相关论文: Simple Quantum Error Correcting Codes
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Traditional quantum error correction involves the redundant encoding of k quantum bits using n quantum bits to allow the detection and correction of any t bit error. The smallest general t=1 code requires n=5 for k=1. However, the dominant…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent…
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…
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…
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…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad.…
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations…
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
Quantum error-correcting code for higher dimensional systems can, in general, be directly constructed from the codes for qubit systems. What remains unknown is whether there exist efficient code design techniques for higher dimensional…
We propose an error correction coding algorithm for continuous quantum variables. We use this algorithm to construct a highly efficient 5-wavepacket code which can correct arbitrary single wavepacket errors. We show that this class of…
Imperfect measurements are a prevalent source of error across quantum computing platforms, significantly degrading the logical error rates achievable on current hardware. To mitigate this issue, rich measurement data referred to as soft…
The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g.…
Calderbank-Shor-Steane (CSS) quantum error-correcting codes are based on pairs of classical codes which are mutually dual containing. Explicit constructions of such codes for large blocklengths and with good error correcting properties are…
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors that are inherently continuous A powerful method to suppress these effects is to use quantum error correction. Typically,…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
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…