Related papers: Fault-tolerant Preparation of Stabilizer States fo…
Stabilizer codes obtained via CSS code construction and Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed-Muller, hyperbolic and affine variety codes are studied. Stabilizer codes with good…
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 correction is a cornerstone of reliable quantum computing, with surface codes emerging as a prominent method for protecting quantum information. Surface codes are efficient for Clifford gates but require magic state…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…
We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
Quantum computing holds the promise of solving problems intractable for classical computers, but practical large-scale quantum computation requires error correction to protect against errors. Fault-tolerant quantum computing (FTQC) enables…
In this paper, we demonstrate a direct correspondence between phase-free ZX diagrams, a graphical notation for representing and manipulating a certain class of linear maps on qubits, and Calderbank-Shor-Steane (CSS) codes, a large family of…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
Given that quantum error correction processes are unreliable, an efficient error syndrome extraction circuit should use fewer ancillary qubits, quantum gates, and measurements, while maintaining low circuit depth, to minimizing the circuit…
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…
We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…
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…
Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
Decoherence is the main problem to be solved before quantum computers can be built. To control decoherence, it is possible to use error correction methods, but these methods are themselves noisy quantum computation processes. In this work…
Achieving scalable, fault-tolerant quantum computation requires quantum memory architectures that minimize error correction overhead while preserving coherence. This work presents a framework for high-dimensional qudit memory in…
The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and…
Fault-tolerance is the future of quantum computing, ensuring error-corrected quantum computation that can be used for practical applications. Resource requirements for fault-tolerant quantum computing (FTQC) are daunting, and hence,…
Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We…