Related papers: The code distance of Floquet codes
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
As quantum error correction (QEC) experiments continue to make rapid progress, there is increased interest in designing experiments with guarantees of logical performance. At present, one difficulty is the lack of a clear connection between…
In this work, we analyze a framework for constructing fault-tolerant measurement schedules of varying lengths by combining stabilizer generators, and prove results about the distance of such schedules by combining according to classical…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
We present a quantum error correcting code with dynamically generated logical qubits. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act…
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
Quantum error-correcting codes (QECCs) sit between noisy quantum hardware and reliable computation, so the code parameters used in practice must be trustworthy. The single number that summarizes a code's strength is its distance, yet…
We investigate the evolution of quantum information under Pauli measurement circuits. We focus on the case of one- and two-dimensional systems, which are relevant to the recently introduced Floquet topological codes. We define local…
We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely…
In order to build a scalable quantum computer error correction will be required to reduce the impact of errors. Implementing error correction in the framework of measurement based computation manifests itself as the construction of fault…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
The Bravyi-K\"onig (BK) theorem is an important no-go theorem for the dynamics of topological stabiliser quantum error correcting codes. It states that any logical operation on a $D$-dimensional topological stabiliser code that can be…
Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multi-level physical systems. Here, we present a general framework and working examples for encoding fault-tolerant logical…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
We demonstrate the existence of a finite temperature threshold for a 1D stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have…
Fault-tolerant quantum computing is crucial for realizing large-scale quantum computation, and the interplay between hardware architecture and quantum error-correcting codes is a key consideration. We present a comparative study of two…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…