Quantum tomography of an entangled three-qubit state in silicon
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-06-07 |
| Journal | Nature Nanotechnology |
| Authors | Kenta Takeda, Akito Noiri, Takashi Nakajima, Jun Yoneda, Takashi Kobayashi |
| Institutions | RIKEN Center for Emergent Matter Science |
| Citations | 101 |
| Analysis | Full AI Review Included |
Quantum Tomography of an Entangled Three-Spin State in Silicon: Engineering Analysis
Section titled âQuantum Tomography of an Entangled Three-Spin State in Silicon: Engineering AnalysisâExecutive Summary
Section titled âExecutive Summaryâ- Core Achievement: Successful generation and characterization of a three-qubit Greenberger-Horne-Zeilinger (GHZ) entangled state using electron spins confined in a silicon/silicon-germanium (Si/SiGe) triple quantum dot array.
- High Fidelity: The GHZ state achieved a state fidelity of 0.880 ± 0.007 (88.0%) via quantum state tomography, comparable to initial demonstrations in superconducting platforms.
- Genuine Entanglement Witnessed: The measured state violates the Mermin-Bell inequality (M = 3.47 ± 0.05), confirming genuine GHZ-class multipartite entanglement that is not biseparable.
- High Single-Qubit Performance: Average single-qubit control fidelities were benchmarked at 99.43% (Q1), 99.57% (Q2), and 99.91% (Q3).
- Noise Mitigation Strategy: A decoupled CZ gate sequence, incorporating Ï pulses (Hahn echo), was implemented to effectively decouple the qubits from quasi-static low-frequency noise (nuclear magnetic and charge noise) during entanglement operations.
- Platform Validation: This result demonstrates the potential of the silicon quantum dot platform for scalable multi-qubit quantum algorithms and is a crucial step toward implementing quantum error correction (QEC).
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| GHZ State Fidelity (FGHZ) | 0.880 ± 0.007 | Dimensionless | Measured via quantum state tomography. |
| Mermin-Bell Witness (M) | 3.47 ± 0.05 | Dimensionless | Violates the biseparable limit (M < 2) by > 28 standard deviations. |
| Single-Qubit Fidelity (Q1) | 99.43 | % | Clifford-based randomized benchmarking. |
| Single-Qubit Fidelity (Q2) | 99.57 | % | Clifford-based randomized benchmarking. |
| Single-Qubit Fidelity (Q3) | 99.91 | % | Clifford-based randomized benchmarking. |
| Two-Qubit Bell State Fidelity | 94.1 | % | Average fidelity for Q2 and Q3 Bell states. |
| T1 Relaxation Time (Q1) | 4.30 | ms | Spin relaxation time. |
| T1 Relaxation Time (Q3) | 1.31 | ms | Spin relaxation time (shortest observed). |
| T2* Dephasing Time (Q1) | 1.82 | ”s | Inhomogeneous dephasing time. |
| T2 Echo Time (Q3) | 45.8 | ”s | Hahn echo extended coherence time (longest observed). |
| External Magnetic Field (Bext) | 0.5275 | T | Applied in-plane field. |
| Zeeman Splitting | ~18 | GHz | Energy separation between spin states. |
| Base Electron Temperature | 40 | mK | Operating temperature in dilution refrigerator. |
| Single-Qubit Rabi Frequency (fRabi) | 6 | MHz | Maximum single-qubit drive speed. |
| Exchange Coupling (J12) | 2.8 | MHz | Nominal coupling between Q1 and Q2. |
| Exchange Coupling (J23) | 12.5 | MHz | Nominal coupling between Q2 and Q3. |
| Qubit Frequency Separation (ÎŽE12) | 435.4 | MHz | Separation due to micro-magnet field gradient. |
| Low-Frequency Charge Noise (S(f=1 Hz)) | 0.2 | ”V/sqrt(Hz) | Measured effective charge noise in the device. |
| Micro-magnet Stack | Ti/Co/Al | 10/250/20 nm | Film thicknesses used to create field gradient. |
Key Methodologies
Section titled âKey MethodologiesâDevice Fabrication and Setup
Section titled âDevice Fabrication and Setupâ- Substrate: Isotopically natural, undoped Si/SiGe heterostructure wafer.
- Quantum Dot Formation: Nanofabricated overlapping aluminum gates (three layers) define the triple quantum dot confinement potential.
- Qubit Encoding: Each dot hosts one electron, using its spin-up and spin-down states as the qubit basis (Q1, Q2, Q3).
- Magnetic Field Gradient: A cobalt micro-magnet placed on top of the array generates a local Zeeman gradient, enabling fast, addressable Electric-Dipole Spin Resonance (EDSR) control.
- Cooling: Sample cooled in a dry dilution refrigerator to a base electron temperature of 40 mK.
Initialization, Readout, and Control
Section titled âInitialization, Readout, and Controlâ- Initialization/Readout (Q1, Q3): Performed via energy-selective tunneling with neighboring electron reservoirs.
- Initialization/Readout (Q2): Achieved indirectly using a combination of resonant SWAP gates (with Q1 or Q3) and energy-selective tunneling.
- Single-Qubit Control: Implemented using EDSR, leveraging the micro-magnet field gradient for frequency addressability (separations > 400 MHz).
- Two-Qubit Control (CZ Gates): Controlled phase (CZ) gates utilize the exchange coupling (Jij) between neighboring spins, controlled by fast gate voltage pulses (virtual gate technique) to maintain the symmetric operation point and minimize charge-noise-induced dephasing.
- Entanglement Protocol: The GHZ state was generated using a sequence of single-qubit rotations (Y/2) and decoupled CZ gates. The decoupled sequence separates the CZ operation into two âCZ gates with Ï pulses inserted, acting as a Hahn echo to suppress quasi-static phase noise.
State Characterization
Section titled âState Characterizationâ- Readout Error Correction: Measured spin-up and spin-down readout fidelities (Fâi, Fâi) were used to correct the raw measured probabilities (PM).
- Quantum State Tomography (QST): The density matrix (Ï) was reconstructed using maximum likelihood estimation based on 27 combinations of single-qubit pre-rotations (I, X/2, Y/2)â3.
- Error Analysis: Errors for QST results were obtained using a Monte-Carlo method assuming multinomial distributions for single-shot probabilities.
Commercial Applications
Section titled âCommercial ApplicationsâThe successful demonstration of high-fidelity, multipartite entanglement in a silicon platform is critical for the development and scaling of fault-tolerant quantum systems.
- Fault-Tolerant Quantum Computing: The GHZ state is essential for implementing Quantum Error Correction (QEC) protocols, which are necessary to manage error accumulation in large-scale quantum processors.
- Scalable Quantum Processors: Silicon quantum dots are highly compatible with standard CMOS manufacturing techniques, offering a promising route for high-density integration and mass production of qubits.
- Quantum Simulation: Multi-qubit arrays enable the simulation of complex quantum phenomena, such as many-body physics and material properties, which are intractable for classical computers.
- Quantum Sensing: The high coherence times (T2 echo up to 45.8 ”s) and precise spin control are foundational for advanced quantum sensors that utilize entangled states for enhanced sensitivity.
- High-Fidelity Gate Development: The techniques developed for noise mitigation (decoupled CZ gates) are directly applicable to improving gate fidelity in other solid-state qubit architectures.