Related papers: Local tensor-network codes
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…
We construct a tensor network representation of the 3d toric code ground state that is stable to a generating set of uniform local tensor perturbations, including those that do not map to local operators on the physical Hilbert space. The…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
There exists a remarkable four-qutrit state that carries absolute maximal entanglement in all its partitions. Employing this state, we construct a tensor network that delivers a holographic many body state, the H-code, where the physical…
Quantum low-density parity-check (QLDPC) codes with good parameters are promising candidates for low-overhead fault-tolerant quantum computing, but their non-local stabilizers require long-range connectivity and frequent qubit movement,…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
We consider a topological stabilizer code on a honeycomb grid, the "XYZ$^2$" code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [J. Phys. A: Math. Theor. 48, 215302…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…
Quantum computers have the potential to change the way we solve computational problems. Due to the noisy nature of qubits, the need arises to correct physical errors occurring during computation. The surface code is a promising candidate…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
This paper presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support…