[Paper Review] Modelling semiconductor spin qubits and their charge noise environment for quantum gate fidelity estimation

M. Mohamed El Kordy Shehata, George Simion+8 more|arXiv (Cornell University)|Oct 10, 2022

Quantum and electron transport phenomena4 citations

TL;DR

This paper presents a co-modeling framework combining electrostatic potential solvers, full configuration interaction (FCI) quantum mechanics, and two-level-fluctuator (TLF) models to simulate charge noise effects in silicon double quantum dot (DQD) spin qubits. It demonstrates that higher quantum dot confinement frequencies improve gate fidelity, achieving >97% X-gate fidelity at 10¹¹ cm⁻² TLF density, while SWAP gates show lower fidelity (~91%) due to higher charge noise sensitivity.

ABSTRACT

The spin of an electron confined in semiconductor quantum dots is currently a promising candidate for quantum bit (qubit) implementations. Taking advantage of existing CMOS integration technologies, such devices can offer a platform for large scale quantum computation. However, a quantum mechanical framework bridging a device's physical design and operational parameters to the qubit energy space is lacking. Furthermore, the spin to charge coupling introduced by intrinsic or induced Spin-Orbit-Interaction (SOI) exposes the qubits to charge noise compromising their coherence properties and inducing quantum gate errors. We present here a co-modelling framework for double quantum dot (DQD) devices and their charge noise environment. We use a combination of an electrostatic potential solver, full configuration interaction quantum mechanical methods and two-level-fluctuator models to study the quantum gate performance in realistic device designs and operation conditions. We utilize the developed models together alongside the single electron solutions of the quantum dots to simulate one- and two- qubit gates in the presence of charge noise. We find an inverse correlation between quantum gate errors and quantum dot confinement frequencies. We calculate X-gate fidelities >97% in the simulated Si-MOS devices at a typical TLF densities. We also find that exchange driven two-qubit SWAP gates show higher sensitivity to charge noise with fidelities down to 91% in the presence of the same density of TLFs. We further investigate the one- and two- qubit gate fidelities at different TLF densities. We find that given the small size of the quantum dots, sensitivity of a quantum gate to the distance between the noise sources and the quantum dot creates a strong variability in the quantum gate fidelities which can compromise the device yields in scaled qubit technologies.

Motivation & Objective

• To develop a quantum mechanical modeling framework that bridges device design and qubit operation in semiconductor spin qubits.
• To quantify the impact of charge noise—modeled via Two-Level-Fluctuators (TLFs)—on one- and two-qubit gate fidelities in realistic silicon double quantum dot (DQD) devices.
• To investigate the correlation between electrostatic noise spectral density and quantum gate infidelity, accounting for spatial variability of noise sources.
• To evaluate gate fidelity dependence on TLF density and distance between noise sources and quantum dots, addressing yield challenges in scalable qubit architectures.

Proposed method

• Employing a 2D electrostatic potential solver to compute realistic confinement potentials in Si-MOS double quantum dots based on actual device geometry.
• Applying full configuration interaction (FCI) methods to solve the many-body Schrödinger equation and compute exchange interaction and qubit energy levels.
• Modeling charge noise using Two-Level-Fluctuators (TLFs) with random spatial distributions to simulate microscopic charge fluctuations.
• Calculating qubit frequency shifts via electric field contributions from TLFs, enabling noise spectral density estimation on the qubit's effective Rabi frequency.
• Using an analytic fidelity model assuming TLF switching only between gate operations to compute average X-gate fidelity as a function of frequency noise spectral density.
• Performing statistical analysis over 100 random TLF distributions to assess variability in gate infidelity and extract correlation trends.

Experimental results

Research questions

• RQ1 How does the confinement frequency of quantum dots affect one-qubit gate fidelity in the presence of charge noise?
• RQ2 What is the impact of TLF density (e.g., 10¹¹ cm⁻²) on X-gate and SWAP-gate fidelities in realistic Si-MOS DQD devices?
• RQ3 How does the spatial distribution of TLFs relative to the quantum dot influence gate fidelity variability and coherence?
• RQ4 Is there a monotonic relationship between electrostatic noise spectral density and qubit frequency noise spectral density in spin qubits?
• RQ5 To what extent does the distance between TLFs and the quantum dot modulate gate fidelity, and how does this affect yield in scalable quantum architectures?

Key findings

• An inverse correlation exists between quantum gate fidelity and charge noise, with higher quantum dot confinement frequencies leading to improved gate performance.
• X-gate fidelities exceed 97% in simulated Si-MOS devices at a typical TLF density of 10¹¹ cm⁻², indicating high resilience to charge noise under optimal confinement.
• SWAP gates driven by exchange interaction show higher sensitivity to charge noise, with fidelities dropping to approximately 91% under the same TLF density.
• The spectral density of qubit frequency noise (NQ) exhibits a monotonic, linear relationship with electrostatic potential noise (N), eliminating third-order variability from electric field effects.
• A power-law correlation (R² = 0.433) is observed between qubit frequency noise spectral density at 1 Hz and X-gate infidelity, with significant variability across different TLF configurations.
• The strong spatial dependence of noise impact—especially distance-dependent coupling—introduces high variability in gate fidelities, posing a challenge for yield in scaled quantum computing platforms.