Nigg, DanielMüller, MarkusMartínez, Esteban A.Schindler, PhilippHennrich, MarkusMonz, ThomasMartín-Delgado Alcántara, Miguel ÁngelBlatt, Rainer2023-06-192023-06-192014-07-180036-807510.1126/science.1253742https://hdl.handle.net/20.500.14352/35594© The Authors. We gratefully acknowledge support by the Spanish MICINN grant FIS2009-10061, FIS2012-33152, the CAM research consortium QUITEMAD S2009-ESP-1594, the European Commission PICC: FP7 2007-2013, Grant No. 249958, the integrated project SIQS (grant No. 600645), the UCM-BS grant GICC-910758, and by the Austrian Science Fund (FWF), through the SFB FoQus (FWF Project No. F4002-N16), as well as the Institut f¨ur Quanteninformation GmbH. This research was supported by the U.S. Army Research Office through grant W911NF14-1-0103.The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant quantum computing (FTQC). Here we present a step towards this by implementing a quantum error correcting code, encoding one qubit in entangled states distributed over 7 trapped-ion qubits. We demonstrate the capability of the code to detect one bit flip, phase flip or a combined error of both, regardless on which of the qubits they occur. Furthermore, we apply combinations of the entire set of logical single-qubit Clifford gates on the encoded qubit to explore its computational capabilities. The implemented 7-qubit code is the first realization of a complete Calderbank-Shor-Steane (CSS) code and constitutes a central building block for FTQC schemes based on concatenated elementary quantum codes. It also represents the smallest fully functional instance of the color code, opening a route towards topological FTQC.engjournal articlehttp://dx.doi.org/10.1126/science.1253742http://science.sciencemag.org/https://arxiv.org/pdf/1403.5426.pdfopen access53Error-correcting codesTrapped ionsRealizationComputersThresholdCircuitsMemory.Física-Modelos matemáticos