相关论文: A theory of single-shot error correction for adver…
Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes,…
For quantum error correction codes the required number of measurement rounds typically increases with the code distance when measurements are faulty. Single-shot error correction allows for an error threshold with only one round of noisy…
Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological codes a single round of local measurements is…
Quantum processors are often affected by biased noise and noisy readout, which reduce reliability and reproducibility. This work combines two complementary strategies to address these challenges. The first is bias tailoring, which aligns…
Quantum hardware rarely suffers equal amounts of bit-flip ($X$) and phase-flip ($Z$) errors; one type is often much more common than the other. A code that is ``bias-tailored'' can exploit this imbalance, lowering the fault-tolerance…
Quantum error correction typically requires repeated syndrome extraction due to measurement noise, which results in substantial time overhead in fault-tolerant computation. Single-shot error correction aims to suppress errors using only one…
We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC), which is a generalization of the stabilizer toric code. The 3D STC can be realized by measuring geometrically-local parity checks of weight at…
Quantum Tanner codes constitute a family of quantum low-density parity-check (LDPC) codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate…
Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return…
Generating samples from the output distribution of a quantum circuit is a ubiquitous task used as a building block of many quantum algorithms. Here we show how to accomplish this task on a noisy quantum processor lacking full-blown error…
Quantum error correction (QEC) with single-shot decoding enables reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum…
Quantum error correction is essential for reliable quantum computation, where surface codes demonstrate high fault-tolerant thresholds and hardware efficiency. However, noise in single-shot measurements limits logical readout fidelity,…
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…
We construct a family of quantum low-density parity-check codes locally equivalent to higher-dimensional quantum hypergraph-product (QHP) codes. Similarly to QHP codes, the proposed codes have highly redundant sets of low-weight stabilizer…
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…
Code-switching is a powerful technique in quantum error correction that allows one to leverage the complementary strengths of different codes to achieve fault-tolerant universal quantum computation. However, existing code-switching…
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.…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
Low-depth parity check (LDPC) codes are a paradigm of error correction that allow for spatially non-local interactions between (qu)bits, while still enforcing that each (qu)bit interacts only with finitely many others. On expander graphs,…