Related papers: Duality in Entanglement-Assisted Quantum Error Cor…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
We generalize the stabilizer formalism for entanglement-assisted quantum error-correcting codes with noisy ebits (EAQECCs-Ne) from the binary case to the general $q$-ary case, where $q$ is a prime power. By leveraging the structure of the…
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…
By solving a problem regarding polynomials in a quotient ring, we obtain the relative hull and the Hermitian hull of projective Reed-Muller codes over the projective plane. The dimension of the hull determines the minimum number of…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…
Two pure orthogonal quantum states can be perfectly distinguished by sequential local action of multiple pairs of parties. However, this process typically leads to the complete dissolution of entanglement in the states being discriminated.…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
The sequential quantum random access code (QRAC) allows two or more decoders to obtain a desired message with higher success probability than the best classical bounds by appropriately modulating the measurement sharpness. Here, we propose…
Multipartite entanglement is a valuable resource for quantum technologies. However, detecting this resource can be challenging: for genuine multipartite entanglement, the detection may require global measurements that are hard to implement…
Universal fault-tolerant quantum computation requires overcoming the Eastin--Knill theorem on quantum error correction (QEC) codes that protect information from noise. This is often accomplished through strategies like magic state…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…
Recent advances in quantum error correction (QEC) across hardware platforms have demonstrated operation near and beyond the fault-tolerance threshold, yet achieving exponential suppression of logical errors through code scaling remains a…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
The discretized Poisson equation matrix (DPEM) in 1D has been shown to require an exponentially large number of terms when decomposed in the Pauli basis when solving numerical linear algebra problems on a quantum computer. Additionally,…
We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…
Quantum entanglement plays a crucial role in quantum computing. Entangling information has important implications for understanding the behavior of quantum programs and avoiding entanglement-induced errors. Entanglement analysis is a static…