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arXiv:0901.0083 · New Journal of Physics

Effects of low-frequency noise cross-correlations in coupled superconducting qubits

Antonio D’Arrigo, Andrea Mastellone, Elisabetta Paladino, G. Falci

Published Nov 20, 2008• 24 citations
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Abstract

We study the effects of correlated low-frequency noise sources acting on a two-qubit gate in a fixed coupling scheme. A decoherence model for the spatial and cross-talk correlations is introduced. The efficiency inside the SWAP subspace is analyzed by combining analytic results based on the adiabatic approximation and numerical simulations. Results critically depend on amplitude of the low-frequency noise with respect to the qubits' coupling strength. Correlations between noise sources induce different qualitative behavior depending on the values of the above parameters. The possibility to reduce dephasing due to correlated low-frequency noise by a recalibration protocol is discussed.

DOI
10.1088/1367-2630/10/11/115006

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We study the effects of noise and decoherence for a double-potential well system, suitable for the fabrication of qubits and quantum logic elements. A random noise term is added to the hamiltonian, the resulting wavefunction found numerically and the density matrix obtained by averaging over noise signals. Analytic solutions using the two-state model are obtained and found to be generally in agreement. In particular, a simple formula for the decoherence rate in terms of the noise parameters in the two-state model is reviewed and verified for the full simulation with the multi-level system. The formalism is extended to describe multiple sources of noise or different "dephasing" axes at the same time. Furthermore, the old formula for the "Turing-Watched Pot" effect is generalized to the case where the environmental interactions do not conserve the "quality" in question. Various forms for the noise signal are investigated. An interesting result is the importance of the noise power at low frequency. If it vanishes there is, in leading order, no decoherence. This is verified in a numerical simulation where two apparently similar noise signals, but differing in the power at zero frequency, give strikingly different decoherence effects. A short discussion of situations dominated by low frequency noise is given.
Understanding error mechanisms in two-qubit gate operations is essential for building high-fidelity quantum processors. While prior studies predominantly treat dephasing noise as either Markovian or predominantly low-frequency, realistic qubit environments exhibit structured, frequency-dependent spectra. Here we demonstrate that noise at frequencies matching the dressed-state energy splitting--set by the inter-qubit coupling strength g--induces a distinct relaxation channel that degrades gate performance. Through combined theoretical analysis and experimental verification on superconducting qubits with engineered noise spectra, we show that two-qubit gate errors scale predictably with the noise power spectral density at frequency 2g, extending the concept of T1ρT_{1ρ}T1ρ​ relaxation to interacting systems. This frequency-selective relaxation mechanism, universal across platforms, enriches our understanding of decoherence pathways during gate operations. The same mechanism sets coherence limits for dual-rail or singlet-triplet encodings.