[Paper Review] Selecting ensembles for rare earth quantum computation

J. J. Longdell M. J. Sellars|ArXiv.org|Oct 16, 2003

Quantum Computing Algorithms and Architecture6 references3 citations

TL;DR

This paper proposes a practical two-qubit gate scheme for rare-earth-ion-based quantum computation using electric dipole-dipole interactions in ensembles, leveraging optical addressing and nuclear spin states for long coherence. It identifies inhomogeneous broadening as a key scalability barrier and evaluates alternatives like single-ion spectroscopy and engineered 'solid-state molecules' to overcome it, concluding ensemble-based approaches are not scalable beyond small qubit counts.

ABSTRACT

We discuss the issues surrounding the implementation of quantum computation in rare-earth-ion doped solids. We describe a practical scheme for two qubit gate operations which utilise experimentally available interactions between the qubits. Possibilities for a scalable quantum computer are discussed.

Motivation & Objective

• To develop a practical two-qubit gate operation using experimentally accessible interactions in rare-earth-ion doped solids.
• To address the scalability challenge of ensemble-based rare-earth quantum computing, particularly due to inhomogeneous broadening in interaction strengths.
• To evaluate alternative architectures—such as single-ion spectroscopy and engineered 'solid-state molecules'—for overcoming decoherence and inhomogeneity limitations.
• To demonstrate that rare-earth systems offer advantages over liquid-state NMR, especially in ground-state initialization and long coherence times.

Proposed method

• Utilizes ensembles of rare-earth ions where qubits are encoded in ground-state hyperfine levels with long coherence times (up to 80 ms).
• Employs optical pumping and frequency-selective addressing to prepare and manipulate qubit states via optical transitions with long coherence (up to 2.6 ms).
• Uses electric dipole-dipole interactions between ions (up to GHz strength) to implement two-qubit gates, with gate operations tailored to local interaction strengths.
• Applies a scheme involving 'anti-holes' in the inhomogeneous line to isolate and control specific ion groups, minimizing unwanted coupling.
• Explores the use of defects in stoichiometric crystals to create identical, frequency-shifted ion clusters resembling 'solid-state molecules' for uniform interaction strength.
• Considers single-ion detection via strong optical driving and photon emission monitoring, with potential for RF repumping to sustain cyclic transitions in symmetric sites.

Experimental results

Research questions

• RQ1 Can two-qubit gates be implemented in rare-earth-ion ensembles using experimentally accessible dipole-dipole interactions?
• RQ2 Why is inhomogeneous broadening a fundamental obstacle to scaling ensemble-based rare-earth quantum computing?
• RQ3 Can engineered defects or single-ion control mitigate the inhomogeneity problem and enable scalable architectures?
• RQ4 How do coherence times and optical manipulation capabilities in rare-earth systems compare to those in liquid-state NMR for quantum computation?
• RQ5 Is it feasible to achieve scalable quantum computation using rare-earth ions without relying on ensemble averaging?

Key findings

• The proposed two-qubit gate scheme using dipole-dipole interactions is experimentally feasible and based on well-established interactions in rare-earth systems.
• Ensemble-based rare-earth quantum computing is limited by inhomogeneous broadening, which causes variable interaction strengths between ions and reduces gate fidelity.
• Scalability is severely constrained because the number of ions satisfying the required spectral and interaction criteria decreases exponentially with qubit count.
• Single-ion spectroscopy and engineered 'solid-state molecules' via defects offer potential pathways to overcome inhomogeneity and enable scalable architectures.
• Cyclic transitions in symmetric sites (e.g., LaCl3) with RF repumping can sustain optical state readout, enabling single-ion detection.
• Nuclear spin states in rare-earth ions offer coherence times up to 80 ms, and lifetimes up to several hours, making them ideal for long-term qubit storage.