Related papers: Learning Better Error Correction Codes with Hybrid…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
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…
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…
Quantum machine learning has emerged as a potential practical application of near-term quantum devices. In this work, we study a two-layer hybrid classical-quantum classifier in which a first layer of quantum stochastic neurons implementing…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
We report two analytical bounds for quantum error-correcting codes that do not have preexisting classical counterparts. Firstly the quantum Hamming and Singleton bounds are combined into a single tighter bound, and then the combined bound…
Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of…
Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We…
This work addresses the challenge of enabling practitioners without quantum expertise to transition from classical to hybrid quantum-classical machine learning workflows. We propose a three-stage framework: starting with a classical…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
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…
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…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…
Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…
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…