Quantum Processor and 152,064 Classical Nodes Compute Electronic Structure at Full Scale

Understanding how quantum and classical computers can work together is crucial for unlocking the full potential of quantum computation, and recent experiments exploring this synergy have been limited in scope. Tomonori Shirakawa from RIKEN’s Center for Computational Science, Javier Robledo-Moreno and Toshinari Itoko from IBM Quantum, along with Vinay Tripathi, Kento Ueda, and Yukio Kawashima, now demonstrate a significant advance by performing the largest ever computation of electronic structure using a combined quantum and classical approach. The team designed a closed-loop workflow connecting an IBM Heron quantum processor with the entire Fugaku supercomputer, comprising 152,064 nodes, to model complex electronic structures beyond the capabilities of traditional methods. This achievement not only pushes the boundaries of quantum-classical integration, but also showcases unprecedented orchestration of computational resources at a scale currently unmatched by any existing classical supercomputer, paving the way for more accurate and efficient simulations of complex materials and molecules.

Symmetry-Adapted Compilation Reduces Quantum Circuit Depth

The research presents a new method for optimising quantum circuits, reducing their complexity without sacrificing accuracy. Scientists developed ‘SYMPAQ’, which leverages inherent symmetries within many quantum algorithms, allowing for a more efficient representation of quantum states and operations and significantly reducing the number of quantum gates required. SYMPAQ demonstrably reduces circuit depth when applied to benchmark quantum algorithms, including Variational Quantum Eigensolver and Quantum Approximate Optimisation Algorithm. Results indicate an average reduction of 30% in circuit depth for Variational Quantum Eigensolver and 20% for Quantum Approximate Optimisation Algorithm, compared to standard compilation techniques, without compromising accuracy.

The method’s effectiveness has been validated through simulations on various quantum hardware architectures, including those with limited connectivity and high error rates. Furthermore, the team introduced a novel algorithm for mapping logical qubits onto physical qubits, considering both the symmetries of the problem and the constraints of the hardware. This mapping algorithm, integrated within SYMPAQ, further enhances the performance and scalability of the optimised circuits, establishing a pathway towards more practical and efficient quantum computation.

Sample-Based Quantum Diagonalization for Molecules

This research details advancements in simulating molecular behaviour using quantum computers, pushing the boundaries of current technology. The team combines Sample-Based Quantum Diagonalization, Density Matrix Embedding Theory, and orbital rotation to accurately solve the Schrödinger equation for complex molecules, implementing these methods using variational quantum algorithms. Researchers have significantly improved Sample-Based Quantum Diagonalization, enhancing its ability to represent complex wavefunctions and optimising algorithms used to find the best circuit parameters. Integration with Density Matrix Embedding Theory reduces the computational cost of simulating larger molecules, while orbital rotation techniques further improve accuracy and efficiency.

A significant focus is placed on mitigating the effects of noise and errors inherent in quantum hardware, utilising techniques like dynamical decoupling and virtual Z gates. Symmetry verification ensures calculated results are consistent with known physical principles, relying on the Qiskit software framework and a custom library for computation. The code and data are openly available for reproducibility and collaboration.

Largest Quantum Electronic Structure Calculation Achieved

Scientists achieved a significant breakthrough in quantum-classical computing by performing the largest electronic structure calculation to date, involving a 72-qubit operator derived from iron-sulfur clusters. This work demonstrates a closed-loop workflow integrating a quantum processor with 152,064 classical nodes of the Fugaku supercomputer, enabling the approximation of electronic structures beyond the reach of traditional diagonalization methods. These results surpass previous state-of-the-art quantum computations, exceeding the accuracy of Sample-based Quantum Diagonalization. The team’s approach builds upon Sample-based Quantum Diagonalization, utilising a Local Unitary Cluster Jastrow circuit and a differential evolution optimizer to efficiently orchestrate quantum and classical resources. To mitigate quantum noise, scientists implemented a self-consistent configuration recovery technique, probabilistically recovering noiseless samples from measured data and building a more accurate subspace for calculations. This integrated approach represents a substantial advancement in the ability to model complex chemical systems with unprecedented scale and accuracy.

Quantum Chemistry via Hybrid Quantum-Classical Computation

This research demonstrates a significant advancement in hybrid quantum-classical computing, successfully integrating a quantum processor with a large-scale classical supercomputer. Scientists achieved a substantial computational feat by approximating the electronic structure of complex iron sulfide clusters, exceeding the capabilities of traditional classical methods. The results show energy calculations for iron sulfide clusters with an error of approximately 0. 1 Eh from state-of-the-art DMRG calculations, demonstrating the potential of this combined approach to extract meaningful signals from current quantum devices.

Furthermore, the improved workflow, featuring a quantum-classical feedback loop, allows for the efficient carryover of configurations, enhancing computational performance. While the work focuses on iron sulfide clusters, the methods developed are broadly applicable to a wide range of electronic structure problems in quantum chemistry. Future research will likely focus on improving the robustness of the quantum hardware and optimising the workflow for larger, more complex systems.