Probing non-Markovian qubit noise and modeling Post Markovian Master Equation

TL;DR

Quantum processors exhibit non-Markovian noise due to bath memory and inter-qubit crosstalk, challenging standard Lindblad models. The authors employ the Post-Markovian Master Equation (PMME) with a reconstructable memory kernel to capture short- and intermediate-time memory effects, validating the framework on IBM superconducting qubits. Through tomography-driven witnesses (CP-divisibility, information backflow) and a direct PMME kernel reconstruction, they reveal oscillatory memory behavior with a kernel around 13 kHz that is largely state-independent, and show that crosstalk can dominate observed memory. This work provides a practical, interpretable model for device memory that can guide layout-aware scheduling, decoupling strategies, and physics-informed simulations toward improved fault-tolerance.

Abstract

Understanding the noise characteristics of quantum processors is crucial when achieving fault-tolerant quantum computing. However, typical qubit designs are often studied under the Markovian approximation, which does not fully capture realistic dynamics. Factors such as qubit-qubit coupling and extended bath correlation times can introduce significant non-Markovian effects into the noise processes. In this study, we employ the Post-Markovian Master Equation (PMME) formalism to characterize memory effects in the noise dynamics. We further experimentally validate the PMME framework using superconducting qubits on an IBM Quantum device, demonstrating clear non-Markovian behavior during circuit execution. Additionally, we quantify the crosstalk effect using an information-theoretic approach and reveal that crosstalk can dominate the observed non-Markovian effects in current quantum hardware.

Figures (8)

• Figure 1: Population decay for 50000 ID gates
• Figure 2: Bloch vector under 5000 ID gates
• Figure 3: Layout of the IBM superconducting quantum processor in the heavy-hex lattice (partial view). Each qubit connects to at most three neighbors. In this example, we select qubits 23, 24, 25, and 34, with qubit 24 serving as the main qubit and the other three acting as spectator qubits.
• Figure 4: Schematic of the basic experimental setup. The circuit is composed of three parts: (1) the state‐preparation unitary $U_{\mathrm{SP}}$, (2) an idling phase implemented by a sequence of identity gates, and (3) the final basis rotations for tomography. By varying the number of identity gates, we control how long the main qubit idles and interacts with its environment. After collecting the measurement statistics, we form a data vector of empirical probabilities and the corresponding POVM operators for either state or process tomography and solve the resulting least‐squares problem. The raw estimates of the density matrix $\hat{\rho}$ and the Choi matrix $\hat{\chi}_t$ are then projected onto the physical subspace to enforce the required properties of a valid quantum state or a trace‐preserving, completely positive map.
• Figure 5: Heat‐maps of the minimum eigenvalue $\lambda_{\min}\bigl[\chi_{t,s}\bigr]$ for the intermediate Choi matrix as a function of start time $s$ and idle time $t$, measured on IBM’s 127-qubit “Strasbourg” processor. (a) Left panel shows the case where the main qubit is number 4 and the spectator qubits are {3, 5, 15}; (b) Right panel uses main qubit 25 with spectators {26, 27, 16}. In each experiment the spectator qubits are initialized in the $|+\rangle$ state and held idle for duration $s$, after which full process tomography is performed on the main qubit at time $t$. The triangular region $s>t$ is masked. Regions with $\lambda_{\min}\approx0$ (light yellow) are CP‐divisible, whereas negative values (orange to purple) indicate CP‐divisibility violations (non-Markovianity).