[Paper Review] Realizing quantum gates with optically-addressable $^{171}$Yb$^{+}$ ion qudits

M. A. Aksenov, I. V. Zalivako+7 more|arXiv (Cornell University)|Oct 17, 2022

Quantum Information and Cryptography4 citations

TL;DR

This paper demonstrates a proof-of-principle two-ququart (d=4) quantum processor using optically-addressable $^{171}$Yb$^+$ ions, encoding qudits in the Zeeman sublevels of the 435.5 nm quadrupole clock transition. It realizes a universal gate set including single-qudit rotations and a two-qudit Mølmer–Sørensen gate, achieving gate fidelities of 83–89% for single-qudit gates and 65% for the two-qudit gate, with laser phase noise identified as the dominant error source.

ABSTRACT

The use of multilevel information carriers, also known as qudits, is a promising path for exploring scalability of quantum computing devices. Here we present a proof-of-principle realization of a quantum processor register that uses optically-addressed $^{171}$Yb$^{+}$ ion qudits in a linear trap. The rich level structure of $^{171}$Yb$^{+}$ ions allows using the Zeeman sublevels of the quadrupole clock transition at 435.5 nm for efficient and robust qudit encoding. We demonstrate the realization of the universal set of gates consisting of single-qudit rotations and a two-qudit Molmer-Sorensen operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way towards further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors and, specifically, exploring properties of $^{171}$Yb$^{+}$ ion qudits.

Motivation & Objective

• To demonstrate a scalable quantum processor architecture based on multilevel $^{171}$Yb$^+$ ions as qudits.
• To implement a universal set of quantum gates using optical addressing of Zeeman sublevels in the 435.5 nm quadrupole transition.
• To evaluate gate fidelities and identify dominant error sources in a trapped-ion qudit system.
• To establish a foundation for future high-fidelity, large-scale qudit-based quantum computing with trapped ions.

Proposed method

• Qudits are encoded in the Zeeman sublevels of the $^2S_{1/2}(F=0)$ and $^2D_{3/2}(F=2)$ states of $^{171}$Yb$^+$, using the 435.5 nm electric quadrupole transition for optical addressing.
• Single-qudit rotations are implemented via resonant laser pulses tuned to specific Zeeman sublevel transitions.
• A two-qudit Mølmer–Sørensen-type gate is realized using bichromatic laser pulses to induce entangling interactions between the two ions.
• Laser phase noise is characterized via ion spectroscopy on a $|0\rangle \to |1\rangle$ transition, enabling extraction of noise power spectral density (PSD).
• Numerical simulations incorporating the extracted laser noise PSD are used to model and validate gate fidelity degradation.
• Gate fidelities are experimentally measured via state tomography and parity oscillation protocols.

Experimental results

Research questions

• RQ1 Can a universal set of quantum gates be realized using optically-addressed $^{171}$Yb$^+$ ion qudits in a linear trap?
• RQ2 What are the dominant error sources limiting gate fidelity in this qudit-based trapped-ion system?
• RQ3 To what extent can the qudit encoding in $^{171}$Yb$^+$ ions emulate a four-qubit processor in terms of computational power?
• RQ4 How does laser phase noise affect the performance of two-qudit entangling gates in this system?
• RQ5 Can the observed fidelities be improved through technical upgrades to the laser stabilization and ion temperature?

Key findings

• The system realizes a universal gate set comprising single-qudit rotations and a two-qudit Mølmer–Sørensen gate, demonstrating the feasibility of qudit-based quantum processing.
• Single-qudit gate fidelities range from 83% to 89%, indicating high-fidelity single-qudit operations.
• The two-qudit gate fidelity is measured at 65%, which is limited primarily by laser phase noise.
• Laser phase noise is identified as the dominant error source through comparison of experimental data with numerical simulations using extracted noise PSD.
• The extracted laser noise PSD, when used in simulations, reproduces the 65% gate fidelity, validating the noise model.
• The results suggest that future improvements in laser stabilization and ion temperature will enable higher-fidelity qudit operations, approaching those reported in similar qubit-based systems.