Simulation of one and two qubit superconducting quantum gates in the presence of non-Markovian 1/f noise
Yinjia Chen, Shuocang Zhang, Qiang Shi
DOI 10.1103/yvx1-nmg5 · Physical Review B
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Abstract
Non-Markovian 1/f noise is a major source of decoherence in superconducting qubits, yet its low-frequency nature poses a significant challenge for accurate simulation. Here, we develop a hierarchical equations of motion (HEOM) framework that enables efficient and reliable modeling of qubit dynamics and gate operations under 1/f noise. Using this approach, we first show that perturbative quantum master equations fail to reproduce the correct dephasing dynamics of a qubit coupled to 1/f noise. We then analyze dynamical decoupling using the Carr-Purcell-Meiboom-Gill (CPMG) protocol with finite-duration pulses. The results reveal that errors accumulate linearly with parity effects in X-CPMG, quadratically in Y-CPMG, and are strongly suppressed in alternating XY sequences. Finally, we extend the framework to simulate a two qubit cross-resonance gate and reconstruct the Pauli transfer matrix to characterize the error channels induced by 1/f noise. Together, these results establish HEOM as a robust and accurate method for simulating the slow non-Markovian 1/f noise in superconducting qubits and provide insights into error mechanisms in both single and two qubit gates.
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