Although I often write about quantum computing, I mainly write about two forms: gate quantum computing and adiabatic quantum computing. There is a third, though, called quantum walks. Quantum walks are found in nature: a quantum walk is how the electron-transfer step in photosynthesis works. Now researchers have gotten entire clouds of atoms to go marching to their quantum beat.

Quantum walks can be implemented with light, but you would need to make a new computer for every calculation. In a Bose-Einstein condensate, however, the roles of light and matter are reversed. Researchers have used this to demonstrate a BEC quantum walk.

## A bevy of quantum computers

Before we get into it, let’s quickly compare the different quantum-computer types. A gate quantum computer is the most familiar. A calculation is performed using discrete logic operations using a collection of gates, and the answer is read out at the end.

Adiabatic quantum computing does not involve discrete operations. Instead, the problem is reworked to be the lowest-energy state of some energy landscape (think that the solution is in the lowest valley in a mountainous region). The trick is to start with a landscape that looks like a smooth bowl and slowly create the mountains so that the quantum bits (qubits) fall into the lowest valley when the process is complete. Reading out the values of the qubits reveals the solution to the problem.

A quantum walk is different from both of these. The problem is encoded as a series of paths. The quantum state takes all possible paths at once, but the paths allow the quantum state to interfere with itself such that the path that encodes the solution has a high probability, while the rest don’t. In other words, you send in some quantum object—say, a photon—and measure where the photon emerges to get the solution.

The trick is to create a set of interlinked paths that encode the problem that you wish to solve. If photons are your qubit, you can do this using optical fibers. Fibers are coupled to each other carefully so that the qubit can travel multiple paths and mix with itself. The strength of the coupling determines “how much” of the photon travels in each fiber, while the lengths of fiber determine if the interference will be constructive or destructive.

Optical quantum walks are lovely, but each device is fixed: the length of fiber and the coupling between different fibers cannot be readily adjusted. Essentially, a computer based on optical quantum walks lacks a programmable element.

## Matter that flows like light

However, in a BEC, the role of light and matter can be interchanged. The BEC is a collective of very cold atoms that are all in the same quantum state. That, essentially, means that the collection behaves like a single particle. When you hit the BEC with a pulse of light, it is given a kick and some momentum, causing it to drift. But the direction of drift depends on the internal state of the BEC.

The internal state is set by applying a microwave pulse. So, for instance, the right microwave pulse will set the BEC into a superposition of two states. If the microwave pulse is followed by a kick from the laser, then the BEC has to move in two directions at once thanks to that superposition.

The researchers showed that the spatial path of the BEC can be manipulated by sequences of microwave and laser pulses, with the controller acting rather like a skilled pinball player. But this is quantum pinball: every time the BEC hits a bumper, the ball goes in multiple directions and hits multiple additional bumpers. To make matters more complicated, the balls cross paths and recombine at various points. Where the paths overlap, the BEC interferes with itself. The interference reduces the probability of finding the BEC on certain paths while increasing it on others—exactly what we want for quantum computations.

## Making light a solid

Where light requires glass fibers that have a fixed coupling between each other (and fixed lengths between coupling points), the BEC version is more flexible. The light kicks move the BEC along in free space, while the microwave pulses act like couplers between different paths. The key point being that the number of light pulses changes the path length, while the strength of the microwave pulse changes the coupling between different paths.

Since neither the light nor the microwave pulses are fixed—they can be changed at any time—the route is programmable.

But there is no computer yet. The researchers have demonstrated that a single BEC can be made to go through a quantum walk. They have not, however, demonstrated that they can encode a problem in that walk.

As far as I can tell, there will be some difficulty making that step. Making a computer means that the different paths should be subject to different microwave pulses. To use the optical fiber analog: after the photon is split to go down two different paths, the left path should be subject to different couplings and path lengths relative to the right path. But, the distances between the different BEC paths are so small that it will be impossible to target the microwave pulse to just one of them. In other words, we can’t stop a microwave source from modifying the internal state of the entire BEC.

Nevertheless, this is a good start. BEC quantum walks have the potential to combine the best of several worlds. BECs operate in the clean world of vacuum and rely on neutral atoms. They should be able to provide a highly reliable and long-lived quantum bit. In this respect, they are rather like ion-trap quantum computers. Furthermore, the quantum walk may provide a way to scale to larger problems without the issue of having to individually address a large collection of qubits. In this respect, the approach is more like adiabatic quantum computing and offers prospects for scaling.

, 2018, DOI: 10.1103/PhysRevLett.121.070402. (About DOIs)