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Transformer-Based Neural Quantum Digital Twins for Many-Body Quantum Simulation and Optimal Annealing Schedule Design

Jianlong Lu, Hanqiu Peng, Ying Chen

TL;DR

The paper tackles the challenge of designing high-fidelity, instance-specific annealing schedules for quantum annealers by reconstructing the full spectral evolution along the anneal path. It introduces Tx-NQDT, a graph-aware Transformer-based digital twin that predicts ground- and first-excited-state energies and coupling matrix elements along s, using Brauer deflation for excited states and transfer learning to propagate across the path. These spectral predictions feed a first-order adiabatic perturbation theory (FOAPT)–based control functional to generate adaptive, hardware-constrained schedules that slow near small gaps. End-to-end validation on D-Wave hardware shows substantial performance gains over linear schedules across multiple problem sizes and difficulty levels, confirming the practicality of spectrum-aware, data-driven control in noisy, real-world devices. The work highlights a scalable, graph-aware neural surrogate for adiabatic dynamics that can guide efficient quantum annealing and motivate future extensions to broader Hamiltonians and uncertainty-aware control.

Abstract

We introduce Transformer-based Neural Quantum Digital Twins (Tx-NQDTs) to simulate full adiabatic dynamics of many-body quantum systems, including ground and low-lying excited states, at low computational cost. Tx-NQDTs employ a graph-informed Transformer neural network trained to predict spectral properties (energy levels and gap locations) needed for annealing schedule design. We integrate these predictions with an adaptive annealing schedule design based on first-order adiabatic perturbation theory (FOAPT), which slows the evolution near predicted small gaps to maintain adiabaticity. Experiments on a D-Wave quantum annealer (N = 10, 15, 20 qubits, 12 control segments) show that Tx-NQDT-informed schedules significantly improve success probabilities despite hardware noise and calibration drift. The optimized schedules achieve success probabilities 2.2-11.7 percentage points higher than the default linear schedule, outperforming the D-Wave baseline in 44 of 60 cases. These results demonstrate a practical, data-driven route to improved quantum annealing performance on real hardware.

Transformer-Based Neural Quantum Digital Twins for Many-Body Quantum Simulation and Optimal Annealing Schedule Design

TL;DR

The paper tackles the challenge of designing high-fidelity, instance-specific annealing schedules for quantum annealers by reconstructing the full spectral evolution along the anneal path. It introduces Tx-NQDT, a graph-aware Transformer-based digital twin that predicts ground- and first-excited-state energies and coupling matrix elements along s, using Brauer deflation for excited states and transfer learning to propagate across the path. These spectral predictions feed a first-order adiabatic perturbation theory (FOAPT)–based control functional to generate adaptive, hardware-constrained schedules that slow near small gaps. End-to-end validation on D-Wave hardware shows substantial performance gains over linear schedules across multiple problem sizes and difficulty levels, confirming the practicality of spectrum-aware, data-driven control in noisy, real-world devices. The work highlights a scalable, graph-aware neural surrogate for adiabatic dynamics that can guide efficient quantum annealing and motivate future extensions to broader Hamiltonians and uncertainty-aware control.

Abstract

We introduce Transformer-based Neural Quantum Digital Twins (Tx-NQDTs) to simulate full adiabatic dynamics of many-body quantum systems, including ground and low-lying excited states, at low computational cost. Tx-NQDTs employ a graph-informed Transformer neural network trained to predict spectral properties (energy levels and gap locations) needed for annealing schedule design. We integrate these predictions with an adaptive annealing schedule design based on first-order adiabatic perturbation theory (FOAPT), which slows the evolution near predicted small gaps to maintain adiabaticity. Experiments on a D-Wave quantum annealer (N = 10, 15, 20 qubits, 12 control segments) show that Tx-NQDT-informed schedules significantly improve success probabilities despite hardware noise and calibration drift. The optimized schedules achieve success probabilities 2.2-11.7 percentage points higher than the default linear schedule, outperforming the D-Wave baseline in 44 of 60 cases. These results demonstrate a practical, data-driven route to improved quantum annealing performance on real hardware.

Paper Structure

This paper contains 53 sections, 2 theorems, 90 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. QUBO and Time-Dependent Hamiltonians
  4. Transformer-based Neural Quantum Digital Twins
  5. Excited–State Modeling with Brauer Deflation and Transfer Learning
  6. Instantaneous Energy Gap and Nonlinear Annealing Schedules
  7. Simulation Experiments
  8. Benchmark: Transverse-Field Ising Model (TFIM)
  9. Generalization: Random Hamiltonian Models (RHM)
  10. Training Protocol and Implementation Details
  11. Spectral Accuracy and Scaling Results
  12. D-Wave Optimization Experiments
  13. Problem instances and hardware embedding.
  14. Instance difficulty classification.
  15. Construction of hardware-compatible schedules.
  16. ...and 38 more sections

Key Result

Theorem 1

Let $H$ be an $n \times n$ Hermitian matrix with eigenvalues $\lambda_1 \leq \dots \leq \lambda_n$, and let $\mathbf{u}_i$ be the eigenvector corresponding to $\lambda_i$. For any $n$-dimensional vector $\mathbf{v}$, the matrix $\tilde{H} = H + \mathbf{u}_i \mathbf{v}^{\dagger}$ has eigenvalues $\la

Figures (10)

  • Figure 1: Tx-NQDT pipeline with FOAPT-guided schedule construction.
  • Figure 2: D-Wave hardware annealing coefficients $A(s)$ (driver) and $B(s)$ (problem) as functions of the normalized anneal parameter $s$. These curves are the schedule inputs used in our Tx-NQDT experiments.
  • Figure 3: Exact vs. learned spectra for representative easy and hard instances at system sizes $N=6,10,15$, and learned spectra at $N=20$.
  • Figure 4: Runtime scaling on Apple M2. Mean epoch wall-clock time versus system size $N$ at fixed $s=0$ (blue: mean over epochs $6-25$; error bars: min/max over the same window). The dashed line is a least-squares fit $t_{\rm epoch}(N)=t_0+aN+bN^2$.
  • Figure 5: Mean success probability for linear versus optimized schedules across sizes ($N=10,15,20$) and difficulty subsets (easy/hard).
  • ...and 5 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Corollary 1
  • proof
  • proof