Quantum Diagonalization Converges on Cuprate Chains with 2 to 6 Plaquettes, Enabling Molecular Simulation
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The challenge of simulating complex molecular systems represents a major hurdle in materials science and quantum chemistry, and researchers continually seek more efficient computational methods. L. Andrew Wray, Cheng-Ju Lin, and Vincent Su, alongside Hrant Gharibyan from BlueQubit Inc., investigated improvements to a technique called sample-based diagonalization, a hybrid quantum-classical algorithm designed for use on emerging quantum computers. Their work focuses on optimising this method for modelling cuprate chains, materials crucial to understanding high-temperature superconductivity, and reveals that enhanced connectivity, higher-order expansions, and alternative molecular orbital bases significantly improve computational convergence. Notably, the team discovered that even the presence of noise on a real quantum computer, specifically a Quantinuum H2 trapped ion device, can surprisingly enhance the accuracy of energy calculations, offering a potentially valuable pathway for overcoming limitations in current quantum hardware. Scientists investigated the scaling of a sample-based quantum diagonalization (SQD) algorithm, a hybrid quantum-classical method for molecular simulation, using copper oxide plaquette chains ranging from 2 to 6 units in length. The research demonstrates that enabling all-to-all connectivity, increasing the expansion order of the SQD algorithm, and employing a non-Hartree-Fock molecular orbital basis all contribute to overcoming sampling bottlenecks. A minimal molecular orbital basis, consisting of two orbitals per copper oxide unit, was used to model the cuprate chain, resulting in a ground state charge density distribution of approximately 1. 4 for Cu 3dx2−y2 orbitals, consistent with expectations for Mott insulating cuprate compounds.
Cuprate Chain Simulation Using Quantum Algorithms This research details a comprehensive investigation into simulating cuprate chains, materials with intriguing electronic properties, using quantum computing techniques. Scientists meticulously constructed a Hamiltonian, a mathematical description of the system’s energy, starting with a tight-binding model and refining it using first-principles calculations. They focused on a minimal active space, selecting only the most important orbitals to reduce computational demands, and mapped the Hamiltonian to a chain basis for easier analysis. Parameters were carefully tuned to match experimental data for SrCuO2, a specific cuprate material, ensuring the model accurately reflects real-world behavior.
The team employed a modified Hartree-Fock (HF+) basis, derived from the single-particle eigenstates of the kinetic Hamiltonian, to better capture mean-field effects, improving the accuracy of the simulations. This basis set was constructed by mixing kinetic basis states using a carefully designed mixing matrix. Scientists then explored how to efficiently sample determinants, representing electronic configurations, from the quantum simulations, averaging over multiple batches to achieve more accurate results. The goal was to reach chemical accuracy, a level of precision equivalent to 1 kcal/mol, and they established convergence criteria based on the stability of the calculated energy. Analysis revealed that the convergence speed and accuracy were influenced by the choice of basis set, the expansion order of the SQD algorithm, and the length of the simulated chain.
The team measured the fraction of the exact ground state projected onto the SQD basis as a function of the number of quantum measurements, or “shots”, demonstrating the algorithm’s ability to converge on larger systems. These findings highlight the importance of accurately representing entanglement within the chain, as the lowest energy spin excitation falls between 0. 1 to 0. 2 eV, emphasizing the need for a robust numerical model to capture these subtle effects.
Scaling Sampled Quantum Diagonalization for Cuprates Scientists demonstrated significant advances in sample-based diagonalization (SQD), a promising algorithm for simulating molecular systems on emerging quantum hardware. They explored scaling the algorithm for cuprate chains, ranging from two to six molecular units, and identified key factors influencing its convergence. Specifically, enabling full connectivity between quantum bits, increasing the order of expansion within the algorithm, and employing alternative molecular orbital bases all contribute to overcoming computational bottlenecks. The findings reveal that achieving efficient SQD sampling does not follow a simple polynomial scaling order, suggesting that representing complex many-body ground states poses inherent challenges for classical computers. Importantly, the researchers found that noise present on an actual quantum device, the Quantinuum H2 trapped ion system, surprisingly improved energy convergence beyond expectations from noise-free simulations. This suggests that error mitigation strategies can complement quantum sampling techniques. By demonstrating competitive computational scaling for a highly entangled cuprate system, this work establishes a pathway toward applying SQD to larger molecules and systems exhibiting strong electronic correlations. The authors acknowledge that the favorable scaling of SQD sampling time may eventually break down as system size increases, requiring higher excitation orders, similar to conventional quantum chemistry methods.
Scaling Sample Diagonalization for Molecular Systems This research demonstrates significant advances in sample-based diagonalization (SQD), a promising algorithm for simulating molecular systems on emerging quantum hardware.
The team successfully explored scaling the algorithm for cuprate chains, ranging from two to six molecular units, and identified key factors influencing its convergence. Specifically, enabling full connectivity between quantum bits, increasing the order of expansion within the algorithm, and employing alternative molecular orbital bases all contribute to overcoming computational bottlenecks. The findings reveal that achieving efficient SQD sampling does not follow a simple polynomial scaling order, suggesting that representing complex many-body ground states poses inherent challenges for classical computers. Importantly, the researchers found that noise present on an actual quantum device, the Quantinuum H2 trapped ion system, surprisingly improved energy convergence beyond expectations from noise-free simulations. This suggests that error mitigation strategies can complement quantum sampling techniques. By demonstrating competitive computational scaling for a highly entangled cuprate system, this work establishes a pathway toward applying SQD to larger molecules and systems exhibiting strong electronic correlations. Future research will likely focus on optimizing the balance between connectivity, fidelity, and clock speed within quantum computers to maximize the accuracy and efficiency of SQD. Further exploration of how noise can be harnessed to improve sampling is also a promising avenue for investigation. 👉 More information 🗞 Convergence of sample-based quantum diagonalization on a variable-length cuprate chain 🧠 ArXiv: https://arxiv.org/abs/2512.04962 Tags: