Microwaves propagating back and forth through a metamaterial have been used to implement a quantum algorithm. The efficiency of the technique was shown to match that of Grover’s search algorithm, with each round-trip of the wavefront corresponding to one iteration of the calculation.

The last place you look

Grover’s search algorithm is an approach to interrogating a database for an output that matches a certain input value. Using classical computation, searching a database of size N would take N iterations, since the correct result could be the Nth entry in the list. Quantum techniques can cut the computation time dramatically, with Grover’s algorithm requiring a number of iterations equal to the square root of N.

Optical, nuclear magnetic resonance, and trapped-ion systems have been used before to implement the algorithm, proving that classical approaches can achieve the same search efficiency without the need for quantum effects like entanglement. Now, writing in Advanced Materials, Weixuan Zhang and colleagues at Beijing Institute of Technology and Tongji University in China claim the first implementation in an electromagnetic metamaterial, with potential applications in wave-based signal processors.

Shaped beam

The researchers’ setup consists of a 3D-printed, perforated dielectric structure into which a Gaussian microwave beam is directed. The searched-for term is defined by the oracle sub-block at one end of the structure. A specific arrangement of air holes at a location along the width of this component makes the beam adopt a spatially dependent phase profile, representing the input to the algorithm.

From the oracle sub-block, the wavefront propagates through two Fourier-transform sub-blocks separated by a phase plate. The purpose of the phase plate is to convert the oracle-imprinted phase pattern into an amplitude signal.

A ceramic reflector at each end of the structure causes the beam to pass back and forth through the metamaterial block, with the electric field amplitude pattern of the wavefront evolving each time. Since Zhang and his team designed the system to implement the simplest quantum algorithm that they could, the search process takes just one-and-a-half iterations (round-trips) to complete, after which the result can be read in the amplitude profile of the beam.

Shorter wavelengths

For this proof of principle, the researchers employed a small searchable database using a macroscopic physical device – the metamaterial block is some tens of centimetres across. Using infrared or visible beams instead could allow more complex search problems to be implemented with chip-scale architectures.