[Paper Review] Upper-Bounds on Qubit Coherence Set by Master Clock Instabilities

William D. Oliver, Harrison Ball+1 more|arXiv (Cornell University)|Jan 10, 2016

Advanced Electrical Measurement Techniques3 citations

TL;DR

This paper identifies that local oscillator (LO) phase noise in laboratory clocks imposes fundamental upper bounds on qubit coherence and operational fidelity, showing that even high-quality LOs limit fidelity to below 10⁻⁴ for operations under 1 μs. It demonstrates that high-frequency phase noise in the LO—indistinguishable from dephasing—cannot be mitigated by dynamic error suppression, establishing a critical role for precision frequency metrology in quantum computing.

ABSTRACT

Experimentalists seeking to improve the coherent lifetimes of quantum bits have generally focused on improvements to qubit designs, materials, and system isolation from environmental perturbations. In the case of the phase degree of freedom in a quantum superposition, however, the coherence that must be preserved is ultimately that of the qubit relative to the system clock, rather than that of the qubit in isolation. In this manuscript we clarify the impact of clock instability on qubit dephasing and provide quantitative estimates of fidelity upper-bounds set by noisy phase fluctuations in the clock. We first indicate analytically that such phase fluctuations in the clock - typically referred to as the local oscillator (LO) - are indistinguishable from a pure dephasing field arising from other environmental mechanisms. Using these results, we apply commonly quoted LO phase-noise specifications to calculate the resultant performance bounds on qubit operational fidelities. We find that laboratory grade LOs contribute error probabilities beyond $10^{-4}$ for operation times $<1\;\mu$s, while the use of precision LOs can suppress error rates by $10^{4}$. We find that in either case phase fluctuations at frequencies far from the carrier dominate operational error rates, and due to their high-frequency spectral content, are difficult to mitigate using dynamic error suppression strategies. Further, we consider the importance of LO noise bandwidth and its impact on the degree to which thermal phase fluctuations in the LO contribute an effective error floor. These observations and analysis of the flow-down effects of such errors on the implementation of benchmarking and quantum error correction protocols highlight challenges and advantages that particular qubit technologies possess in the context of phase-noise-induced errors and motivate enhanced research in precision frequency metrology.

Motivation & Objective

• To clarify how local oscillator (LO) phase noise in laboratory clocks imposes fundamental limits on qubit coherence and operational fidelity.
• To quantify the upper bounds on qubit fidelity imposed by clock instability, particularly phase fluctuations in the system's reference clock.
• To analyze the spectral characteristics of LO noise and determine its impact on error rates, especially at high frequencies.
• To evaluate the role of LO noise bandwidth in establishing an effective error floor due to thermal phase fluctuations.
• To assess the implications of these phase-noise-induced errors for quantum benchmarking and quantum error correction protocols.

Proposed method

• Analytically demonstrates that phase fluctuations in the local oscillator (LO) are physically indistinguishable from a pure dephasing field arising from environmental interactions.
• Applies standard LO phase-noise specifications (e.g., phase spectral density) to model the resulting dephasing rates in qubit systems.
• Uses spectral analysis to show that high-frequency phase noise components—far from the carrier—dominate the error contribution.
• Evaluates the effectiveness of dynamic error suppression (e.g., dynamical decoupling) in mitigating such noise, finding limited utility due to high-frequency content.
• Considers the thermal phase noise contribution from the LO, modeling its bandwidth-limited spectral shape and its impact on the error floor.
• Translates LO noise specifications into upper bounds on operational fidelity using standard quantum process fidelity calculations.

Experimental results

Research questions

• RQ1 To what extent does local oscillator phase noise limit the achievable fidelity in superconducting and other qubit systems?
• RQ2 Why are high-frequency phase fluctuations in the clock source particularly detrimental and difficult to suppress with dynamic decoupling?
• RQ3 How does the bandwidth of LO phase noise influence the effective error floor in qubit operations?
• RQ4 What are the quantitative bounds on qubit fidelity imposed by typical laboratory-grade and precision LOs?
• RQ5 How do phase-noise-induced errors affect the reliability of quantum benchmarking and quantum error correction protocols?

Key findings

• Laboratory-grade local oscillators contribute error probabilities exceeding 10⁻⁴ for operation times shorter than 1 μs, setting a hard upper bound on achievable fidelity.
• The use of precision local oscillators can suppress error rates by a factor of 10⁴ compared to standard laboratory-grade LOs.
• Phase fluctuations at frequencies far from the carrier frequency dominate the error rate, despite their high-frequency nature.
• High-frequency spectral components of LO noise are largely unaffected by dynamic error suppression techniques, limiting their utility in mitigating such errors.
• Thermal phase fluctuations in the LO contribute to an effective error floor, with the magnitude of this floor dependent on the noise bandwidth of the LO.
• The analysis reveals that clock instability is a critical, often overlooked, source of dephasing that constrains the performance of near-term quantum processors.