Related papers: Puncturing Quantum Stabilizer Codes
Quantum stabilizer codes often struggle with syndrome errors due to measurement imperfections. Typically, multiple rounds of syndrome extraction are employed to ensure reliable error information. In this paper, we consider phenomenological…
We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional…
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions…
First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Spin qubits in quantum dots provide a promising platform for realizing large-scale quantum processors since they have a small characteristic size of a few tens of nanometers. One difficulty of controlling e.g., a few thousand qubits on a…
Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit…
We present some results that show that bounds from classical coding theory still work in many cases of quantum coding theory.
Floquet codes are a recently discovered type of quantum error correction code. They can be thought of as generalising stabilizer codes and subsystem codes, by allowing the logical Pauli operators of the code to vary dynamically over time.…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or…
The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of…
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…
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
The quantum hashing bound guarantees that rates up to $1-H(p_I, p_X, p_Y, p_Z)$ are achievable for memoryless Pauli channels, but it is not generally tight. A known way to improve achievable rates for certain asymmetric Pauli channels is to…
The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the…