Related papers: Tensor Networks and Quantum Error Correction
In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important…
Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
Quantum Error Correction (QEC) is the process of detecting and correcting errors in quantum systems, which are prone to decoherence and quantum noise. QEC is crucial for developing stable and highly accurate quantum computing systems,…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
Quantum error correcting codes (QECC) are the key ingredients both for fault-tolerant quantum computation and quantum communication. Teleportation-based error correction (TEC) helps in detecting and correcting operational and erasure errors…
We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is con- structed via the tensor product of parity check matrices of the two…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…
We give an algorithm that converts any tensor network (TN) into a sequence of local unitaries whose composition block-encodes the network contraction, suitable for Quantum Eigenvalue / Singular Value Transformation (QET/QSVT). The…
In this article, we present the unbalanced quantum error correcting codes(one-party-QECC), a novel idea for correcting unbalanced quantum errors. In some quantum communication tasks using entangled pairs, the error distributions between two…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
We systematically study the fundamental competition between quantum error correction (QEC) and continuous symmetries, two key notions in quantum information and physics, in a quantitative manner. Three meaningful measures of approximate…
Quantum computers have the possibility of a much reduced calculation load compared with classical computers in specific problems. Quantum error correction (QEC) is vital for handling qubits, which are vulnerable to external noise. In QEC,…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
Large-scale quantum computers promise transformative speedups, but their viability hinges on fast and reliable quantum error correction (QEC). At the center of QEC are decoders-classical algorithms running on hardware such as FPGAs, GPUs,…
Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…
When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…