Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits

Abstract: Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform inter-qubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor due to their potential for scalability and miniaturization. However, their weak interactions with the environment, which leads to their long coherence times, makes inter-qubit operations challenging. We perform a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography we measure the full density matrix of the system and determine the concurrence and the fidelity of the generated state, providing proof of entanglement.

• The paper demonstrates controlled entanglement of electrostatically coupled S-T0 qubits using a dynamically decoupled pulse sequence that achieves a maximum concurrence of 0.44.
• It employs a precise experimental setup with double quantum dots and RF state reading to enable robust qubit initialization and manipulation.
• The study highlights that improved charge noise management could boost entanglement fidelity above 90% for scalable quantum computing.

Analysis of Entanglement in Electrostatically Coupled Singlet-Triplet Qubits

The research document titled "Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits" presents a detailed investigation into the entanglement of singlet-triplet ($S$-$T_{0}$) qubits via electrostatic coupling, which is critical for the advancement of quantum computing. The primary focus of this paper is the implementation of controlled two-qubit operations that maintain the qubits' coherence over time, allowing for effective generation and manipulation of entangled states.

The significance of this research lies in the potential of spin qubits for scalability and minimization, crucial for building effective quantum processors. The $S$-$T_{0}$ qubits harness the joint spins of two electrons within a two-level quantum system. The research notes that the inherent weak interaction of spin qubits with their environment benefits coherence time but raises challenges in inter-qubit operations. This study overcomes these obstacles by employing a dynamically decoupled sequence that preserves two-qubit interaction while mitigating environmental noise.

Methodological Approach

The experimental setup features two electrons confined within a double quantum dot (QD) in a GaAs-AlGaAs substrate, utilizing local top gates to manipulate electron configurations. This configuration enables robust qubit initialization processes, rapid state reading via RF-techniques, and consistent application of Pauli blockade methods for precise state determination.

The researchers fabricate two capacitively coupled singlet-triplet qubits. They capitalize on the electrostatic interaction between qubits to implement a two-qubit operation. Such operation varies the qubit precession frequency due to the differential charge configurations induced by $S$ and $T_{0}$ states, thus leading to state-dependent electric fields.

The authors present an entangling pulse sequence modulating exchange interactions with applied external magnetic fields to facilitate state coupling, ultimately forming a Controlled-Phase (CPHASE) gate derived from this dipole-dipole interaction.

Key Results

The experiment's success is demonstrated by state tomography, which quantitatively assesses the entanglement via concurrence and fidelity measures. Through systematic calcuation of the density matrix, they confirm entanglement, achieving a maximum concurrence of 0.44. Additionally, they report a Bell state fidelity peaking at 0.72 for $\tau=140$ns, useful for benchmarking entangled states' generation efficiency.

Critically, their results indicate fidelity oscillations corresponding to entangled states' decoherence dynamics. As the parameters evolve, the entangled state's fidelity diminishes, emphasizing the need for strategies like dynamically decoupled sequences to counteract decoherence effects.

Implications and Future Directions

This paper makes substantial contributions towards scalable quantum computation architectures by demonstrating electrostatically mediated entanglement in $S$-$T_{0}$ qubits. In practice, reducing the entanglement generation time relative to qubit coherence times is paramount. The authors speculate that implementing electrostatic couplers might drastically improve the coupling strength and, therefore, the entanglement fidelity above 90%.

Future work should focus on understanding charge noise origins that limit $T_2^{echo}$, further optimizing the quantum control sequences, and experimentally validating quantum algorithms and error correction codes. The exploration of entanglement also allows researchers to explore the complex dynamics of nuclear environments—a quintessential quantum, many-body challenge.

In essence, the study not only advances methods for entangling specific qubit systems but also sets the foundation for greater exploration in entangled state dynamics and quantum computational applications.