We introduce fault-tolerant (FT) architectures for error correction with the XZZX cluster state based on performing measurements of two-qubit Pauli operators Z⊗Z and X⊗X, or fusions, on a collection of few-body entangled resource states. Our construction is tailored to effectively correct noise that predominantly causes faulty X⊗X measurements during fusions. This feature offers a practical advantage in linear optical quantum computing with dual-rail photonic qubits, where failed fusions only erase X⊗X measurement outcomes. By applying our construction to this platform, we find a record-high threshold to fusion failures exceeding 25% in the experimentally relevant regime of nonzero loss rate per photon, considerably simplifying hardware requirements.
Fusion-based quantum computation is a promising quantum computing model where small-sized photonic resource states are simultaneously entangled and measured by fusion gates. Such operations can be readily implemented with scalable photonic hardware: resource states can be deterministically generated by quantum emitters and fusions require only shallow linear-optical circuits. Here, we propose fusion-based architectures tailored to the capabilities and noise models in quantum emitters. We show that high tolerance to dominant physical error mechanisms can be achieved, with fault-tolerance thresholds of 8% for photon loss, 4% for photon distinguishability between emitters, and spin noise thresholds well above memory-induced errors for typical spin-photon interfaces. Our construction and analysis provide guidelines for the development of photonic quantum hardware targeting fault-tolerant applications with quantum emitters.
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.
We propose fault-tolerant architectures based on performing projective measurements in the Greenberger-Horne-Zeilinger (GHZ) basis on constant-sized, entangled resource states. We present linear-optical constructions of the architectures, where the GHZ-state measurements are encoded to suppress the errors induced by photon loss and the probabilistic nature of linear optics. Simulations of our constructions demonstrate high single-photon-loss thresholds compared to the state-of-the-art linear-optical architecture realized with encoded two-qubit fusion measurements performed on constant-sized resource states. We believe this result shows a resource-efficient path to achieving photonic fault-tolerant quantum computing.
The realisation of a fault-tolerant universal quantum computer requires the ability to implement and control large scale quantum systems while maintaining physical noise levels sufficiently low to avoid errors in the computation. Fusion-Based Quantum Computation (FBQC) – a framework in which entangling fusion measurements are performed between constant-size entangled resource states – has emerged as a promising approach to achieve this, especially in the context of Linear Optical Quantum Computing (LOQC). Most FBQC schemes proposed so far use physical fusions between two qubits. In this thesis, we study the impact of using multi-way fusions, which act on more physical qubits simultaneously, on the error tolerance and resource overhead of linear optical FBQC architectures. The main challenge of LOQC is that entangling operations are inherently non-deterministic, leading to large resource overheads. The success probability is known to decrease exponentially with the number of input qubits. We introduce novel fusion circuits which succeed at higher rates and/or entangle subsets of inputs upon failure. We present a framework to analyse the impact of noise on these circuits and describe the resulting errors as effective Pauli error channels on the input qubits. We also examine the application of multi-way fusion circuits within a linear optical FBQC architecture. We find that they can be used to generate resource states with significantly reduced Pauli error rates and footprint compared to two-way fusions alone, in turn resulting in linear optical FBQC architectures with higher error tolerance and lower resource overheads. We also investigate their use as primitives of the computation, applied between different resource states, and find evidence that two-way fusions remain preferable in this context due to their lower erasure rate.
Bell state measurements (BSMs) play a significant role in quantum information and quantum computing, in particular in fusion-based quantum computing (FBQC). The FBQC model is a framework for universal quantum computing, provided that we are able to perform entangling measurements, called fusions, on qubits within small entangled resource states. Here, we analyze the usage of different linear-optical BSM circuits as fusions in the FBQC schemes and numerically evaluate hardware requirements for fault-tolerance in this framework. We examine and compare the performance of several BSM circuits with varying additional resources and estimate the requirements on losses for every component of the linear-optical realization of fusions under which errors in fusion networks caused by these losses can be corrected. Our results show that fault-tolerant quantum computing in the FBQC model is possible with currently achievable levels of optical losses in an integrated photonic implementation, provided that we can create and detect single photons of the resource states with a total marginal efficiency higher than 0.973.
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.