Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise. In this work, we demonstrate that quantum low density parity check codes can be similarly bias-tailored. We introduce a bias-tailored lifted product code construction that provides the framework to expand bias-tailoring methods beyond the family of 2D topological codes. We present examples of bias-tailored lifted product codes based on classical quasi-cyclic codes and numerically assess their performance using a belief propagation plus ordered statistics decoder. Our Monte Carlo simulations, performed under asymmetric noise, show that bias-tailored codes achieve several orders of magnitude improvement in their error suppression relative to depolarising noise.
Belief-propagation (BP) decoders play a vital role in modern coding theory, but they are not suitable to decode quantum error-correcting codes because of a unique quantum feature called error degeneracy. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check (LDPC) codes with a loss function tailored to error degeneracy. Training substantially improves the performance of BP decoders for all families of codes we tested and may solve the degeneracy problem which plagues the decoding of quantum LDPC codes.
Surface code is an error-correcting method that can be applied to the implementation of a usable quantum computer. At present, a promising candidate for a usable quantum computer is based on superconductor-specifically transmon. Because errors in transmon-based quantum computers appear biasedly as Z type errors, tailored surface and XZZX codes have been developed to deal with the type errors. Even though these surface codes have been suggested for lattice structures, since transmons-based quantum computers, developed by IBM, have a heavy-hexagon structure, it is natural to ask how tailored sur…
Fault-tolerant cluster states form the basis for scalable measurement-based quantum computation. Recently, new stabilizer codes for scalable circuit-based quantum computation have been introduced that have very high thresholds under biased noise where the qubit predominantly suffers from one type of error, e.g. dephasing. However, extending these advances in stabilizer codes to generate high-threshold cluster states for biased noise has been a challenge, as the standard method for foliating stabilizer codes to generate fault-tolerant cluster states does not preserve the noise bias. In this wor…
Self-correcting quantum memories demonstrate robust properties that can be exploited to improve active quantum error-correction protocols. Here we propose a cellular automaton decoder for a variation of the color code where the bases of the physical qubits are locally rotated, which we call the XYZ color code. The local transformation means our decoder demonstrates key properties of a two-dimensional fractal code if the noise acting on the system is infinitely biased towards dephasing, namely, no string-like logical operators. As such, in the high-bias limit, our local decoder reproduces the b…
Hardware-Tailored Resource Estimation for Magic-State Distillation on Silicon Spin Qubits
Cavendish Lab., Department of Physics, Univ. of Cambridge（剑桥大学卡文迪什实验室物理系）；Hitachi Cambridge Lab.（日立剑桥实验室）；Department of Computer Science and Technology, Univ. of Cambridge（剑桥大学计算机科学与技术系）
We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise model, with independent bit and phase flips occurring at different rates, we show that a single code greatly outperforms the well-studied Steane code across the full range of parameters of the noise model, including for unbiased noise. In fact, this tailored code performs almost optimally when compared with 10,000 randomly selected stabilizer codes of comparab…
Quantum non-demolition measurements as a practical primitive for fault-tolerant computation against biased noise
Alice & Bob（爱丽丝与鲍勃公司）；Laboratoire de Physique de l’École Normale Supérieure, École Normale Supérieure, Centre Automatique et Systèmes, Mines Paris, Université PSL, CNRS, Inria（巴黎高等师范学院物理实验室，巴黎高等师范学院，自动系统与矿业学院，巴黎高等矿业学院，PSL大学，法国国家科学研究中心，法国国家信息与自动化研究所）
The code capacity threshold for error correction using qubits which exhibit asymmetric or biased noise channels is known to be much higher than with qubits without such structured noise. However, it is unclear how much this improvement persists when realistic circuit level noise is taken into account. This is because implementations of gates which do not commute with the dominant error un-bias the noise channel. In particular, a native bias-preserving controlled-NOT (CX) gate, which is an essential ingredient of stabilizer codes, is not possible in strictly two-level systems. Here we overcome …
Recent work has demonstrated that high-threshold quantum error correction is possible for biased-noise qubits, provided one can implement a controlled-not (CX) gate that preserves the bias. Bias-preserving CX gates have been proposed for several biased-noise qubit platforms, most notably Kerr cats. However, experimentally measuring the noise bias is challenging as it requires accurately estimating certain low-probability Pauli errors in the presence of much larger state preparation and measurement (SPAM) errors. In this paper, we introduce bias randomized benchmarking (BRB) as a technique for …
The Magic Scroll: Leveraging biased noise to improve magic state cultivation in register-based architectures
Silicon Quantum Computing Pty. Ltd.（硅量子计算有限公司）；UNSW Sydney（新南威尔士大学）；Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, UNSW Sydney（新南威尔士大学物理学院量子计算与通信技术卓越中心）
Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the noise is biased towards dephasing. Here we introduce an efficient high-threshold decoder for a noise-tailored surface code based on minimum-weight perfect matching. The decoder exploits the symmetries of its syndrome under the action of biased noise and generalises to the fault-tolerant regime where measurements are unreliable. Using this decoder, we obtain fau…
