Showing 1–7 of 7 results for author: Bai, L

Quantum Transformer BSDE Solver via Multi-Layer Fully-Connected Variational Quantum Circuits

Authors: Howard Su, Huan-Hsin Tseng, Chi-Sheng Chen, Lance Bai

Abstract: Solving high-dimensional parabolic partial differential equations (PDEs) is important in engineering, physics, and stochastic control. Deep BSDE methods reformulate semilinear PDEs as backward stochastic differential equations and admit a model-based reinforcement learning interpretation, where trajectories are generated from known stochastic dynamics while a trainable model learns the gradient-re… ▽ More Solving high-dimensional parabolic partial differential equations (PDEs) is important in engineering, physics, and stochastic control. Deep BSDE methods reformulate semilinear PDEs as backward stochastic differential equations and admit a model-based reinforcement learning interpretation, where trajectories are generated from known stochastic dynamics while a trainable model learns the gradient-related control process. We propose a Quantum Transformer BSDE solver based on Multi-Layer Fully-Connected Variational Quantum Circuits (FC-VQC). The method treats the normalized state trajectory as time--coordinate tokens and applies causal self-attention to learn interactions in the adapted BSDE gradient process. All trainable model parameters are contained within the FC-VQC embedding, projection, feed-forward, and decoder modules, while attention and structural operations remain classical and parameter-free. Experiments on three d=36 PDE benchmarks show that QTransformer consistently improves over the non-attentive FC-VQC baseline and outperforms the classical Transformer at compact hidden widths, while the wider classical Transformer achieves the best overall accuracy. These results demonstrate that combining causal attention with FC-VQC provides an effective quantum architecture for high-dimensional BSDE trajectory learning. △ Less

Submitted 27 July, 2026; originally announced July 2026.

Comments: 4 pages, 2 figures

Detecting Complex-Energy Braiding Topology in a Dissipative Atomic Simulator with Transformer-Based Geometric Tomography

Authors: Yang Yue, Nan Li, Xin Zhang, Chenhao Wang, Zeming Fang, Zhonghua Ji, Liantuan Xiao, Suotang Jia, Yanting Zhao, Liang Bai, Ying Hu

Abstract: Machine learning (ML) is shaping our exploration of topological matter, whose existence is inherently tied to the geometry of quantum states or energy spectra. In non-Hermitian systems, distinctive spectral geometry can lead to topological braiding of complex-energy bands, yet directly probing this topology-geometry interplay remains challenging. Here, we introduce a Transformer-based ML framework… ▽ More Machine learning (ML) is shaping our exploration of topological matter, whose existence is inherently tied to the geometry of quantum states or energy spectra. In non-Hermitian systems, distinctive spectral geometry can lead to topological braiding of complex-energy bands, yet directly probing this topology-geometry interplay remains challenging. Here, we introduce a Transformer-based ML framework to capture this interplay and experimentally demonstrate it in a dissipative cold-atom simulator. Using a Bose-Einstein condensate, we engineer tunable dissipative two-level systems whose complex eigenenergies form braids. Owing to the density-dependent dissipation, the instantaneous energy braids exhibit topologically distinct structures at short and long times. The Transformer not only accurately predicts topological invariants for diverse energy braids but also, through its self-attention mechanism, autonomously highlights band crossings as the governing underlying geometric feature. Our work paves the way for ML-guided exploration of non-Hermitian topological phases in cold atoms and beyond. △ Less

Submitted 26 March, 2026; originally announced March 2026.

Comments: 6 figures,accepted by Nature Communications

Time-Varying Strong Coupling and Its Induced Time Diffraction of Magnon Modes

Authors: Jinwei Rao, Yi-Pu Wang, Zhijian Chen, Bimu Yao, Kaixin Zhao, Chunke Wei, Congyi Wang, Runze Li, Li-Hui Bai, Wei Lu

Abstract: Time-varying media break the temporal translation symmetry of wave propagation in materials, enabling advanced wave manipulations. However, this novel phenomenon has been rarely explored in magnonic systems due to the significant challenge of achieving a sudden and prominent change in magnon dispersion within materials. Here, we construct a time-varying strong coupling between two magnon modes, an… ▽ More Time-varying media break the temporal translation symmetry of wave propagation in materials, enabling advanced wave manipulations. However, this novel phenomenon has been rarely explored in magnonic systems due to the significant challenge of achieving a sudden and prominent change in magnon dispersion within materials. Here, we construct a time-varying strong coupling between two magnon modes, and observe a change in the beats of Rabi-like oscillations near the pulse edges. Using a frequency-comb spectroscopy technique developed in this work, we characterize the frequency conversion of magnon modes induced by the time-varying strong-coupling effect. Moreover, we construct time slits with adjacent time interfaces and demonstrate, for the first time, the double-slit time diffraction of magnon modes, analogous to the well-known Young's double-slit experiment. These findings rely solely on the time-varying strong magnon coupling, independent of device reconfiguration. Our results open avenues for applications such as all-magnetic mixers or on-chip GHz sources. △ Less

Submitted 18 December, 2024; v1 submitted 11 November, 2024; originally announced November 2024.

Multi-Reference UCCSD Variational Quantum Algorithm for Molecular Ground State Energies

Authors: Di Wu, C. L. Bai, H. Sagawa, H. Q. Zhang

Abstract: We implement the Multi-Reference Unitary Coupled Cluster Singles and Doubles (MR-UCCSD) model with a quantum circuit that conserves the particle number to study the ground state energies of LiH, BeH$_2$, and H$_6$. This approach simplifies the MR-UCCSD computation by integrating quantum computing techniques, and reduces its complexity. As a profit of the better MR states, our MR-UCCSD approach sat… ▽ More We implement the Multi-Reference Unitary Coupled Cluster Singles and Doubles (MR-UCCSD) model with a quantum circuit that conserves the particle number to study the ground state energies of LiH, BeH$_2$, and H$_6$. This approach simplifies the MR-UCCSD computation by integrating quantum computing techniques, and reduces its complexity. As a profit of the better MR states, our MR-UCCSD approach satisfies systematically the predefined errors below 10$^{-5}$ Hartree,which is the highest precision of single reference UCCSD approach, along the whole bond length with only hundreds of CNOT gates, and meets satisfactory the requirements of both computational precision and quantum resource reduction. △ Less

Submitted 14 April, 2025; v1 submitted 29 August, 2024; originally announced August 2024.

Comments: 6 pages, 3 figures

Quantum-enhanced rubidium atomic magnetometer based on Faraday rotation via 795-nm Stokes operator squeezed light

Authors: Lele Bai, Xin Wen, Yulin Yang, Lulu Zhang, Jun He, Yanhua Wang, Junmin Wang

Abstract: With the help of Stokes operator S2 squeezed state (also called polarization squeezed state (PSS)) of 795-nm light, rubidium-87 (87Rb) atomic magnetometer based on Faraday rotation has been implemented and characterized.The PSS of Stokes operator S2 of 795-nm light has been prepared by means of coherently combining the polarization coherent state (PCS) of a linearly p-polarized bright 795-nm light… ▽ More With the help of Stokes operator S2 squeezed state (also called polarization squeezed state (PSS)) of 795-nm light, rubidium-87 (87Rb) atomic magnetometer based on Faraday rotation has been implemented and characterized.The PSS of Stokes operator S2 of 795-nm light has been prepared by means of coherently combining the polarization coherent state (PCS) of a linearly p-polarized bright 795-nm light beam and a linearly s-polarized squeezed vacuum state (SVS) generated by a 397.5-nm ultraviolet laser pumped sub-threshold optical parametric oscillator (OPO) with a PPKTP bulk crystal inside the OPO cavity.PSS with a squeezing level of -3.7 has been achieved around the analysis frequency of 10 kHz. At different transitions of D1 line, various frequency detuning, and reasonable atomic vapor cells temperature, Faraday rotation has been measured and compared.To decrease absorption (scattering) losses and the back-action from atomic spin noise to the probe beams polarization noise for maintaining the quantum properties of PSS of Stokes operator S2 of 795-nm light, we had to run our magnetometer with 87Rb vapor cells temperature below 60, at which the PSS was almost destroyed.The sensitivities of magnetic field measurement were characterized via measuring signal-to-noise ratio of the alternating current (AC) calibrated magnetic field signal with a balanced polarimeter. Under the conditions of the atomic number density of 5.8*1010 /cm3 and the probe beam with a detuning of - 400 MHz relative to the 5S1/2 (Fg=2) - 5P1/2 (Fe=1) transition of 87Rb D1 line, a typical sensitivity of 19.5 pT/Hz1/2 has been achieved employing PSS of Stokes operator S2 as the probe, compared with a sensitivity of 28.3 pT/Hz1/2 using PCS as the probe.We preliminarily demonstrated that the quantum-enhanced sensitivity in a Faraday-rotation-based 87Rb atomic magnetometer with the help of PSS of 795-nm light. △ Less

Submitted 5 December, 2021; v1 submitted 30 November, 2021; originally announced December 2021.

Comments: 8 pages, 5 figures J. Opt. 23 (2021) 085202

Enhancement of spin noise spectroscopy of rubidium atomic ensemble by using of the polarization squeezed light

Authors: Lele Bai, Lulu Zhang, Yongbiao Yang, Rui Chang, Yao Qin, Jun He, Xin Wen, Junmin Wang

Abstract: We measured the spin noise spectroscopy (SNS) of rubidium atomic ensemble with two different atomic vapor cells (filled with the buffer gases or coated with paraffin film on the inner wall), and demonstrated the enhancement of signal to noise ratio (SNR) by using of the polarization squeezed state (PSS) of 795 nm light field with Stokes operator S2 squeezed. PSS is prepared by locking the relative… ▽ More We measured the spin noise spectroscopy (SNS) of rubidium atomic ensemble with two different atomic vapor cells (filled with the buffer gases or coated with paraffin film on the inner wall), and demonstrated the enhancement of signal to noise ratio (SNR) by using of the polarization squeezed state (PSS) of 795 nm light field with Stokes operator S2 squeezed. PSS is prepared by locking the relative phase between the squeezed vacuum state of light obtained by a sub-threshold optical parametric oscillator and the orthogonal polarized local oscillator beam by means of the quantum noise lock. Under the same conditions, PSS can be employed not only to improve SNR, but also to keep the full width at half maximum (FWHM) of SNS unchanged, compared with the case of using polarization coherent state (PCS), and the enhancement of SNR is positively correlated with the squeezing level of PSS. With the increase of probe laser power and atomic number density, the SNR and FWHM of SNS will increase correspondingly. With the help of PSS of Stokes operator S2, quantum enhancement of both SNR and FWHM of SNS signal has been demonstrated by controlling optical power of the S2 polarization squeezed light beam or atomic number density in our experiments. △ Less

Submitted 18 November, 2021; originally announced November 2021.

Laser Intensity Noise Suppression for Preparing Audio-Frequency 795 nm Squeezed Vacuum State of Light at Rubidium D1 Line

Authors: Lele Bai, Xin Wen, Yulin Yang, Jun He, Junmin Wang

Abstract: Laser intensity noise suppression has essential effects on preparation and characterization of the audio-frequency squeezed vacuum state of light based on a sub-threshold optical parametric oscillator (OPO).We have implemented two feedback loops by using relevant acousto-optical modulators (AOM) to stabilize the intensity of 795-nm near infrared (NIR) fundamental laser and 397.5-nm ultraviolet (UV… ▽ More Laser intensity noise suppression has essential effects on preparation and characterization of the audio-frequency squeezed vacuum state of light based on a sub-threshold optical parametric oscillator (OPO).We have implemented two feedback loops by using relevant acousto-optical modulators (AOM) to stabilize the intensity of 795-nm near infrared (NIR) fundamental laser and 397.5-nm ultraviolet (UV) laser generated by cavity-enhanced frequency doubling.Typical peak-to-peak laser intensity fluctuation with a bandwidth of $\sim10$ kHz in a half hour has been improved from $\pm7.45$$\%$ to $\pm0.06$$\%$ for 795-nm NIR laser beam, and from $\pm9.04$$\%$ to $\pm0.05$$\%$ for 397.5-nm UV laser beam, respectively. The squeezing level of the squeezed vacuum state at 795 nm prepared by the sub-threshold OPO with a PPKTP crystal has been improved from -3.3 to -4.0 dB around 3$\sim$9 kHz of audio analysis frequency range. △ Less

Submitted 10 March, 2020; originally announced March 2020.

Comments: 5 pages, 4 figures

Journal ref: Applied Sciences, Vol.10, No. 4 (2020) 1415