Generative quantum eigensolver learns from hardware at 70 qubits

Kunal Kumar of IBM Quantum, alongside colleagues from Mitsubishi Chemical Corporation and Keio University, has demonstrated a generative quantum eigensolver trained with quantum hardware at a scale of 70 qubits. The team trained policies to generate circuits for sample-based quantum diagonalization, initially using simulation before incorporating the IBM Heron processor ibm_kobe into the training loop.

This approach yielded circuits for organotin hydroxides, models for materials used in extreme-ultraviolet lithography, that achieve accuracy within 15 mHa of a density-matrix renormalization group reference in 27 of 28 runs. At 56-70 qubits, these circuits require 34 to 72 times fewer two-qubit gates than alternative methods.

Hardware-Trained GQE for 70-Qubit Quantum Diagonalization

This difference in computational cost occurred while training generative quantum eigensolver policies, a technique where quantum hardware provides feedback to refine circuit generators beyond the capabilities of classical simulation. The training process involved analyzing the energy, raw-shot counts and excitation histograms generated by the. Researchers used a sample-based quantum diagonalization approach, employing an ansatz circuit U(θ) acting on $2n_o$ qubits, where $n_o$ represents the number of active spatial orbitals.

This circuit, when applied to the Hartree-Fock state, produces the state |ψ_θ⟩, which is then used to calculate the energy of the system. The resulting energy, alongside the shot and excitation histograms, forms the basis for refining the circuit parameters.

Sample-Based Quantum Diagonalization of Organotin Hydroxides

The generative quantum eigensolver (GQE) policies used in this work use transformers conditioned on molecular descriptors to create state-preparation circuits for sample-based quantum diagonalization, a technique extending beyond the capabilities of exact classical simulation. This focus allowed for the application of policies trained on transition-metal complexes without retraining, demonstrating a degree of transfer learning across chemical systems.

The resulting circuits, tested from 32 to 70 qubits, were evaluated against a density-matrix renormalization group (DMRG) reference, with 27 of 28 runs at 46-70 qubits falling within 15 milli-Hartree of the DMRG benchmark, achieving a median accuracy of 4.5 milli-Hartree.

Transformer Policies Conditioned on Molecular Descriptors

This approach allows for the creation of circuits tailored to specific molecular properties, streamlining the process of quantum state preparation for sample-based quantum diagonalization. The system’s design incorporates a problem-specific operator pool from which these gate tokens are selected, enabling a focused search for efficient circuit configurations. During training, a reward penalty was implemented to prevent the circuits from collapsing into configurations that solely sample the Hartree-Fock determinant, ensuring exploration of a wider range of potential solutions.

This hardware training phase, conducted with the IBM Heron processor ibm_kobe, involved 150 iterations at both 46 and 70 qubits, using feedback from the quantum hardware to refine the generative policies. The use of the ibm_kobe processor is notable as it represents a step towards using real quantum devices for algorithm development, moving beyond purely simulated environments.

Application of these trained policies to Sn(OH)₃-Me and its hydrates, minimal models of organotin photoresists, demonstrated their versatility without requiring further retraining. This level of agreement suggests the policies effectively capture the essential quantum features of these molecules, and in all eight runs, the trained policy outperformed an untrained control, confirming the benefit of the hardware-informed training process. The results of 43 trained runs showed 13 within 1 mHa and 42 within 15 mHa against DMRG, demonstrating the potential for high-precision quantum calculations on these systems.

Training GQE Policies with Noiseless Simulation & IBM Heron

Training on a noiseless simulator provided a foundation for subsequent hardware-based learning, a strategy designed to stabilize performance under the constraints of real quantum devices. The generative quantum eigensolver policies were initially refined using simulations of molecules up to 32 qubits, before transitioning to training with the IBM Heron processor ibm_kobe. This two-stage curriculum used the strengths of both approaches, allowing the policies to learn from exact calculations initially and then adapt to the noise inherent in quantum hardware.

A classical CCSD(T) reference energy was incorporated into the training process through an admission gate and two auxiliary reward terms, providing a benchmark for evaluating circuit performance. This approach allowed the system to score circuits based on their performance under device noise and transpilation constraints, effectively teaching the policies to generate circuits robust to hardware limitations.

The resulting policies were then applied without retraining to organotin hydroxides, specifically models of organotin photoresists, ranging from 32 to 70 qubits. After a single round of hardware sampling, followed by classical processing, the policies achieved a median error of 2.8 mHa against density-matrix renormalization group (DMRG) results across 43 trained runs. 42 fell within 15 mHa, demonstrating the potential for accurate energy estimations even with limited hardware feedback.

Hardware Training & Reward Penalty for Circuit Diversity

The use of a reward penalty during training was important for preventing the generative quantum eigensolver from collapsing into circuits that solely sampled the Hartree-Fock determinant. However, the tuned reward exhibited a less robust tail, with three of its best circuits exceeding 30 mHa in error, a threshold none of the Hartree-Fock penalty circuits surpassed. This difference in robustness led the team to prioritize the simpler Hartree-Fock penalty as the primary configuration for these initial single-seed runs.

This work demonstrates the feasibility of training a circuit generator with quantum hardware integrated into the learning loop at the 70-qubit scale. The researchers acknowledge that the tuned reward did not demonstrably improve hardware results, making the Hartree-Fock penalty the main configuration due to its consistent performance. The ability to train policies in this manner opens avenues for using quantum hardware’s unique feedback capabilities beyond the limitations of classical simulation.

Performance of Trained Circuits vs. DMRG Reference

The median error across these successful runs was 4.5 mHa, demonstrating the policy’s ability to approximate molecular energies with increasing computational scale. This reduction in gate complexity is particularly important as quantum hardware struggles with the errors that accumulate with each additional gate operation.

Analysis of the generated circuits also revealed differences in circuit depth, even when achieving comparable accuracy to LUCJ. The algorithm successfully applied policies, trained initially on transition-metal complexes, without retraining to Sn(OH)₃-Me and its hydrates, molecules serving as minimal models for organotin photoresists used in extreme-ultraviolet lithography, across qubit counts from 32 to 70.

Scaling Quantum Chemistry Beyond Classical Limits

The ability to use quantum hardware for algorithm training extends beyond the limits of classical simulation, as demonstrated by recent work achieving results at 70 qubits. This scale represents an advancement in applying generative quantum eigensolvers (GQE) to complex chemical systems, moving beyond the capabilities of traditional computational methods. By actively discouraging this behavior, the researchers improved the robustness of the generated circuits, allowing for more reliable and accurate energy estimations.

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