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We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted…
The integration of quantum error correction codes and homomorphic encryption schemes is essential for achieving fault-tolerant secure cloud quantum computing. However, owing to the significant overheads associated with these schemes, their…
Recent advances in quantum error-correction (QEC) have shown that it is often beneficial to understand fault-tolerance as a dynamical process, a circuit with redundant measurements that help correct errors, rather than as a static code…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
Several notions of code products are known in quantum error correction, such as hyper-graph products, homological products, lifted products, balanced products, to name a few. In this paper we introduce a new product code construction which…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Secure quantum networks are a bedrock requirement for developing a future quantum internet. However, quantum channels are susceptible to channel noise that introduce errors in the transmitted data. The traditional approach to providing…
Quantum computers promise to solve problems that are intractable for classical computers, but qubits are vulnerable to many sources of error, limiting the depth of the circuits that can be reliably executed on today's quantum hardware.…
Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…