Generation of multipartite entanglement between spin-1 particles with bifurcation-based quantum annealing
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2022-09-02 |
| Journal | Scientific Reports |
| Authors | Yuichiro Matsuzaki, Takashi Imoto, Yuki Susa |
| Institutions | National Institute of Advanced Industrial Science and Technology |
| Citations | 5 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive SummaryāThis research proposes and simulates a scheme for generating multipartite entanglement (GHZ states) between spin-1 particles using bifurcation-based Quantum Annealing (QA).
- Core Value Proposition: The method efficiently generates GHZ states, which are critical resources for entanglement-enhanced quantum sensing and quantum error correction.
- Physical System: The scheme is designed for implementation using Nitrogen Vacancy (NV) centers in diamond, which function as natural spin-1 qubits arranged in a one-dimensional chain with dipole-dipole interactions.
- Methodology: Entanglement is achieved through adiabatic evolution by dynamically controlling the effective detuning (Dā) and the amplitude of globally applied microwave driving fields (Ī»x(t)).
- Implementation Advantage: The protocol requires only global application of microwave pulses, eliminating the need for complex, high-precision individual addressing of each NV center.
- Performance: Numerical simulations demonstrate high fidelity (F > 0.999) in unitary dynamics and robust performance (F ā 0.9) even when including realistic decoherence (Ī³ = 0.5 kHz) and strain effects for systems up to L=3 spins.
- Symmetry Protection: The total Hamiltonian commutes with a parity operator, which suppresses non-adiabatic transitions between the desired GHZ+ state and the unwanted GHZ- state, ensuring high fidelity despite a small energy gap near the end of the annealing process.
Technical Specifications
Section titled āTechnical Specificationsā| Parameter | Value | Unit | Context |
|---|---|---|---|
| Spin System | NV Centers | Diamond | Spin-1 particles |
| Total Annealing Time (T) | 0.1 | ms | Simulation time for L=2, L=3, L=4 |
| Typical Zero-Field Splitting (D0/2Ļ) | 2.88 | GHz | Standard experimental value for NV centers |
| Simulated D0/2Ļ (RWA) | 40 | MHz | Used for computational efficiency (Rotating Wave Approximation) |
| Microwave Frequency (Ļ/2Ļ) | 40 | MHz | Used in RWA simulations |
| Transverse Field Amplitude (B/2Ļ) | 340 | kHz | Maximum amplitude of Gaussian driving field |
| Initial Detuning (Dā/2Ļ) | 400 | kHz | Effective longitudinal field at t=0 |
| Strain (Ex(j)/2Ļ) | 0 to 16 | kHz | Tested range for strain effects |
| Flip-Flop Coupling (J12/2Ļ) | 30 | kHz | Dipole-dipole interaction strength |
| Ising Coupling (I12/2Ļ) | 60 | kHz | Dipole-dipole interaction strength |
| Decoherence Rate (Ī³) | 0.5 | kHz | Used in GKSL master equation simulations |
| Unitary Fidelity (L=2, Ex=0) | >0.999 | - | Ideal performance |
| Fidelity (L=4, RWA, Ī³=0.5 kHz) | 0.89 | - | Performance for largest simulated system |
Key Methodologies
Section titled āKey MethodologiesāThe scheme relies on implementing bifurcation-based Quantum Annealing (QA) in a system of coupled spin-1 NV centers via global microwave control.
- System Configuration: Spin-1 NV centers are arranged in a one-dimensional chain, leveraging their intrinsic dipole-dipole (flip-flop Jjk and Ising Ijk) interactions for coupling.
- Initial State Preparation: The system is initialized in the trivial ground state, where all spins are in the |0> state, achieved under a large positive detuning Dā.
- Hamiltonian Definition: The total Hamiltonian H = HD + HP is defined in a rotating frame (using the Rotating Wave Approximation, RWA) where the detuning Dā = D0 - Ļ acts as the effective longitudinal field.
- Adiabatic Control of Detuning (Dā): The effective detuning Dā is slowly decreased over the annealing time T (0.1 ms) using a hyperbolic tangent function: Dā = D0 tanh[M(t - T/2)/T]. This mimics the gradual reduction of the transverse field in conventional QA.
- Microwave Driving Field (Ī»x(t)): A global microwave field is applied along the x-direction, with its amplitude Ī»x(t) controlled by a Gaussian pulse centered at T/2, ensuring the quantum fluctuation is induced primarily in the middle of the QA process.
- Symmetry Protection: The protocol utilizes the fact that the total Hamiltonian commutes with a parity operator P. This symmetry ensures that the initial state, which belongs to the GHZ+ sector, cannot transition to the GHZ- sector, thereby protecting the fidelity of the target state even when the energy gap is minimal.
- Decoherence Modeling: Performance under realistic conditions is evaluated using the GKSL master equation, incorporating a decoherence rate (Ī³) associated with magnetic field noise typical for NV centers.
Commercial Applications
Section titled āCommercial ApplicationsāThis technology, focused on generating high-fidelity multipartite entanglement in solid-state spin systems, is highly relevant to several advanced engineering fields:
- Quantum Computing: GHZ states serve as fundamental entangled resources for building quantum circuits and implementing measurement-based quantum computation protocols.
- Quantum Sensing and Metrology: Entanglement-enhanced quantum sensors (e.g., magnetometers, thermometers) utilize GHZ states to achieve sensitivity scaling beyond the Standard Quantum Limit (Heisenberg limit).
- Quantum Communication and Networking: GHZ states are essential for quantum network encoding, acting as a resource for constructing error-correcting codes and enabling distributed quantum computation.
- Solid-State Qubit Development: The use of NV centers in diamond confirms their viability as robust, room-temperature spin-1 qubits suitable for scalable quantum information processing architectures.
- Microwave Engineering: The reliance on precise, time-dependent global microwave fields necessitates advanced control systems for generating and shaping high-frequency pulses (in the MHz to GHz range).
View Original Abstract
Abstract Quantum annealing is a way to solve a combinational optimization problem where quantum fluctuation is induced by transverse fields. Recently, a bifurcation-based quantum annealing with spin-1 particles was suggested as another mechanism to implement the quantum annealing. In the bifurcation-based quantum annealing, each spin is initially prepared in $$|0\rangle$$ <mml:math xmlns:mml=āhttp://www.w3.org/1998/Math/MathMLā> <mml:mrow> <mml:mo>|</mml:mo> <mml:mn>0</mml:mn> <mml:mo>ā©</mml:mo> </mml:mrow> </mml:math> , let this state evolve by a time-dependent Hamiltonian in an adiabatic way, and we find a state spanned by $$|\pm 1\rangle$$ <mml:math xmlns:mml=āhttp://www.w3.org/1998/Math/MathMLā> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>Ā±</mml:mo> <mml:mn>1</mml:mn> <mml:mo>ā©</mml:mo> </mml:mrow> </mml:math> at the end of the evolution. Here, we propose a scheme to generate multipartite entanglement, namely GHZ states, between spin-1 particles by using the bifurcation-based quantum annealing. We gradually decrease the detuning of the spin-1 particles while we adiabatically change the amplitude of the external driving fields. Due to the dipole-dipole interactions between the spin-1 particles, we can prepare the GHZ state after performing this protocol. We discuss possible implementations of our scheme by using nitrogen vacancy centers in diamond.