Related papers: Flag fault-tolerant error correction for any stabi…
The high overhead of fault-tolerant measurement sequences (FTMSs) poses a major challenge for implementing quantum stabilizer codes. Here, we address this problem by constructing efficient FTMSs for the class of quantum Hamming codes…
Consider a 2-D square array of qubits of extent $L\times L$. We provide a proof that the minimum weight perfect matching problem associated with running a particular class of topological quantum error correction codes on this array can be…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum…
The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…
The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
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 introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…
Achieving scalable, fault-tolerant quantum computation requires quantum memory architectures that minimize error correction overhead while preserving coherence. This work presents a framework for high-dimensional qudit memory in…
The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact…
We propose quaternion-based strategies for quantum error correction by extending quantum mechanics into quaternionic Hilbert spaces. Building on the properties of quaternionic quantum states, we define quaternionic analogues of Pauli…
Fracton topological phases have a large number of materialized symmetries that enforce a rigid structure on their excitations. Remarkably, we find that the symmetries of a quantum error-correcting code based on a fracton phase enable us to…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
Stabiliser codes with large weight measurements can be challenging to implement fault-tolerantly. To overcome this, we propose a Floquetification procedure which, given a stabiliser code, synthesises a novel Floquet code that only uses…