Related papers: Quantum error correction below the surface code th…
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
Quantum error correction is essential for realizing scalable quantum computation. Among various approaches, low-density parity-check codes over higher-order Galois fields have shown promising performance due to their structured sparsity and…
The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of…
We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. We show how to use our method to analyze hypothetical quantum computers with various…
The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…
A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
Quantum error correction works effectively only if the error rate of gate operations is sufficiently low. However, some rare physical mechanisms can cause a temporary increase in the error rate that affects many qubits; examples include…
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment.…
In the shallow sub-threshold regime, fault-tolerant quantum computation requires a tremendous amount of qubits. In this paper, we study the error correction in the deep sub-threshold regime. We estimate the physical error rate for achieving…
In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient…
When storing encoded qubits, if single faults can be corrected and double faults postselected against, logical errors only occur due to at least three faults. At current noise rates, having to restart when two errors are detected prevents…
The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
We study the fundamental limits on the reliable storage of quantum information in lattices of qubits by deriving tradeoff bounds for approximate quantum error correcting codes. We introduce a notion of local approximate correctability and…
To date, a great deal of attention has focused on characterizing the performance of quantum error correcting codes via their thresholds, the maximum correctable physical error rate for a given noise model and decoding strategy. Practical…
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…