Probing Critical Behavior of Long-Range Transverse-Field Ising Model through Quantum Kibble-Zurek Mechanism

Li, B.-W.; Wu, Yukai; Mei, Quanxin; Yao, Ruixiao; Lian, Wenqian; Cai, Meihan; Wang, Yaogong; Qi, Ben; Yao, Liqiang; He, Longfei; Zhou, Z.-C.; Duan, L.-M.

doi:10.1103/prxquantum.4.010302

Cited by 14 publications

(5 citation statements)

References 47 publications

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“…离子阱量子计算实验通常设计合适的约束电场, 让离子沿着离子阱的轴线方向排列成间距几微米的一维阵列, 从而可以利用聚焦的激光束对各个离子进行单独寻址操控. 利用该方法, 国际上已实现了对 13个离子的单比特量子逻辑门平均保真度 99.98%, 以及全连通的双比特量子逻辑门保真度 98.5% -99.3% [8] , 并在53离子 [9] 和61离子 [10] 的一维阵列上演示了量子模拟实验. 然而, 一维构型所能提供的离子数并不能满足离子阱量子计算机的规模化需求.…”

Section: 为了获得可独立操控的多个量子比特主流的unclassified

Research progress of ion trap quantum computing

Wu,

Duan

2023

Acta Phys. Sin.

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Ion trap is one of the leading physical platforms to implement quantum computation. Currently, high-fidelity elementary quantum operations above the fault-tolerant threshold, including state preparation, measurement and universal gates, have been demonstrated for tens of ionic qubits. One important future research direction is to further enlarge the qubit number to the scale required for solving practical problems while maintaining the high performance of individual qubits. This paper introduces the current mainstream schemes for scalable ion trap quantum computation like quantum charge-coupled device (QCCD) and ion-photon quantum network, and describes the main limiting factors in current research. Then we further explore new schemes to scale up the qubit number like two-dimensional ion crystals and dual-type qubit, and discuss the future research directions.

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Section: 为了获得可独立操控的多个量子比特主流的unclassified

Research progress of ion trap quantum computing

Wu,

Duan

2023

Acta Phys. Sin.

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“…More contrasts between time-dependent and time-independent KZMs can be found in [10,12]. While there have been many theoretical [35][36][37][38][39][40][41][42][43][44] and experimental [45][46][47][48][49][50][51][52][53][54][55][56] studies on the time-dependent KZM, the time-independent KZM has been less explored and awaits more investigations.…”

Section: Introductionmentioning

confidence: 99%

Structure and scaling of Kitaev chain across a quantum critical point in real space

He,

Chien

2024

J. Phys.: Condens. Matter

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The spatial Kibble-Zurek mechanism (KZM) is applied to the Kitaev chain with inhomogeneous pairing interactions that vanish in half of the lattice and result in a quantum critical point separating the superfluid and normal-gas phases in real space. The weakly-interacting BCS theory predicts scaling behavior of the penetration of the pair wavefunction into the normal-gas region different from conventional power-law results due to the non-analytic dependence of the BCS order parameter on the interaction. The Bogoliubov-de Gennes (BdG) equation produces numerical results confirming the scaling behavior and hints complications in the strong-interaction regime. The limiting case of the step-function quench reveals the dominance of the BCS coherence length in absence of additional length scale. Furthermore, the energy spectrum and wavefunctions from the BdG equation show abundant in-gap states from the normal-gas region in addition to the topological edge states.

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“…The systems can be driven by a time-dependent or time-independent ramp. The KZM has inspired a plethora of theoretical [13,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] and experimental [52][53][54][55][56][57][58][59][60][61][62][63] studies to verify or compare the KZ scaling. The majority of the investigations have focused on time-dependent quenches of the parameters, where the excitations follow a power-law dependence of the transition rate [37][38][39]43], including the Bose-Hubbard model [45][46][47][48][49] and spinor Bose-Einstein condensates (BEC) [50,51].…”

Section: Introductionmentioning

confidence: 99%

Proximity effect and spatial Kibble-Zurek mechanism in atomic Fermi gases with inhomogeneous pairing interactions

Parajuli¹,

Chien²

2023

Preprint

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Introducing spatially tunable interactions to atomic Fermi gases makes it feasible to study two phenomena, the proximity effect and spatial Kibble-Zurek mechanism (KZM), in a unified platform. While the proximity effect of a superconductor adjacent to a normal metal corresponds to a stepfunction quench of the pairing interaction in real space, the spatial KZM is based on a linear drop of the interaction that can be modeled as a spatial quench. After formulating the Fermi gases with spatially varying pairing interactions by the Bogoliubov-de Gennes (BdG) equation, we obtain the profiles of the pair wavefunction and its correlation function to study their penetration into the noninteracting region. For the step-function quench, both correlation lengths from the pair wavefunction and its correlation function follow the BCS coherence length and exhibit the same scaling behavior. In contrast, the exponents from the two correlation lengths are different in the spatial quench. Only the exponent from the pair correlation function agrees with the KZM prediction. Therefore, the spatial quench allows more refined analyses of the correlation lengths from different physical quantities. Moreover, adding a weakly interacting bosonic background does not change the scaling behavior. We also discuss relevant experimental techniques that may realize and verify the inhomogeneous phenomena.

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Probing Critical Behavior of Long-Range Transverse-Field Ising Model through Quantum Kibble-Zurek Mechanism

Cited by 14 publications

References 47 publications

Research progress of ion trap quantum computing

Research progress of ion trap quantum computing

Structure and scaling of Kitaev chain across a quantum critical point in real space

Proximity effect and spatial Kibble-Zurek mechanism in atomic Fermi gases with inhomogeneous pairing interactions

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