Keeping One Step Ahead of Errors in Quantum Computation

Courtesy of Quitemad |

Researchers have conducted a work on the use of two families of Topological Quantum Codes for error correction in quantum systems. One of the most important achievements has consisted in beating the previously known qubit-error-rate by 75 percent. This opens the way for future improvements.

This research has been coordinated by Miguel Angel Martin-Delgado, Professor at the Universidad Complutense de Madrid and QUITEMAD Coordinator, along with Hector Bombin and Helmut Kraztgraber, researchers of the QUITEMAD Scientific Consortium, together with an international group of scientists from Switzerland (R. Andrist) and Japan (M. Ozheki). It has been conducted with the access to the most powerful supercomputer in Spain — Magerit-2 — at the Supercomputing and Visualization Center of Madrid (CeSViMa.), and supercomputers in U. Texas and ETH (Zurich). The result of this research places scientists one step closer to the success of quantum computation and closer to the major challenge — in the long term — of building large quantum computers.

The study has been published in the *Physical Review* X journal (Americam Physical Society) and also widely commented by Prof. Daniel Gottesman, Perimeter Institute, Waterloo, Canada, and also researcher at the Perimeter Institute, and colleagues who focus this work on the study of both topological toric and color codes, determining the degree of protection provided against the more generic form of errors.

Quantum computers are much more vulnerable to noise than classical computers. This is because the quantum states of the tiny qubits can be altered by the smallest noise, which easily leads to errors. Because of the inevitable presence of decoherence effects in the systems, is necessary to have adequate error correction schemes and protect information from noise. Error correction is then a matter of great importance for the success of quantum computing. A very promising approach, and currently the best candidate for practical implementations, is the one that uses topological error correction codes. The error correcting performance of a topological code is essentially captured by the so-called ‘error threshold.’ So, while the noise level is below the natural threshold of the code in question, the noise-induced errors can be completely corrected by well-designed manipulations, involving only a few qubits. However, for some of the topological reference codes, to find out what is the threshold of the most generic form of noise disturbance turns out to be a difficult technical challenge.

In general, an error correction code quantum works by, first, defining a set of error-identifying quantum measurements and, then, making measurements to identify the error (set the called “error sindrome”), and finally, prescribing and executing a set of quantum operations for errors correction on the qubits. A topological code is featured by two fundamental characteristics: First, all the necessary quantum measurements for the error correction are “local,” involving only a few qubits that can be viewed as “neighbors.” Second, there is no local operation which alone can change the entire computer encoded status. In essence, “topological” means robustness against local disturbances of the environment. The two families of topological codes uopn which the work has focused on are the toric codes and color codes. In the first case, the physical qubits are placed on the square lattice-like grid on the surface of a torus; in the latter, on the vertices of a trivalent, eg. hexagonal lattice, the architecture of the qubit connectivity dictated by the nature of quantum measurements involved in the codes.

A previous work of Dennis, Kitaev, Landahl and Preskill in 2004, pioneered the conceptual approach of determining the error threshold, by mapping the quantum problem on a classical model of spin. The form of the noise investigated was, however, only one of three possible fundamental types. However, Hector Bombin and colleagues study the case of a more generic form of noise, which includes not only the three types of noise, but also the correlations between them. It has succeeded in showing that, for the form of the considered noise, the corresponding classical counterpart of the toric code is an 8-vertex spin model. The error threshold then corresponds to the point — in the classical statistical model — where a magnetic ordering transition is lost due to the underlying disorder in the classical spins, which is equivalent to the presence of faulty qubits. Using Monte Carlo simulations and some duality arguments, it is possible to find the error threshold to be at approximately 19 percent — higher than what was previously thought. It is remarkable that the assignation of the color codes leads to new types of classical eight-vertex models with interaction but, at the same time, their error thresholds are also found at 19 percent. This is very novel from the viewpoint of statistical mechanics systems.

The researchers assure that this interdisciplinary effort places us to a closer step toward the final goal of building hight-error-tolerance and large-scale quantum computers, and also that is possible to advance that this work will be of interest to the statistical mechanics community.

**Citations:** *Phys. Rev.* X, Volume 2, Issue 2; Phys. Rev. X 2, 021004 (2012). “Strong Resilience of Topological Codes to Depolarization.”

“Viewpoint: Keeping One Step Ahead of Errors,” Daniel Gottesman, Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada. Published April 30, 2012 | *Physics* 5, 50 (2012) | DOI: 10.1103/Physics.5.50: ‘Statistical mechanical models are the key to understanding the performance of error correction in topological quantum computers.’