Computer scientists have only begun to realize the potential of quantum computing and algorithms, where computers use quantum principles to store data in qubits. One thing that could help in the development of algorithms is the "quantum walk," which involves the movement of a particle as a superposition of all possible states. Until recently, quantum walks were a theoretical construct. However, according to Science, physicists in Germany are now able to make cesium atoms arranged in an optical lattice perform a physical quantum walk.

Quantum walks were first proposed by physicist Richard Feynman and are, in terms of probability, the opposite of a random walk. A random walk might be modeled by a person flipping a coin, and for each flip he steps left for heads and right for tails. In this case, his most probable location is the center, with the probability distribution tapering off in either direction. A quantum walk involves the use of internal states and superpositions, and results in the hypothetical person "exploring" every possible position simultaneously.

When a quantum walker flips a coin, it directs him to move one way, but he maintains an "internal state" that moves the other way, making him a superposition of both directions of movement. During a quantum walk, as the quantum object takes more steps, it becomes "delocalized" over all available positions, as if its presence is blurred.

A second feature of quantum walking is matter-wave interference, as when the person flips heads and next flips tails. The second step makes the new superposition overlap the old one, and the new superposition can either amplify the old position or remove it. After all this occurs and the desired number of steps have been taken, an attempted observation will collapse the superposition and "resolve" the object to a single position.

As previously mentioned, a random walk's probability distribution has a single peak tapering off in either direction. A quantum walk's probability distribution generally has two peaks placed evenly on either side of the starting position. However, this distribution can vary depending on the initial internal state of the particle doing the walking, which can cause the final position to strongly favor one side or the other.

While it has been asserted that quantum walks might be observable in many different systems, it has long been a theoretical construct. This has changed with scientists' ability to realize a quantum walk with laser-cooled cesium atoms held in the potential wells of a one-dimensional optical lattice. Using Hadamard-type gates, which perform a sort of Fourier transform on the atoms, the cesium atoms' physical and internal states can be shifted, resulting in a distribution of locations like that seen in a theoretical quantum walk, with two peaks or one heavily-favored off-center peak.

The authors of the new paper were able to replicate the theoretical quantum behavior on walks of up to ten steps and could refocus the delocalized particle backwards through the gates to its initial site on the lattice.

The ability to conduct quantum walks has enormous implications for the field of computer science. Quantum algorithms abandon the use of transistors and bits in favor of "qubits," or quantum binary digits. While a bit can only hold one piece of data, like a 0 or 1, a qubit can hold a superposition of all possible states of data (a 0, a 1, or both). Furthermore, a qubit can be entangled with other qubits to hold all possible collective states—three qubits can simultaneously hold states 000, 001, 011, and so on, covering all combinations.

Science, 2009. DOI: 10.1126/science.1174436

Listing image by Kevin Wolfe