Ten-Qubit Systems Now Fully Profiled with New Error-Checking Technique

A new technique addresses key challenges in error characterisation for multi-qubit quantum computers, a barrier to improving device performance. Ashe Miller at Quantum Performance Laboratory, and colleagues in collaboration with Sandia National Laboratories, present a scalable method called linearized gate set tomography to overcome limitations in current approaches. The method uses sparse error models and linear approximations with data from shallow circuits, enabling characterisation of larger systems than previously possible. Simulations of a ten-qubit system, incorporating coherent and stochastic errors including coherent crosstalk, demonstrate the strong accuracy of the technique even with unmodelled errors.

Linearized tomography enables scalable error characterisation in ten-qubit systems

Error characterisation has, for the first time, been achieved on ten-qubit quantum systems, a substantial leap from previous limitations of approximately three qubits. This advance stems from the development of linearized gate set tomography, a technique employing sparse error models and linear approximations to enable scalable error characterisation. Quantum computers, while promising, are inherently susceptible to errors arising from various sources including environmental noise, imperfect control pulses, and qubit decoherence. These errors accumulate during computation, limiting the fidelity and reliability of quantum algorithms. Traditional error characterisation methods, such as randomized benchmarking, often struggle to scale to larger qubit numbers and frequently rely on simplified error models, typically assuming errors are purely stochastic Pauli errors, which fail to capture the full complexity of physical error mechanisms. Linearized gate set tomography addresses these limitations by providing a more comprehensive and scalable approach.

A ten-qubit system’s simulations verified the technique’s precision, encompassing coherent and stochastic errors, SPAM errors arising from state preparation and measurement, and coherent crosstalk between qubits. Randomly generated error rates, ranging from 0 to 10⁻³ for stochastic errors and -10⁻² to 10⁻², were incorporated to demonstrate the method’s ability to handle a broad spectrum of error magnitudes. The technique leverages the principles of gate set tomography (GST), which aims to characterise the complete set of quantum operations implemented on a device. However, standard GST becomes computationally intractable for systems with many qubits due to the exponential growth in the number of parameters to be estimated. Linearized GST mitigates this issue by employing a sparse error model, focusing on the most significant error terms and approximating the remaining terms linearly. This simplification significantly reduces the computational burden, enabling characterisation of larger systems. Analysis of 1,000 depth-15 random circuits revealed accurate estimations of error rates, even with only 1,000 shots per circuit, indicating durability against statistical noise, and the technique accurately learned both Hamiltonian and Pauli stochastic errors. The use of shallow circuits is crucial; deeper circuits would exacerbate the inaccuracies introduced by the linear approximation, as errors would propagate and accumulate more significantly.

By focusing on the most impactful error types, this technique simplifies analysis and unlocks the potential for more reliable quantum computation. It circumvents the computational burden of modelling every potential error source, allowing analysis of more complex quantum systems and identification of errors even when they don’t perfectly fit pre-defined models. The sparse error model employed prioritises the identification of dominant error terms, such as single-qubit rotations and two-qubit interactions, while approximating less significant errors. This approach reduces the number of parameters that need to be estimated, making the characterisation process more efficient and scalable. Utilising data from relatively shallow circuits minimised inaccuracies inherent in the linear approach, achieving accurate error profiling even with unmodelled errors present. The technique’s ability to accurately learn both Hamiltonian and Pauli stochastic errors is particularly noteworthy, as it demonstrates its capacity to capture a wider range of error behaviours than methods that rely solely on Pauli error models. Hamiltonian errors represent continuous, coherent distortions of the quantum state, while Pauli errors are discrete, stochastic flips of the qubit state.

Advancing quantum computation through thorough error identification in multi-qubit systems

Accurate error characterisation is vital for building quantum computers capable of tackling complex problems beyond the reach of classical machines. Linearized gate set tomography offers a pathway to understanding errors in systems exceeding the limitations of previous approaches. The ability to accurately characterise errors is paramount for developing effective error mitigation and correction strategies. Error mitigation techniques aim to reduce the impact of errors on computation without requiring full error correction, while error correction involves encoding quantum information in a redundant manner to protect it from errors. Both approaches rely on a detailed understanding of the underlying error mechanisms. However, the method currently relies on a linear approximation to simplify calculations, and the extent of this systematic error in increasingly complex quantum circuits remains an open question. Further research is needed to quantify the impact of this approximation and explore methods for improving its accuracy, potentially through the use of higher-order approximations or adaptive error models.

Existing methods struggle with systems beyond a few qubits, or rely on assumptions about error types that may not reflect reality. Establishing a scalable method for characterising errors represents a key advance in quantum computing, moving beyond limitations previously imposed by system size and simplified error assumptions. The implications of this work extend beyond fundamental error characterisation. The insights gained from this technique can be used to optimise qubit control pulses, improve device design, and develop more robust quantum algorithms. A comprehensive grasp of error sources will ultimately be essential for realising the full potential of quantum computation and developing algorithms that can outperform their classical counterparts. The development of scalable error characterisation techniques is therefore a crucial step towards building fault-tolerant quantum computers, which are necessary for solving computationally challenging problems in fields such as drug discovery, materials science, and financial modelling. The technique’s demonstrated performance on a ten-qubit system provides a promising foundation for scaling up to even larger and more complex quantum systems, paving the way for practical quantum computation.

The researchers developed a scalable method, linearized gate set tomography, to characterise errors in many-qubit quantum systems. This technique overcomes limitations of previous methods by using a linear approximation and sparse error models, allowing for analysis of up to ten qubits without overly simplifying the underlying error mechanisms. Understanding these errors is crucial for optimising qubit control and improving quantum device design. The authors note that further research is needed to refine the accuracy of the linear approximation used in their calculations.