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Scientific Reports

Generation of multipartite entanglement between spin-1 particles with bifurcation-based quantum annealing

Yuichiro Matsuzaki, Takashi Imoto, Yuki Susa

Published Sep 2, 2022• 5 citations
Publisher

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 [Formula: see text], let this state evolve by a time-dependent Hamiltonian in an adiabatic way, and we find a state spanned by [Formula: see text] 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.

DOI
10.1038/s41598-022-17621-1

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\n\nDiamond defect spins have emerged as potential qudits (d-dimensional quantum bit) in quantum information and quantum computing. A new scheme is proposed for realizing entangled states of GHZ (Greenberger-Horne-Zeilinger) class in a 3-qudit solid-state register. The qudits are the electron spin-1 carried by the negatively charged nitrogen-vacancy color center (NV−1) in diamond and the nuclear spin-$\\frac{1}{2}$ of two carbon-13 impurities in the first neighbour shell. Multipartite entanglements between qudits are obtained by bringing the spin system in the vicinity of a level anticrossing. The degree of entanglement between all three qudits is quantified rigorously. GHZ and GHZ-like entangled states have applications in quantum communication and computation protocols.\n

Europhysics Letters (EPL)•Jul 1, 2016•1 citation
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 [Formula: see text], let this state evolve by a time-dependent Hamiltonian in an adiabatic way, and we find a state spanned by [Formula: see text] 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.
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⟩|0\rangle∣0⟩, let this state evolve by a time-dependent Hamiltonian in an adiabatic way, and we find a state spanned by ∣±1⟩|\pm 1\rangle∣±1⟩ 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.
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⟩, let this state evolve by a time-dependent Hamiltonian in an adiabatic way, and we find a state spanned by | ± 1⟩ 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.
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrodinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Preparing ground states of Hamiltonians is important in the condensed matter physics and the quantum chemistry. The interaction Hamiltonians typically contain not only diagonal but also off-diagonal elements. Although quantum annealing provides a way to prepare a ground state of a Hamiltonian, we can only use the Hamiltonian with Ising interaction by using currently available commercial quantum annealing devices. In this work, we propose a quantum annealing for the XXZ model, which contains both Ising interaction and energy-exchange interaction, by using inductively coupled superconducting flux qubits. The key idea is to use a recently proposed spin-lock quantum annealing where the qubits are driven by microwave fields. As long as the rotating wave approximation is valid, the inductive coupling between the superconducting flux qubits produces the desired Hamiltonian in the rotating frame, and we can use such an interaction for the quantum annealing while the microwave fields driving play a role of the transverse fields. To quantify the performance of our scheme, we implement numerical simulations, and show that we can prepare ground states of the two-dimensional Heisenberg model with a high fidelity.
\n\nDiamond defect spins have emerged as potential qudits (d-dimensional quantum bit) in quantum information and quantum computing. A new scheme is proposed for realizing entangled states of GHZ (Greenberger-Horne-Zeilinger) class in a 3-qudit solid-state register. The qudits are the electron spin-1 carried by the negatively charged nitrogen-vacancy color center (NV−1) in diamond and the nuclear spin-frac12\\frac{1}{2}frac12 of two carbon-13 impurities in the first neighbour shell. Multipartite entanglements between qudits are obtained by bringing the spin system in the vicinity of a level anticrossing. The degree of entanglement between all three qudits is quantified rigorously. GHZ and GHZ-like entangled states have applications in quantum communication and computation protocols.\n