相关论文: Homomorphic Quantum Error Correction
The integration of quantum error correction codes and homomorphic encryption schemes is essential for achieving fault-tolerant secure cloud quantum computing. However, owing to the significant overheads associated with these schemes, their…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error…
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…
The gold-standard for security in quantum cryptographic protocols is information-theoretic security. Information-theoretic security is surely future-proof, because it makes no assumptions on the hardness of any computational problems and…
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…
Quantum computers promise to solve problems that are intractable for classical computers, but qubits are vulnerable to many sources of error, limiting the depth of the circuits that can be reliably executed on today's quantum hardware.…
The Hamiltonian model of quantum error correction code in the literature is often constructed with the help of its stabilizer formalism. But there have been many known examples of nonadditive codes which are beyond the standard quantum…
The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…
As quantum computing matures into a practical paradigm, the need for secure and private quantum computation on untrusted hardware becomes increasingly urgent. While classical fully homomorphic encryption has enabled computation over…
The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…
Homomorphic Encryption (HE) allows secure and privacy-protected computation on encrypted data without the need to decrypt it. Since Shor's algorithm rendered prime factorisation and discrete logarithm-based ciphers insecure with quantum…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and…
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting…
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming…
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…