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Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens…
Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are…
Decoherence of quantum states is a major hurdle towards scalable and reliable quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the error correction overhead and obviate the need for energy-intensive noise reduction…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
Leakage errors arise when the quantum state leaks out of some subspace of interest, for example, the two-level subspace of a multi-level system defining a computational `qubit' or the logical code space defined by some quantum…
Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise which is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates are…
Quantum error-correcting codes, such as subspace, subsystem, and Floquet codes, are typically constructed within the stabilizer formalism, which does not fully capture the idea of fault-tolerance needed for practical quantum computing…
The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of…
The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
Error filtration is a method for encoding the quantum state of a single particle into a higher dimensional Hilbert space in such a way that it becomes less sensitive to phase noise. We experimentally demonstrate this method by distributing…
Recently, a lot of effort has been devoted towards designing erasure qubits in which dominant physical noise excites leakage states whose population can be detected and returned to the qubit subspace. Interest in these erasure qubits has…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…