The requirements for fault-tolerant quantum error correction can be simplified by leveraging structure in the noise of the underlying hardware.In this work, we identify a new type of structured noise motivated by neutral-atom qubits, biased erasure errors, which arises when qubit errors are dominated by detectable leakage from only one of the computational states of the qubit.We study the performance of this model using gate-level simulations of the XZZX surface code.Using the predicted erasure fraction and bias of metastable 171 Yb qubits, we find a threshold of 8.2% for two-qubit gate errors, which is 1.9 times higher than the threshold for unbiased erasures and 7.5 times higher than the threshold for depolarizing errors.Surprisingly, the improved threshold is achieved without bias-preserving controlled-NOT gates and, instead, results from the lower noise entropy in this model.We also introduce an XZZX cluster state construction for measurement-based error correction, hybrid fusion, that is optimized for this noise model.By combining fusion operations and deterministic entangling gates, this construction preserves the intrinsic symmetry of the XZZX code, leading to a higher threshold of 10.3% and enabling the use of rectangular codes with fewer qubits.We discuss a potential physical implementation using a single plane of atoms and movable tweezers.
The requirements for fault-tolerant quantum error correction can be simplified by leveraging structure in the noise of the underlying hardware.In this work, we identify a new type of structured noise motivated by neutral-atom qubits, biased erasure errors, which arises when qubit errors are dominated by detectable leakage from only one of the computational states of the qubit.We study the performance of this model using gate-level simulations of the XZZX surface code.Using the predicted erasure fraction and bias of metastable 171 Yb qubits, we find a threshold of 8.2% for two-qubit gate errors, which is 1.9 times higher than the threshold for unbiased erasures and 7.5 times higher than the threshold for depolarizing errors.Surprisingly, the improved threshold is achieved without bias-preserving controlled-NOT gates and, instead, results from the lower noise entropy in this model.We also introduce an XZZX cluster state construction for measurement-based error correction, hybrid fusion, that is optimized for this noise model.By combining fusion operations and deterministic entangling gates, this construction preserves the intrinsic symmetry of the XZZX code, leading to a higher threshold of 10.3% and enabling the use of rectangular codes with fewer qubits.We discuss a potential physical implementation using a single plane of atoms and movable tweezers.
Abstract 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 work, we overcome this barrier by introducing a generalization of the cluster state that allows us to foliate stabilizer codes in a bias-preserving way. As an example of our approach, we construct a foliated version of the XZZX code which we call the XZZX cluster state. We demonstrate that under a circuit-level-noise model, our XZZX cluster state has a threshold more than double the usual cluster state when dephasing errors are more likely than errors that cause bit flips by a factor of order ~100 or more.
Abstract Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for 171 Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable electronic level, such that gate errors predominantly result in transitions to disjoint subspaces whose populations can be continuously monitored via fluorescence. We estimate that 98% of errors can be converted into erasures. We quantify the benefit of this approach via circuit-level simulations of the surface code, finding a threshold increase from 0.937% to 4.15%. We also observe a larger code distance near the threshold, leading to a faster decrease in the logical error rate for the same number of physical qubits, which is important for near-term implementations. Erasure conversion should benefit any error correcting code, and may also be applied to design new gates and encodings in other qubit platforms.
Identifying the best families of quantum error correction (QEC) codes for near-term experiments is key to enabling fault-tolerant quantum computing. Ideally, such codes should have low overhead in qubit number, high physical error thresholds, and moderate requirements on qubit connectivity to simplify experiments, while allowing for high logical error suppression. Quantum low-density parity-check (LDPC) codes have been recently shown to provide a path towards QEC with low qubit overhead and small logical error probabilities. Here, we demonstrate that when the dominant errors are erasures, as can be engineered in different quantum computing architectures, quantum LDPC codes additionally provide high thresholds and even stronger logical error suppression in parameter regimes that are accessible to current experiments. Using large-scale QEC numerical simulations, we benchmark the performance of two families of high-rate quantum LDPC codes, namely the so-called Clifford-deformed La-cross codes and the bivariate bicycle codes, under a noise model strongly biased towards erasure errors. Both codes outperform the surface code by offering up to orders of magnitude lower logical error probabilities. Interestingly, we find that this decrease in the logical error probability may not be accompanied by an increase in the code threshold, as different QEC codes benefit differently from large erasure fractions. While here we focus on neutral atom qubits, the results also hold for other quantum platforms, such as trapped ions and superconducting qubits, for which erasure conversion has been demonstrated.
Leveraging noise bias, where phase-flip errors dominate over bit-flips, can drastically reduce the hardware overhead of fault-tolerant quantum computation, but existing approaches require bias-preserving CNOT gates whose implementation remains experimentally challenging and is provably impossible for strictly two-dimensional systems. We show that high-fidelity quantum non-demolition (QND) multi-qubit Pauli Z measurements provide an equally powerful yet more accessible primitive. We demonstrate that such measurements can fully replace bias-preserving CNOT gates for compiling all operations required by bias-tailored error correction, including stabilizer measurements for repetition codes, XZZX surface codes, and LDPC codes. We propose concrete physical implementations of this primitive for two platforms: solid-state nuclear spins coupled to electron spin ancillas, and dissipatively stabilized superconducting cat qubits. Through circuit-level numerical simulations, we show that an asymmetric XZZX surface code implemented with weight-four QND Z measurements achieves a phase-flip threshold of ∼1.25% and provides a qubit overhead reduction of up to 6× compared to a bias-unaware surface code at noise bias η=104. In the regime of very large bias, a repetition code with QND Z measurements attains a threshold of ∼2.3% and achieves overhead comparable to that of a bias-preserving CNOT scheme, without requiring such a gate. Our results establish QND multi-Z measurements as a practical and hardware-efficient route to fault-tolerant quantum computation for a broad class of biased-noise platforms.
Quantum error correction (QEC) for generic errors is challenging due to the demanding threshold and resource requirements. Interestingly, when physical noise is biased, we can tailor our QEC schemes to the noise to improve performance. Here we study a family of codes having XZZX-type stabilizer generators, including a set of cyclic codes generalized from the five-qubit code and a set of topological codes that we call generalized toric codes (GTCs). We show that these XZZX codes are highly qubit efficient if tailored to biased noise. To characterize the code performance, we use the notion of effective distance, which generalizes code distance to the case of biased noise and constitutes a proxy for the logical failure rate. We find that the XZZX codes can achieve a favorable resource scaling by this metric under biased noise. We also show that the XZZX codes have remarkably high thresholds that reach what is achievable by random codes, and furthermore they can be efficiently decoded using matching decoders. Finally, by adding only one flag qubit, the XZZX codes can realize fault-tolerant QEC while preserving their large effective distance. In combination, our results show that tailored XZZX codes give a resource-efficient scheme for fault-tolerant QEC against biased noise.
Recently, significant effort has been devoted towards designing erasure qubits in which dominant physical noise excites detectable leakage states that can be returned to the qubit subspace. Interest in these erasure qubits has been driven by studies showing that the requirements for fault-tolerant quantum error correction are significantly relaxed when noise in every gate operation is dominated by erasures. However, these studies assume perfectly accurate erasure checks after every gate operation which generally come with undesirable time and hardware overhead costs. In this work, we investigate the consequences of using an imperfect but overhead-efficient erasure check for fault-tolerant quantum error correction with the surface code. We show that, under physically reasonable assumptions on the imperfect erasure checks, the threshold error rate is still at least over twice that for Pauli noise. We also study the impact of imperfect erasure checks on the effective error distance and find that it degrades the effective distance under a general error model in which a qubit suffers from depolarizing noise when interacting with a leaked qubit. We then identify a more restrictive but realistic noise model for a qubit that interacts with a leaked qubit, under which the effective error distance is twice that for Pauli noise. We apply our analysis to recently proposed superconducting dual-rail erasure qubits and show that achieving good-performance surface code quantum memories with relaxed system requirements is possible.