相关论文: Quantum error-correcting codes associated with gra…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise…
Fault tolerant protocol assumes the application of error correction after every quantum gate. However, correcting errors is costly in terms of time and number of qubits. Here we demonstrate that quantum error correction can be applied…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
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…
The known quantum error-correcting codes are typically built on approximative open-quantum-system models such as Born--Markov master equations. However, it is an open question how such codes perform in actual physical systems that, to some…
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 synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
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…
Error operator bases for systems of any dimension are defined and natural generalizations of the bit/sign flip error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of…
Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum…
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric…
A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
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…
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…