[Paper Review] Entanglement and Quantum Gate Operations with Spin-Qubits in Quantum Dots

John Schliemann, Daniel Loss|arXiv (Cornell University)|Oct 8, 2001

Quantum and electron transport phenomena3 references3 citations

TL;DR

This paper proposes a solid-state quantum computing architecture using spin-qubits in quantum dots, where electron indistinguishability induces entanglement-like correlations during gate operations. By tuning tunneling barriers, it achieves high-fidelity quantum gates—such as the 'square root of swap'—with maximal entanglement (η = 1) and exponentially suppressed double occupancy, demonstrating that indistinguishable fermions enable robust quantum gate operations via correlated many-body states.

ABSTRACT

We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations. We summarize recent results concerning this type of quantum correlations of indistinguishable particles.

Motivation & Objective

• To provide a foundational understanding of quantum entanglement between distinguishable parties in quantum information theory.
• To address the challenge of describing entanglement-like quantum correlations in systems of indistinguishable fermions, such as electrons in quantum dots.
• To demonstrate how quantum gate operations (e.g., swap and square root of swap) can be implemented in quantum dot architectures while accounting for electron statistics.
• To quantify the role of electron indistinguishability in generating non-classical correlations during gate operations, beyond standard entanglement measures.
• To explore the implications of these correlations for scalable solid-state quantum computation, particularly in the context of fault-tolerant gate design.

Proposed method

• Uses the biorthogonal Schmidt decomposition to analyze entanglement in bipartite systems of distinguishable qubits.
• Applies the antisymmetrized Fock space formalism to describe the full many-body state of two indistinguishable electrons in a double quantum dot.
• Models quantum gate operations via time-dependent tunneling pulses between quantum dots, with the tunneling amplitude tH(t) controlled to achieve specific gate operations.
• Introduces a correlation measure η(t) to quantify entanglement-like correlations during gate operations, particularly during the transient regime when double occupancy is non-zero.
• Analyzes the dynamics of the system using the Hubbard Hamiltonian with effective on-site repulsion UH to describe electron-electron interactions.
• Demonstrates that the 'square root of swap' gate can be implemented by halving the pulse duration T, resulting in a maximally entangled superposition of |↑↓⟩ and |↓↑⟩ states with η = 1.

Experimental results

Research questions

• RQ1 How can quantum entanglement be rigorously defined and quantified in systems of indistinguishable fermions, such as electrons in quantum dots?
• RQ2 To what extent do electron statistics and antisymmetrization lead to entanglement-like correlations that differ from standard bipartite entanglement between distinguishable particles?
• RQ3 Can high-fidelity quantum gate operations (e.g., swap and square root of swap) be achieved in quantum dot spin-qubit systems despite the presence of double occupancy during gate evolution?
• RQ4 What is the role of the correlation measure η(t) in characterizing the degree of quantum correlation during transient gate operations?
• RQ5 How do time-dependent tunneling pulses and effective electron-electron interactions (UH) influence the fidelity and coherence of quantum gate operations in such systems?

Key findings

• The 'square root of swap' gate operation can be implemented by halving the tunneling pulse duration T, resulting in a maximally entangled state with η = 1.
• During the gate operation, the system evolves into a highly correlated state with significant contribution from spin-singlet configurations, leading to η(t) approaching its maximum value.
• Even with tunneling pulses on a time scale comparable to ℏ/UH, the swap process achieves high fidelity due to exponential suppression of double occupancy after the pulse ends.
• The correlation measure η(t) captures both spin and orbital entanglement during the transient phase, indicating that the system is in a strongly correlated many-body state.
• After the tunneling pulse is switched off, the double occupancy amplitude is exponentially suppressed, allowing the two electrons to be treated as effectively distinguishable, and the final state exhibits standard bipartite entanglement.
• The results show that indistinguishable electrons in quantum dots can serve as efficient entanglers, enabling robust quantum gate operations essential for scalable quantum computation.