Importantly, QECCs can be embedded in the resource states for MBQC in several inequivalent ways 33, 34, 35, and of particular theoretical interest, due to their large thresholds, are the topological QECC embeddings 36, 37, 38, 39, 40, 41, 42. Photonic technologies 13 have enjoyed enormous success in the generation of a variety of resource states for MBQC 14, 15, 16, 17, 18 and in the implementation of computational primitives 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32. In MBQC, an algorithm is enacted by performing sequential measurements on the resource state in such a way that the output of the computation is stored in the unmeasured qubits. In this context, a computational paradigm, especially well suited for quantum error correction, is measurement-based quantum computation 10, 11, 12 (MBQC), in which a resource state consisting of many entangled qubits is prepared before the computation starts. A great deal of effort is currently being invested in designing new quantum codes to increase the threshold. Here, the threshold theorem 7 ensures that a quantum computer built with faulty, unreliable components can still be used reliably to implement quantum tasks using QECC techniques 8, 9, so long as the noise affecting its parts is below a given threshold. This enhancement is crucial for enabling a range of speedups in quantum algorithms. It was realized early on that using QECCs 2, 3, 4, 5, 6 to counteract the effects of decoherence and noise provides a means to increase the coherence time of the encoded information. Quantum error-correcting codes (QECCs) constitute fundamental building blocks in the design of quantum computer architectures 1. Our results show that graph state codes are a promising approach for achieving scalable quantum information processing. The graph we realize is setup independent, thus it could be employed in other physical settings. We are able to reliably detect errors and correct against qubit loss.

We use an all-optical setup to encode quantum information into photons representing a four-qubit graph state. Here we report an experimental demonstration of error correction using a graph state code. Depending on the graph’s structure, errors can be detected and corrected in an efficient way using measurement-based techniques. However, recently a family of entangled resources known as graph states has emerged as a versatile alternative for protecting quantum information.

Previous work tackling this problem has relied on the original circuit model for quantum computing. Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise.

Tree quantum error correction