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We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal…
We study the protection of information in nearly critical topological quantum codes, constructed by perturbing topological stabilizer codes towards continuous quantum phase transitions. Our focus is on the transverse-field toric code…
Entanglement-assisted quantum error-correcting (EAQEC) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the…
A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable…
We consider hierarchically implemented quantum error correction (HI-QEC), in which the fidelities of logical qubits are differentially optimized to enhance the capabilities of quantum devices in scientific applications. By employing qubit…
Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to…
Searches for axion and axionlike dark matter based on solid-state spin qubits are fundamentally limited by strong longitudinal dephasing, which rapidly suppresses the sensitivity gains offered by entanglement. Here we show that quantum…
Spin ensembles are promising quantum technological platforms, but their utility relies on the ability to perform quantum error correction (QEC) for the specific decoherence in these systems. Typical QEC for ensembles requires addressing…
Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes,…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded…
We establish a symmetry-operator framework for designing quantum error correcting~(QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes…
We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
We introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle"…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an…
Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity…