Related papers: Quantum Error Correction with the Toric-GKP Code
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are…
Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to…
Gaussian loss channels are of particular importance since they model realistic optical communication channels. Except for special cases, quantum capacity of Gaussian loss channels is not yet known completely. In this paper, we provide…
Geometrically local quantum codes, which are error correction codes embedded in $\mathbb{R}^D$ with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to…
Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
The Gottesman-Kitaev-Preskill (GKP) error correcting code encodes a finite dimensional logical space in one or more bosonic modes, and has recently been demonstrated in trapped ions and superconducting microwave cavities. In this work we…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
In the field of fault-tolerant quantum computing, continuous-variable systems can be utilized to protect quantum information from noise through the use of bosonic codes. These codes map qubit-type quantum information onto the larger bosonic…
To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available…
The Gottesman-Kitaev-Preskill (GKP) error correcting code uses a bosonic mode to encode a logical qubit, and has the attractive property that its logical Clifford gates can be implemented using Gaussian unitary gates. In contrast, a direct…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However,it is still challenging to experimentally generate the…
Kitaev's toric code is arguably the most studied quantum code and is expected to be implemented in future generations of quantum computers. The renormalisation decoders introduced by Duclos-Cianci and Poulin exhibit one of the best…
Quantum bits are more robust to noise when they are encoded non-locally. In such an encoding, errors affecting the underlying physical system can then be detected and corrected before they corrupt the encoded information. In 2001,…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
We introduce a new class of random Gottesman-Kitaev-Preskill (GKP) codes derived from the cryptanalysis of the so-called NTRU cryptosystem. The derived codes are good in that they exhibit constant rate and average distance scaling $\Delta…