IBM proposes scalable quantum noise model

The actual capabilities of contemporary quantum processors are largely limited by noise. Eventually, this problem will be solved by quantum error correction, but in the meantime, we can use error mitigation techniques to improve performance.

Probabilistic error cancellation (PEC) is one such technique, which works by forming a model of the noise associated with one or more gates in a quantum circuit. By generating circuit instances with inverse noise distribution samples, we can effectively eliminate these gate noises and improve the accuracy of the measured observations.

A major challenge for PEC is to find a noise model that is scalable in terms of the number of quantum bits, that captures the correlated noise, and that can be efficiently learned and manipulated. Recently, Ewout van den Berg, Kristan Temme, and others from IBM Quantum Quantum, in a paper in Nature Physics, proposed a practical protocol that satisfies all these criteria simultaneously - a Pauli-Lindblad noise model.

The research results, titled "Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors processors)," was published May 8 in the journal Nature Physics.

Noise models

Learning the noise channel

Error-mitigating time evolution of Ising spin chains.

Mitigating sampling overhead

For common quantum bit topologies, where the number of parameters is linear in the number of quantum bits, "learning" can be efficiently accomplished by a combination of circular benchmarks and non-negative least-squares fitting; the particular structure of the noise model leads to particularly simple algorithms for sampling from the inverse.

Combining these new models allowed the team to learn and mitigate noise on the concurrent CNOT gate layer, and the experimental team also demonstrated the power of PEC on a problem scale that was previously far from solvable.

In summary, this result demonstrates for the first time a practical way - extended probabilistic error cancellation - to eliminate errors caused by noise at high-weighted observation points throughout the circuit. Of course, the noise fidelity of the model reconstruction, and the error-mitigating observations also validate that Lindbladian learning is accurate, efficient, and scalable.

In conclusion, the team says, "We expect our learning protocol to become a powerful characterization and benchmarking tool, and more broadly to enable the study and mitigation of noise in quantum processors to a new scale."

Reference links:

[1]https://research.ibm.com/publications/probabilistic-error-cancellation-with-sparse-pauli-lindblad-models-on-noisy-quantum- processors

[2]https://www.nature.com/articles/s41567-023-02042-2

[3]https://arxiv.org/pdf/2201.09866.pdf

[4]https://mp.weixin.qq.com/s/6PFoh68ufoqSyXE2rS-iTw