Related papers: Quantum error correction meets continuous symmetri…
The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hope for eventually realizing practical quantum computers. In…
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
To perform reliable quantum computation, quantum error correction is indispensable. In certain cases, continuous covariance symmetry of the physical system can make exact error correction impossible. In this work we study the approximate…
Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
Reliable execution of large-scale quantum algorithms requires robust underlying operations and this challenge is addressed by quantum error correction (QEC). Most modern QEC protocols rely on measurements and feed-forward operations, which…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate…
Achieving fault-tolerant quantum computation (FTQC) demands simultaneous progress in physical qubit performance and quantum error correction (QEC). This work reviews and benchmarks experimental advancements towards FTQC across leading…
Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Quantum error mitigation (QEM) is typically viewed as a suite of practical techniques for today's noisy intermediate-scale quantum devices, with limited relevance once fault-tolerant quantum computers become available. In this work, we…
A major challenge in performing quantum error correction (QEC) is implementing reliable measurements and conditional feed-forward operations. In quantum computing platforms supporting unconditional qubit resets, or a constant supply of…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
We analyze the long time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is…
Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards…
The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction…