Scalable, Accurate, and Honest Approximation of Correlated-Qubit Noise

Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computations. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits and is therefore accurate, it is, however, computationally expensive as it requires resources that grow exponentially with the qubit number. In this talk, I will present an efficient systematic construction of approximate noise channels, where their accuracy can be enhanced by incorporating noise components with higher qubit-qubit correlation degree. To formulate such approximate channels, I will first present a method, dubbed the cluster expansion approach, to decompose the Lindbladian generator of an actual Markovian noise channel into components based on interqubit correlation degree. I then demonstrate how to generate a k-th order approximate noise channel by truncating the cluster expansion and incorporate noise components with correlations only up to the k-th degree. The constructed approximate noise channels are required to be accurate and also "honest", i.e., the actual errors are not underestimated in our physical models. As an example application, I will apply this method to model noise in a three-qubit quantum processor that stabilizes a [[2,0,0]] codeword, which is one of the four Bell states. I will show that for realistic noise strength typical of fixed-frequency superconducting qubits coupled via always-on static interactions, correlated noise beyond two-qubit correlation can significantly affect the code simulation accuracy. Since our approach provides a systematic noise characterization, it enables the potential for scalable, accurate, and honest approximation to simulate large numbers of qubits from full modeling or experimental characterizations of small enough quantum subsystems, which are efficient but still retain essential noise features of the entire device.