The researchers claim this demonstrates for the first time how quantum walks of several electrons can help to implement quantum computation.

In quantum computing, quantum walks are the quantum analogue of classical random walks, where the current state is described by a probability distribution over all possible positions.

In this study, researchers Alexey Melnikov and Leonid Fedichkin had a system of two qudits implemented as two entangled electrons quantum-walking around the so-called cycle graph.

The entanglement of the two electrons is caused by the mutual electrostatic repulsion experienced by like charges. It is possible to create a system of even more qudits in the same volume of semiconductor material. To do this, it is necessary to connect quantum dots in a pattern of winding paths and have more wandering electrons.

The quantum walks approach to quantum computation is convenient because it is based on a natural process. Nevertheless, the presence of two identical electrons in the same structure was a source of additional difficulties that had remained unsolved.

The phenomenon of particle entanglement plays a pivotal role in quantum information processing. However, in experiments with identical particles, it is necessary to distinguish so-called false entanglement, which can arise between electrons that are not interacting, from genuine entanglement.

To do this, the scientists performed mathematical calculations for both cases, viz., with and without entanglement. They observed the changing distribution of probabilities for the cases with 6, 8, 10, and 12 dots, i.e., for a system of two qudits with three, four, five, and six levels each. The scientists demonstrated that their proposed system is characterized by a relatively high degree of stability.

It has long been a dream to build a universal quantum computer, but so far researchers have been unable to connect a sufficient number of qubits. The work of the Russian researchers brings this one step closer to a future where quantum computations are commonplace.

And although there are algorithms that quantum computers could never accelerate, others would still benefit enormously from devices able to exploit the potential of large numbers of qubits (or qudits). These alone would be enough to save us a couple of thousand years.

Leonid Fedichkin, Expert at the Russian Academy of Sciences and Associate Professor at MIPT’s Department of Theoretical Physics, writes:

“By studying the system with two electrons, we solved the problems faced in the general case of two identical interacting particles. This paves the way toward compact high-level quantum structures.”

The work is covered in the Nature paper Quantum walks of interacting fermions on a cycle graph.

A quantum computer would be capable of molecular modelling that takes into account all interactions between the particles involved. This in turn would enable the development of highly efficient solar cells and new drugs. To have practical applications, a quantum computer needs to incorporate hundreds or even thousands of qubits. And that is where it gets tricky.

The qubit is the basic element of a quantum computer. The essential property of a qubit is its ability to be in a superposition of the two basis states: A|0⟩+B|1⟩. But the unstable nature of the connection between qubits remains the major obstacle preventing the use of quantum walks of particles for quantum computation.