Adaptive surface code for quantum error correction in the presence of temporary or permanent defects
Adam Siegel, Armands Strikis, Thomas Flatters, Simon C. Benjamin
Abstract
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may correspond to individual qubits or to clusters and could potentially disrupt the code sufficiently to generate logical errors. In this paper, we explore a novel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>a</mml:mi><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>p</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>e</mml:mi></mml:math> approach for surface code quantum error correction on a defective lattice. We show that combining an appropriate defect detection algorithm and a quarantine of the identified zone allows one to preserve the advantage of quantum error correction at finite code sizes, at the cost of a qubit overhead that scales with the size of the defect. Our numerics indicate that the code's threshold need not be significantly affected; for example, for a certain scenario where small defects repeatedly arise in each logical qubit, the noise threshold is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2.7</mml:mn><mml:mi mathvariant="normal">&#x0025;</mml:mi></mml:math> (versus the defect-free case of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2.9</mml:mn><mml:mi mathvariant="normal">&#x0025;</mml:mi></mml:math>). These results pave the way to the experimental implementation of large-scale quantum computers where defects will be inevitable.