set of linear equations provides an exponential speedup by comparison with classical alternatives.

Considering the volume of research on quantum computing, there are surprisingly few quantum algorithms that are known to perform faster than their classical counterparts—the most famous example being Shor’s algorithm for factoring a large number.

Writing in Physical Review Letters, Aram Harrow at the University of Bristol, UK, and Avinatan Hassidim and Seth Lloyd at MIT in the US propose a quantum algorithm for solving a set of linear equations that, within some constraints, is exponentially faster that any classical algorithm. The algorithm could potentially have widespread applicability in fields as varied as biostatistics, ecology, and engineering, all of which rely heavily on solving linear equations.

Strictly speaking, the algorithm of Harrow et al. does not find the solution to the linear equations, but some function of the solution, such as a comparison between two stable states that evolve according to different processes. Though many real-world systems may not fall into the limited set of conditions the authors consider, this proposal provides another example to help us understand why quantum algorithms work better than classical ones. – Jessica Thomas

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