Tsinghua University Team Models MPO Framework for Correlated Readout Error Mitigation

A new approach to tackling readout errors, a key limitation in current quantum computers, has been developed by Yuchen Guo and Shuo Yang at Tsinghua University, in collaboration with Frontier Science Centre for Quantum Information and Hefei National Laboratory. Guo and colleagues present a tensor-network framework that accurately models correlated readout errors as a matrix product operator, offering a sharp improvement over existing methods which assume these errors are independent. The scalable technique, validated through experiments on superconducting processors and simulations with up to 20 qubits, not only characterises these errors more effectively but also mitigates their impact on vital quantum tasks such as observable estimation and random circuit sampling. Furthermore, the framework’s compatibility with tensor-network quantum error correction opens avenues for enhanced noise-aware quantum data processing and represents a flexible step towards reliable near-term quantum computation.

Spatial correlations in qubit readout errors enable scalable quantum modelling

Error rates, when estimating nonlocal observables, dropped from levels requiring exponential resources for characterisation to near-linear scaling with system size, enabling accurate modelling beyond 20 qubits. This substantial reduction in computational complexity stems from a new tensor-network framework representing readout errors as a matrix product operator. Traditional methods often treat readout errors as independent events occurring on each qubit, simplifying the analysis but neglecting crucial spatial correlations. However, in physical quantum processors, particularly those utilising superconducting qubits, errors on neighbouring qubits are frequently correlated due to shared environmental noise, cross-talk, or imperfections in control signals. The matrix product operator (MPO) provides a compact and efficient way to represent these correlations, capturing the influence of one qubit’s readout error on its neighbours. The MPO effectively parameterises the readout process, allowing for a more accurate description of the overall error landscape. This is achieved by representing the readout operator as a chain of matrices, where each matrix describes the local effect of the error on a single qubit and the connections between matrices encode the spatial correlations. The dimensionality of these matrices is carefully controlled to maintain computational tractability, enabling scaling to larger systems.

Mitigation gains were achieved with the framework applied to random circuit sampling, even using a calibration dataset comprising just 20 qubits, a substantial improvement over traditional methods needing exponentially increasing resources for similar accuracy. Random circuit sampling is a benchmark task used to assess the performance of quantum computers, involving running a randomly generated quantum circuit and measuring the output distribution. Readout errors distort this distribution, making it difficult to verify the correctness of the computation. The tensor-network framework allows for the estimation of the readout error rates and correlations from a calibration dataset, which is then used to correct the measured results. The fact that this can be achieved with only 20 qubits is significant, as it demonstrates the potential for practical application on near-term devices. Conventional error mitigation techniques often require exponentially larger calibration datasets to achieve comparable accuracy, making them impractical for larger systems. Integrating this tensor-network approach with quantum error correction decoding, specifically for the surface code, allowed joint inference of both data and readout errors, suggesting potential for more robust logical qubit operations. The surface code is a leading candidate for fault-tolerant quantum computation, relying on encoding logical qubits into a larger number of physical qubits and using error correction to protect against noise. By jointly inferring data and readout errors during the decoding process, the framework can improve the accuracy of the error correction and reduce the logical error rate. Numerical simulations revealed that the sample cost for characterising errors grows almost linearly with system size, a sharp reduction compared to the exponential scaling of conventional techniques.

This scalable approach promises to unlock more reliable data processing on near-term quantum computers, overcoming a key obstacle to dependable computation. The ability to accurately characterise and mitigate readout errors is crucial for extracting meaningful results from noisy quantum processors. Without effective error mitigation, the information obtained from quantum computations can be severely corrupted, rendering the results unreliable. This framework provides a pathway towards achieving more accurate and trustworthy quantum computations, paving the way for exploring more complex algorithms and applications. These results highlight substantial progress, but the framework currently assumes short-range correlations between qubits, and its performance in systems with long-range interactions or more complex error topologies remains an open question. Further research will focus on extending the framework’s capabilities to accommodate these intricate scenarios and exploring its limitations in larger, more complex quantum systems. Investigating alternative tensor-network architectures, such as projected entangled pair states (PEPS), could potentially address the limitations of MPOs in capturing long-range correlations. Additionally, exploring the use of machine learning techniques to learn the error model directly from data could further improve the accuracy and efficiency of the framework.

Addressing limitations of short-range error correction in scalable quantum processors

The team at Tsinghua University has delivered a significant advance in tackling readout errors, inaccuracies when determining a quantum system’s state, which plague early quantum computers. Readout errors arise from imperfections in the measurement process, where the quantum state of a qubit is projected onto a classical bit. These imperfections can be caused by a variety of factors, including noise in the measurement electronics, imperfect qubit control, and decoherence. The current framework prioritises short-range correlations between qubits, however, and the behaviour of systems where errors are linked across greater distances remains largely unexplored. This limitation is important because real-world quantum devices often exhibit long-range interactions, potentially diminishing the effectiveness of this approach as processors scale up. Long-range interactions can arise from various sources, such as capacitive coupling between qubits or shared environmental noise affecting distant qubits. A scalable method for mitigating readout errors using a tensor-network framework has now been established. Validated on superconducting processors and simulations with up to 20 qubits, the framework captures spatial correlations between qubits, reducing the computational cost of error analysis. The use of superconducting qubits is particularly relevant, as these devices are currently among the most advanced platforms for building quantum computers. Offering a valuable step forward for near-term quantum computing, this new framework could begin to unlock more complex quantum processing in the coming decade, although its applicability to systems with long-range interactions requires further investigation. Future work will likely involve exploring methods to extend the framework to incorporate long-range correlations, potentially through the use of more sophisticated tensor-network architectures or by combining it with other error mitigation techniques.

The researchers developed a new framework using tensor networks to model and reduce readout errors in quantum processors. This is important because these errors limit the reliability of information obtained from current quantum computers, particularly when qubits interact. Validated on systems of up to 20 qubits, the framework efficiently captures correlations between qubits, improving error analysis compared to previous methods. The authors intend to extend this work by investigating how to incorporate long-range correlations into the model for even greater accuracy.