Synopsis: Traveling with a Quantum Salesman

Quantum computing could speed up certain algorithms for solving the famous traveling salesman problem.
Synopsis figure
Robert Allison/SAS

A traveling salesman may seem like a relic from a bygone era, but the emblematic problem facing this profession hasn’t gone away: what’s the shortest path for visiting multiple cities and then returning home? The traveling salesman problem (TSP) can describe many situations, such as the optimization of electric wiring or business scheduling. But it becomes computationally intense for a large number of cities or other elements. New work by Dominic Moylett and colleagues at the University of Bristol, UK, shows how quantum computing could potentially speed up TSP algorithms.

There are several ways to help a traveling salesman pick his route. The brute force method is to compute the distance for every possible itinerary. For n cities, this would involve roughly n! computations, which becomes astronomically large as n grows. A quantum computer could provide a quadratic speedup by reducing the number of computations to n!. However, recent efforts have come up with “shortcut” classical algorithms that can solve the TSP with less than 2n steps, which is significantly better than the quantum brute force treatment.

Could shortcut algorithms benefit from quantum computing? Moylett and colleagues considered a special type of shortcut involving so-called backtracking. In the classical case, one iteratively selects a road between cities, assigns it a value of “traveled on” or “not traveled on,” and then checks whether this assignment is consistent with forming a complete route through each city. For quantum backtracking, the team assigns a superposition of “traveled on” and “not traveled on” to each road and then simultaneously checks both. The results show that a near-quadratic speedup can be obtained when the number of roads leaving each city is small.

This research is published in Physical Review A.

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics based in Lyon, France.


Features

More Features »

Announcements

More Announcements »

Subject Areas

Quantum Information

Previous Synopsis

Geophysics

How Ice Bridges Form

Read More »

Next Synopsis

Related Articles

Viewpoint: Linking Two Quantum Dots with Single Photons
Photonics

Viewpoint: Linking Two Quantum Dots with Single Photons

Researchers have transferred quantum information from one quantum dot to another dot 5 m away using photonic qubits as the relay. Read More »

Viewpoint: Photonic Hat Trick
Optics

Viewpoint: Photonic Hat Trick

Two independent groups have provided the first experimental demonstration of genuine three-photon interference. Read More »

Viewpoint: Microwave Quantum States Beat the Heat
Quantum Information

Viewpoint: Microwave Quantum States Beat the Heat

A new quantum communication protocol is robust in the presence of thermal noise, paving the way for all-microwave quantum networks. Read More »

More Articles