Abstract In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial overhead in algorithm repetitions. On the flip side, we also found classical algorithms able to efficiently simulate both the noisy and noiseless versions of our specific variants of the Hadamard test. We propose to use these algorithms as a benchmark of the biasness of the noise at the scale of large circuits. The bias being checked on a full computational task makes our benchmark sensitive to crosstalk or time-correlated errors, which are usually invisible from individual gate tomography. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to 106 gates, several orders of magnitude larger than circuits not exploiting a noise-bias. Our benchmark is applicable for an arbitrary noise-bias, beyond Pauli models.
Abstract In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial overhead in algorithm repetitions. On the flip side, we also found classical algorithms able to efficiently simulate both the noisy and noiseless versions of our specific variants of the Hadamard test. We propose to use these algorithms as a benchmark of the biasness of the noise at the scale of large circuits. The bias being checked on a full computational task makes our benchmark sensitive to crosstalk or time-correlated errors, which are usually invisible from individual gate tomography. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to 106 gates, several orders of magnitude larger than circuits not exploiting a noise-bias. Our benchmark is applicable for an arbitrary noise-bias, beyond Pauli models.
Qubits with strongly biased noise, in which phase-flip errors are orders of magnitude more frequent than bit-flips, arise both naturally, as in electron and nuclear spins, and by engineering, as in stabilized cat qubits. This noise structure holds the promise of reducing the daunting hardware overhead of fault-tolerant quantum computing, but exploiting it requires physical operations that do not convert frequent phase-flips into rare bit-flips. In this review, we analyze the most prominent fault-tolerant protocols for biased-noise qubits, organized according to the available set of such bias-preserving operations. When this set is restricted to the CZ gate together with preparation and measurement in the X basis, we show that the complexity of the required syndrome extraction gadgets essentially cancels the benefit of the noise bias: at experimentally relevant error rates, one may as well ignore the bias and rely on standard error correction designed for depolarizing noise. The situation changes drastically when a bias-preserving CX gate is available: the hierarchy of errors can then be reflected in the structure of the code, with frequent phase-flips corrected by a dedicated high-threshold code and rare bit-flips by concatenation with a high-rate code. The same hierarchy also enables hardware-efficient preparation of magic states. Finally, as a bias-preserving CX is forbidden in naturally biased platforms and challenging in engineered ones, we present a measurement-based architecture in which a high-fidelity quantum non-demolition readout of multi-qubit Pauli Z operators takes its place, extending these overhead reductions to a much broader range of physical platforms.
Ubiquitous noise sources in quantum systems remain a key obstacle to building quantum computers, necessitating the use of quantum error correction codes. Recently, error-correcting codes tailored for noise-biased systems have been shown to offer high fault-tolerance thresholds and reduced hardware overhead, positioning noise-biased qubits as promising candidates for building universal quantum computers. However, quantum operations on these platforms remain challenging, and their noise structures have not yet been rigorously benchmarked to the same extent as those of conventional quantum hardware. In this work, we develop a comprehensive quantum control toolbox for a scalable noise-biased qubit, detuned Kerr-cat qubit, including initialization, universal single-qubit gates, and quantum nondemolition readout. We systematically characterize the noise structure of these operations using gate set tomography and dihedral randomized benchmarking, achieving high local gate fidelities, with [Formula: see text] and [Formula: see text]. Notably, the noise bias of the detuned Kerr-cat qubit approaches 250 with a phase-flip time of [Formula: see text], which outperforms its resonant-Kerr-cat qubit counterparts as reported previously, representing a state-of-the-art performance benchmark for Kerr-cat qubits. Moreover, our results reveal a critical overestimation of operational noise bias inferred from bit-flip and phase-flip times alone, highlighting the necessity of a precise and direct benchmarking for noise-biased qubit operations. Our work thus establishes a framework for systematically characterizing and validating the performance of quantum operations in structured-noise architectures, which lays the groundwork for implementing efficient quantum error correction in next-generation architectures.
Fault-tolerant quantum design relies on simulating noisy quantum error correction (QEC) circuits with hundreds to thousands of physical qubits and large circuit depths. High-throughput stabilizer simulators, such as Stim, are the de facto tools for this regime. However, these simulators typically support only Clifford gates and stochastic Pauli noise. As a result, more realistic device noise models-such as coherent control errors and thermal relaxation-are often approximated using Pauli Twirling. This replacement offers speed but can introduce inaccuracies.
To address this, we propose QuasiStim for scalable exact QEC simulation of realistic noise, with QuasiFold as a compiler frontend and DeltaFrame as a sampling backend. QuasiFold lowers sampling overhead by merging equivalent non-Pauli sites in the quantum circuit. DeltaFrame samples the resulting stabilizer trajectories by reusing precomputed predicted references instead of resimulating the full tableau for each shot.
QuasiFold can reduce the number of shots by over 100× on bivariate-bicycle (BB) codes. Compared to a per-shot tableau simulator, DeltaFrame is 166×--1331× faster on rotated surface-code memory under coherent RZ noise as d grows from 5 to 35. QuasiStim also makes the PTA bias measurable: the gap is non-negligible and varies with noise strength, decoder, and circuit schedule.
QuasiStim will be open-sourced upon publication at https://github.com/isaachyw/QuasiStim
The increasing scale of near-term quantum hardware motivates the need for efficient noise characterization methods, since qubit and gate level techniques cannot capture crosstalk and correlated noise in many qubit systems. While scalable approaches, such as cycle benchmarking, are known for special classes of quantum circuits, the characterization of noise in general circuits with non-Clifford gates has been an unreachable task. We develop an algorithm that can sample-efficiently estimate the total amount of noise induced by a layer of arbitrary non-Clifford gates, including all crosstalks, and experimentally demonstrate the method on IBM Quantum hardware. Our algorithm is inspired by Google's quantum supremacy experiment and is based on random circuit sampling. In their paper, Google observed that their experimental linear cross entropy was consistent with a simple uncorrelated noise model, and claimed this coincidence indicated that the noise in their device was uncorrelated -- a key step in hardware development towards fault tolerance. As an application, we show that our result provides formal evidence to support such a conclusion.
As quantum devices grow in size while remaining affected by noise, a key challenge is to determine when and how they can surpass classical computation on practical tasks. This requires the development of highly efficient classical simulation algorithms. Pauli backpropagation algorithms are among the most promising, having shown efficiency in simulating certain classes of parameterized quantum circuits, strong candidates for near‑term quantum advantage, under random circuit assumptions and depolarizing noise. However, their efficiency had not been demonstrated for more realistic nonunital noise models, such as amplitude damping, which better capture the behaviour of current hardware. We close this gap by adapting Pauli backpropagation to most single‑qubit noise channels, including nonunital noise, and proving that it remains efficient under these conditions. Our algorithm is parallelizable, memory‑efficient, and requires no assumptions on the locality of the observable, the geometry of the hardware, or the depth of the circuit. While hardware noise can strongly affect computational power in highly structured, fault‑tolerant circuits, our findings indicate little difference for most near‑term variational architectures. This establishes Pauli backpropagation as an efficient method for simulating noisy quantum devices under realistic noise assumptions.While these advances improve our ability to reproduce noisy expectation values of observables, many practical applications, including combinatorial optimization, require direct access to the bitstrings output by quantum circuits, as these encode candidate solutions. Classical replication of such noisy samples has so far been limited beyond the random circuit setting. To bridge this gap, we first focus on problems whose objective functions depend only on two‑body correlations, such as Max‑Cut, and apply Gaussian randomized rounding to the circuit's two‑qubit marginals. This produces classical samples whose expected cost is provably close to that of the noisy quantum device. Large‑scale simulations and experiments on IBMQ hardware confirm that the rounded samples reproduce the full energy distribution, with similar behaviour under various noise models. Coupled with Pauli backpropagation for efficiently estimating noisy marginals, this yields an end‑to‑end classical sampler operating in polynomial time for a broad class of variational circuits. Our results therefore show that sufficiently noisy quantum circuits for combinatorial optimization can be sampled from classically, clarifying where near‑term hardware may or may not outperform classical algorithms.Finally , we go beyond one and two‑body marginals and present an algorithm that samples valid bitstrings directly from a maximum‑entropy distribution matching the given expectation values of the quantum circuit. This method does not rely on the locality or sparsity of the problem's Hamiltonian and performs well across a variety of quantum circuits, including deep circuits on many qubits. When combined with Pauli propagation or error mitigation, it provides a practical pipeline for obtaining samples from quantum circuits in the near term, where full error correction might not yet be available.
We present a simple, malleable and low-overhead approach for improving generic biased quantum error mitigation (QEM) methods, achieving up to 15% fidelity improvements over standard QEM on 100-qubit circuits with up to 2000 entangling gates. We do so by constructing verifiable benchmark circuits which mirror the application circuit's native-gate structure and thus noise profile. These circuits can be used to benchmark and mitigate the bias of the underlying error mitigation method, requiring only the application circuit and hardware native gate set. We present two methods for generating benchmark circuits; one is agnostic to the target hardware at the expense of a small overhead of single-qubit gates, while the other is specific to the IBM superconducting hardware and has no gate overhead. As a corollary, we introduce benchmarked-noise zero-noise extrapolation (bnZNE) as a simple adaptation of zero-noise extrapolation (ZNE), one of the most popular error mitigation methods. We consider as an example the bias-mitigated ZNE and bnZNE of Trotterized Hamiltonian simulations, observing that our approaches outperform standard ZNE using both small-scale classical simulations and 100-qubit utility-scale experiments on the IBM superconducting hardware. We consider the measurement of both single-site observables as well as two-site correlations along a one-dimensional qubit chain. We also provide a software package for implementing the error mitigation techniques used in this research.