Related papers: Understanding holographic error correction via uni…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We study the holographic map in AdS/CFT, as modeled by a quantum error correcting code with exact complementary recovery. We show that the map is determined by local conditional expectations acting on the operator algebras of the…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
We describe a simple quantum error correcting code built out of a time-dependent transverse field Ising model. The code is similar to a repetition code, but has two advantages: an $N$-qubit code can be implemented with a finite-depth…
Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the non-local operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a…
In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…
The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…
We generalize Helberg's number-theoretic construction of multiple insertion-deletion correcting binary codes to non-binary alphabets and describe a linear decoding algorithm for correcting multiple deletions.
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary…
Laboratory hardware is rapidly progressing towards a state where quantum error-correcting codes can be realised. As such, we must learn how to deal with the complex nature of the noise that may occur in real physical systems. Single qubit…
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…
This manuscript presents a construction method for quantum codes capable of correcting multiple deletion errors. By introducing two new alogorithms, the alternating sandwich mapping and the block error locator, the proposed method reduces…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
The Penrose tiling (PT) is an intrinsically non-periodic way of tiling the plane, with many remarkable properties. A quantum error-correcting code (QECC) is a clever way of protecting quantum information from noise, by encoding the…
We propose a holographic image restoration method using an autoencoder, which is an artificial neural network. Because holographic reconstructed images are often contaminated by direct light, conjugate light, and speckle noise, the…
We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an…