Synopsis

The quantum shortcut to a solution

Physics 2, s102
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


Subject Areas

Quantum Information

Related Articles

Distant Memories Entangled
Quantum Information

Distant Memories Entangled

On the road to a quantum internet, researchers demonstrate entanglement of two memory elements located 12.5 km apart in an urban environment. Read More »

Hiding Secrets Using Quantum Entanglement
Quantum Information

Hiding Secrets Using Quantum Entanglement

Three experiments demonstrate the key elements of a quantum cryptographic scheme that predictions indicate should be unhackable, bringing the promise of quantum encryption technologies a step closer to reality. Read More »

Quantum-Aided Machine Learning Shows Its Value
Quantum Information

Quantum-Aided Machine Learning Shows Its Value

A machine-learning algorithm that includes a quantum circuit generates realistic handwritten digits and performs better than its classical counterpart. Read More »

More Articles