Related papers: Grand Unification of continuous-variable codes
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…
Quantum computation using optical modes has been well-established in its ability to construct deep neural networks. These networks have been shown to be flexible both architecturally as well as in terms of the type of data being processed.…
In recent years, squeezed cat codes with resilience to specific types of loss have been proposed as a step toward realizing fault-tolerant optical quantum computers. However, error correction for squeezed cat codes requires a strong…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
Quantum computers have advanced rapidly in qubit count and gate fidelity. However, large-scale fault-tolerant quantum computing still relies on quantum error correction code (QECC) to suppress noise. Manually or experimentally verifying the…
Continuous-Variable Quantum Key Distribution (CVQKD) at large distances has such high noise levels that the error-correcting code must have very low rate. In this regime it becomes feasible to implement random-codebook error correction,…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We…
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…
The Gottesman-Kitaev-Preskill (GKP) code was proposed in 2001 by Daniel Gottesman, Alexei Kitaev, and John Preskill as a way to encode a qubit in an oscillator. The GKP codewords are coherent superpositions of periodically displaced…
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…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes as ingredient codes for a quantum error-correcting code is proposed. That is, we find quantum regular LDPC codes with various weight distributions. Furthermore our…
The Quantum Computer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantum computers. In this paper we apply the QCC to the problem of…
Continuous-variable quantum computing architectures based upon the Gottesmann-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate because one can achieve fault-tolerance with a probabilistic supply of GKP states and…
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 propose an autonomous quantum error correction scheme using squeezed cat (SC) code against the dominant error source, excitation loss, in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation…
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…
The popular qubit framework has dominated recent work on quantum kernel machine learning, with results characterising expressivity, learnability and generalisation. As yet, there is no comparative framework to understand these concepts for…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…