Quantum information processing has practical applications like exponential speed ups in optimisation problems or the simulation of complex quantum systems. However, well controlled quantum systems realised experimentally to process the information are sensitive to noise. The progress in leading experimental platforms like superconducting qubits or trapped ions has al-lowed the realisation of high-fidelity quantum processors known as Noisy Intermediate-Scale Quantum (NISQ) devices with roughly 50 qubits. NISQ devices are meant to be large enough to show, despite their imperfections, an advantage over classical processors in some computational tasks and pro-vide a rich playground to prove principles for future quantum algorithms and protocols. However, quantum processors need to be scaled up to imple-ment quantum algorithms that are relevant for practical applications. For this purpose, Quantum Error Correction (QEC) codes, which encode the information in multi-partite quantum states that are generally highly en-tangled, become crucial to eliminate the errors introduced by noise sources like qubit loss. Here we introduce a protocol to correct qubit loss, i.e., the impossibility to access the information encoded in a qubit, in the color code, a leading candidate for fault-tolerant quantum computation. We show that the achieved tolerance of 46(1)% to qubit loss is related to a novel percola-tion problem on three coupled lattices. Our work shows the high robustness of the color under our protocol and has practical importance for implemen-tations of fault-tolerant QEC. In our second line of research we propose and analyse local entanglement witnesses as efficient and platform-agnostic detectors of the entanglement between qubit subsystems, providing a de-scription of the entanglement structure in, in principle, arbitrarily large quantum systems. Since entanglement is a genuinely quantum property used as a resource in most quantum algorithms, local witnesses, which can be implemented with current technology, are of interest for current and future quantum processors.
Critique of fault-tolerant quantum information processing
