[Paper Review] Intrinsic Noise of the Single Electron Box

Laurence Cochrane, Ashwin A. Seshia+1 more|arXiv (Cornell University)|Sep 29, 2022

Quantum and electron transport phenomena4 citations

TL;DR

This paper develops a noise model for the radio-frequency Single-Electron Box (SEB) by analyzing intrinsic current noise arising from stochastic electron tunnelling under periodic gate voltage excitation. Using a master equation formalism and Markov Monte Carlo simulations, it identifies the noise as cyclostationary, with spectral correlations that significantly impact signal-to-noise ratio in qubit readout, and provides conditions for experimental detection and suppression of this noise to enhance readout fidelity.

ABSTRACT

The radio-frequency Single-Electron Box is becoming an attractive charge sensor for semiconductor-based quantum computing devices due to its high sensitivity and small footprint, which facilitates the design of highly connected qubit architectures. However, an understanding of its ultimate sensitivity is missing due to the lack of a noise model. Here, we quantify the intrinsic noise of the Single-Electron Box arising from stochastic cyclic electron tunnelling between a quantum dot and a reservoir driven by a periodic gate voltage. We use both a master equation formalism and Markov Monte Carlo simulations to calculate the gate noise current, and find the noise mechanism can be represented as a cyclostationary process. We consider the implications of this cyclostationary noise on the ultimate sensitivity of Single-Electron Box sensors for fast, high-fidelity readout of spin qubits, in particular evaluating results for radio-frequency reflectometry implementations and the backaction of the sensor on a qubit. Furthermore, we determine the conditions under which the intrinsic noise limit could be measured experimentally and techniques by which the noise can be suppressed to enhance qubit readout fidelity.

Motivation & Objective

• To establish a theoretical and computational framework for modeling intrinsic noise in the radio-frequency Single-Electron Box (SEB), a promising charge sensor for semiconductor quantum computing.
• To address the lack of a noise model for SEBs analogous to the well-established shot noise model for Single-Electron Transistors (SETs).
• To quantify how time-varying noise spectra and spectral correlations affect signal-to-noise ratio in rf-reflectometry-based spin qubit readout.
• To identify experimental conditions under which the intrinsic noise limit can be measured and strategies to suppress it for improved measurement fidelity.

Proposed method

• Formulates the SEB's stochastic electron tunnelling under periodic gate excitation as a cyclostationary process using a master equation approach.
• Derives the time-dependent current noise spectral density $ S_I(t, u) $, treating it as a periodic function of time due to the driving frequency $ u_0 $.
• Introduces spectral correlation functions $ S_I^{n heta_0}( u) $, defined as the Fourier components of $ S_I(t, u) $, to capture time-varying noise dynamics.
• Performs Markov Monte Carlo simulations of the time-inhomogeneous Markov process governing electron tunnelling, with discrete time steps $ au = T/N_ ext{Δ} $.
• Models the SEB's small-signal equivalent circuit, including quantum capacitance and Sisyphus resistance, and incorporates feedback from tunnelling events via IIR digital filters derived from Laplace-domain transfer functions.
• Implements synchronous demodulation numerically by downmixing the output voltage with a local oscillator and applying a low-pass filter, followed by decimation and power spectral density estimation.

Experimental results

Research questions

• RQ1 How does the intrinsic noise of the SEB behave under high-frequency periodic gate excitation, and can it be described as a cyclostationary process?
• RQ2 What is the role of spectral correlation functions $ S_I^{n heta_0}( u) $ in degrading or enhancing the signal-to-noise ratio during rf-reflectometry-based qubit readout?
• RQ3 Under what experimental conditions can the intrinsic noise limit of the SEB be measured, and what are the key parameters affecting detectability?
• RQ4 How can the intrinsic noise of the SEB be suppressed to improve the fidelity of fast, high-fidelity spin qubit readout?

Key findings

• The intrinsic noise of the SEB is not stationary but cyclostationary, with the noise spectral density $ S_I(t, u) $ varying periodically at the driving frequency $ u_0 $, which invalidates standard stationary noise models.
• Spectral correlation functions $ S_I^{n heta_0}( u) $—analogous to noise harmonics—must be considered in signal processing, as they significantly affect the signal-to-noise ratio after synchronous demodulation.
• Simulations show convergence of spectral correlation estimates at $ N_ ext{Δ} = 2^{11} $ samples per cycle, validating the numerical method for accurate noise characterization.
• The zero-frequency noise power spectrum $ S_X(0) $ is estimated via FFT-based periodogram with standard error derived from $ N = 500 $ simulation trials.
• The cyclostationary nature of the noise leads to a trochoidal modulation of the measured noise power with local oscillator phase $ heta $, described by $ S_X( heta) = S_X^0 + riangle S_X an(2 heta + heta_0) $, enabling extraction of $ S_X $ and $ riangle S_X $.
• The model enables identification of parameter regimes where intrinsic noise dominates, providing a roadmap for experimental detection and suppression strategies to enhance qubit readout fidelity.