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arXiv:quant-ph/0606158 · Physical Review Letters

Correcting Low-Frequency Noise with Continuous Measurement

Lin Tian

Published Apr 13, 2007• 12 citations
arXivHTMLPDF

Abstract

Low-frequency noise presents a serious source of decoherence in solid-state qubits. When combined with a continuous weak measurement of the eigenstates, low-frequency noise induces a second-order relaxation between the qubit states. Here, we show that the relaxation provides a unique approach to calibrate the low-frequency noise in the time domain. By encoding one qubit with two physical qubits that are alternatively calibrated, quantum-logic gates with high fidelity can be performed.

DOI
10.1103/physrevlett.98.153602

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Low-frequency noise presents a serious source of decoherence in solid-state qubits. When combined with a continuous weak measurement of the eigenstates, low-frequency noise induces a second-order relaxation between the qubit states. Here, we show that the relaxation provides a unique approach to calibrate the low-frequency noise in the time domain. By encoding one qubit with two physical qubits that are alternatively calibrated, quantum-logic gates with high fidelity can be performed.
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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.
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We measured the integrated low frequency flux noise (∼1 mΦ0) of an rf SQUID as a flux qubit by fitting the resonant peaks from photon assistant tunneling (PAT). The energy relaxation time Tl between the ground and first excited states in the same potential well, measured directly in time domain, is 3 ns. From these results we identified low frequency flux noise as the dominant source of decoherence. In addition, we found that the measured values of integrated flux noise in three qubits of various sizes differ more than an order of magnitude.