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The successful operation of quantum computers relies on protecting qubits from decoherence and noise, which--if uncorrected--will lead to erroneous results. Because these errors accumulate during an algorithm, correcting them is a key requirement for large-scale and fault-tolerant quantum information processors. Besides computational errors, which can be addressed by quantum error correction.sup.1-9, the carrier of the information can also be completely lost or the information can leak out of the computational space.sup.10-14. It is expected that such loss errors will occur at rates that are comparable to those of computational errors. Here we experimentally implement a full cycle of qubit loss detection and correction on a minimal instance of a topological surface code.sup.15,16 in a trapped-ion quantum processor. The key technique used for this correction is a quantum non-demolition measurement performed via an ancillary qubit, which acts as a minimally invasive probe that detects absent qubits while imparting the smallest quantum mechanically possible disturbance to the remaining qubits. Upon detecting qubit loss, a recovery procedure is triggered in real time that maps the logical information onto a new encoding on the remaining qubits. Although the current demonstration is performed in a trapped-ion quantum processor.sup.17, the protocol is applicable to other quantum computing architectures and error correcting codes, including leading two- and three-dimensional topological codes. These deterministic methods provide a complete toolbox for the correction of qubit loss that, together with techniques that mitigate computational errors, constitute the building blocks of complete and scalable quantum error correction. A deterministic correction of errors caused by qubit loss or leakage outside the computational space is demonstrated in a trapped-ion experiment by using a minimal instance of the topological surface code., Author(s): Roman Stricker [sup.1] , Davide Vodola [sup.2] [sup.3] [sup.4] , Alexander Erhard [sup.1] , Lukas Postler [sup.1] , Michael Meth [sup.1] , Martin Ringbauer [sup.1] , Philipp Schindler [sup.1] [...]

The accuracy of logical operations on quantum bits (qubits) must be improved for quantum computers to outperform classical ones in useful tasks. One method to achieve this is quantum error correction (QEC), which prevents noise in the underlying system from causing logical errors. This approach derives from the reasonable assumption that noise is local, that is, it does not act in a coordinated way on different parts of the physical system. Therefore, if a logical qubit is encoded non-locally, we can--for a limited time--detect and correct noise-induced evolution before it corrupts the encoded information.sup.1. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a non-local qubit: a superposition of position eigenstates that forms grid states of a single oscillator.sup.2. However, the implementation of measurements that reveal this noise-induced evolution of the oscillator while preserving the encoded information.sup.3-7 has proved to be experimentally challenging, and the only realization reported so far relied on post-selection.sup.8,9, which is incompatible with QEC. Here we experimentally prepare square and hexagonal GKP code states through a feedback protocol that incorporates non-destructive measurements that are implemented with a superconducting microwave cavity having the role of the oscillator. We demonstrate QEC of an encoded qubit with suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous-variable systems and, in contrast to previous implementations of QEC.sup.10-14, can mitigate all logical errors generated by a wide variety of noise processes and facilitate fault-tolerant quantum computation. Quantum error correction of Gottesman-Kitaev-Preskill code states is realized experimentally in a superconducting quantum device., Author(s): P. Campagne-Ibarcq [sup.1] , A. Eickbusch [sup.1] , S. Touzard [sup.1] , E. Zalys-Geller [sup.1] , N. E. Frattini [sup.1] , V. V. Sivak [sup.1] , P. Reinhold [sup.1] [...]

Quantum computing becomes viable when a quantum state can be protected from environment-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) (1-6) [...]