Quantum error correction (QEC) is essential for building reliable quantum computers, but its effectiveness hinges on accurately understanding and modelling noise. A new paper published in the Quantum journal, "Accurate and Honest Approximation of Correlated Qubit Noise," presents a novel approach to tackle this challenge.
While a full simulation of actual noisy quantum devices gives accurate information about correlated noise among all qubits, it is computationally expensive since it requires resources that grow exponentially with the number of qubits. It is, therefore, crucial to come up with methods to approximate noise in large quantum systems that are scalable yet still can accurately capture the essential feature of the actual noise. Our work provides a way to accomplish exactly this task.
The paper introduces a "cluster expansion approach" to systematically decompose noise in quantum devices based on qubit-qubit correlation (in other words, we separate the noise into different components based on which and how many qubits in the quantum system that the noise component impacts on).
Furthermore, we present a systematic way to construct approximate noise models using the decomposition obtained from the cluster expansion approach where we generate a k-th order approximate noise model by including all noise components that affect up to k number of qubits.
Our method goes beyond traditional noise models, such as Pauli noise, as it can also be used for multi-level qubit systems with leakage. Moreover, our noise model also considers multi-qubit noise beyond just one and two-qubit noise as normally assumed in standard noise models, thus offering a more realistic representation of noise in quantum systems.
Why is this important? Current QEC strategies often rely on simplified noise models, which may not accurately reflect the complex noise characteristics of real quantum devices. The cluster expansion approach provides a systematic way to characterise multi-qubit noise correlations, leading to more accurate simulations and potentially better QEC code strategies and hardware designs.
In the paper, we demonstrate the effectiveness of our cluster expansion approach by applying it to model noise in a three-qubit quantum processor. We found that, already for such a small quantum processor, noise components beyond two-qubit correlations can significantly impact the accuracy of code simulations. This highlights the importance of considering multi-qubit noise correlations for effective QEC.
The above figure shows the simulation results for a [[2, 0, 2]] code, computed using the second-order and third-order approximate noise channels for linear and triangular connectivities. Our approach can be used beyond just the three-qubit processors shown above. Thus, it enables the potential for a honest, accurate and scalable approximate simulation of the performance of large quantum systems.
Check out the full paper here.