Synopsis: Treasure hunt

A new approach proves that a quantum random walk is faster than the classical version at finding marked points on a graph.

Many classical computer algorithms make use of random walks. Among these are spatial search algorithms, which are mathematically equivalent to the task of finding a marked element on a graph. The speed of such an algorithm is characterized by its “hitting time,” which is defined as the expectation value of the number of steps needed to reach a marked state.

It has long been suspected that a suitable quantum algorithm must exist that performs the same search with far fewer steps—of the order of the square root of the classical hitting time—but attempts to simply generalize the classical random walk to the quantum case have only been partially successful.

In an article appearing in Physical Review A, Hari Krovi, Maris Ozols, and Jérémie Roland at NEC Laboratories, Inc., in the US, have finally succeeded in developing a quantum algorithm, which for any reversible random walk and any set of marked vertices, has a running time that scales like the square root of the classical hitting time. Rather than base their algorithm on a conventional quantum walk, they resort to what is called the “adiabatic quantum-computing paradigm.” Here, the solution to the graph problem is obtained as the endpoint of the “trajectory” that the ground state of a Hamiltonian takes as a parameter, s, is slowly varied.

This type of adiabatic quantum computation is equivalent to the more familiar “circuit” model of quantum computation, which means that a formulation of the search problem in terms of more than one quantum model should be possible [1]. – Julio Gea-Banacloche

[1] H. Krovi, F. Magniez, M. Ozols, and J. Roland, in Proceedings of the 37th International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 6198 (Springer, New York, 2010), pp. 540–551.


Announcements

More Announcements »

Subject Areas

Quantum Information

Previous Synopsis

Astrophysics

Solar lab

Read More »

Next Synopsis

Semiconductor Physics

A bumpy road

Read More »

Related Articles

Synopsis: Pinpointing Qubits in a 3D Lattice
Quantum Information

Synopsis: Pinpointing Qubits in a 3D Lattice

Researchers manipulate atomic qubits individually in a three-dimensional optical lattice. Read More »

Viewpoint: Sending Quantum Messages Through Space
Quantum Information

Viewpoint: Sending Quantum Messages Through Space

Fragile photon states useful for quantum communication can be faithfully transmitted and distinguished over a link between an orbiting satellite and a telescope on Earth. Read More »

Synopsis: Good Vibrations
Quantum Information

Synopsis: Good Vibrations

With the assistance of lattice vibrations, quantum dots perform as single-photon emitters. Read More »

More Articles