Related papers: Stabilizer formalism for generalized concatenated …
In this paper, we define and study \emph{quantum cyclic codes}, a generalisation of cyclic codes to the quantum setting. Previously studied examples of quantum cyclic codes were all quantum codes obtained from classical cyclic codes via the…
Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum…
In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes $L_k$ and $L_k^{+}$, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in…
Quantum Error Correction (QEC) is essential for fault-tolerant quantum copmutation, and its implementation is a very sophisticated process involving both quantum and classical hardware. Formulating and verifying the decomposition of logical…
Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a new way to express stabilizer states and further improve the…
Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
We introduce a quantum strategy from nonlocal games to improve the stabilizer approximation we proposed previously. The resulting approach turns out to be a qubit-by-qubit gauging procedure for standard stabilizers, which could involve…
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…
CSS codes are a subfamily of stabilizer codes especially appropriate for fault-tolerant quantum computations. A very simple method is proposed to encode a general qudit when a Calderbank-Shor-Steane quantum code, defined over a q-ary…
Systems of neutral kaons can be used to observe entanglement and the violation of Bell inequalities. The decay of these particles poses some problems, however, and recently an effective formalism for treating such systems has been derived.…
The entanglement-assisted stabilizer formalism can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs). In this work, we construct some new entanglement-assisted quantum MDS…
The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density…
Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
The stabilizer formalism for quantum error-correcting codes has been, without doubt, the most successful at producing examples of quantum codes with strong error-correcting properties. In this paper, we discuss strong automorphism groups of…
We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing,…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.