Related papers: Quantum codes do not fix isotropic errors
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels. By now, a plethora of families of codes is known, but there is no…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
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…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
Blind Quantum Computation (BQC) is a delegation computing protocol that allows a client to utilize a remote quantum server to implement desired quantum computations while keeping her inputs, outputs, and algorithms private. However, qubit…
Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a…
Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
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…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Fast quantum data transmission faces several shortcomings such as the indistinguishability of some partly overlapping signals, the channel noises, and so on. Based on the encoded quantum data transmission protocol, an unconventional scheme…
This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed.…
In quantum error correction, it is an important assumption that errors on different qubits are independent. In our previous work [Phys. Rev. A {\bf 92}, 052320 (2015)], the generality of the concatenated five-qubit code has been investgated…
Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…