Quantum Simulation Efficiency Gains with Correlated Electronic System Analysis.

Researchers achieve substantial gains in calculating the properties of correlated electronic systems using a combination of classical methods and partial shadow tomography. This approach reduces computational demands by almost two orders of magnitude and exhibits increased resilience to noise, enabling accurate modelling of complex materials like nickel oxide and its spin gap.

The accurate modelling of electronic structure represents a persistent challenge in computational chemistry and materials science, demanding computational resources that scale rapidly with system complexity. Researchers are now investigating quantum computation as a potential means to circumvent these limitations, yet current implementations require substantial optimisation to deliver practical advantage. A team comprising Connor Lenihan, Oliver J Backhouse, and M J Bhaseen from King’s College London, alongside Tom W A Montgomery and Phalgun Lolur from Capgemini Quantum Lab, detail a novel approach in their paper, “Excitation Amplitude Sampling for Low Variance Electronic Structure on Quantum Computers”. Their work combines classical computational heuristics with a quantum technique called partial shadow tomography, enabling more efficient extraction of information from complex quantum systems encoded on near-term quantum devices.

The resulting protocols demonstrably reduce the number of quantum measurements, or ‘shots’, required to achieve a given level of accuracy in energy estimation, while also exhibiting resilience to the noise inherent in current quantum hardware. Furthermore, the team extends this methodology to calculate properties beyond energy, including the volume-dependence of the spin gap in Nickel Oxide, demonstrating potential application to realistic, correlated materials.
Determining electronic energy in correlated quantum systems presents a considerable computational challenge, restricting progress in materials modelling and chemical simulations.

Conventional ab initio methods, which derive results from fundamental principles rather than empirical data, demand substantial computational resources and frequently struggle with the complexity of many-body interactions – the interactions between multiple electrons within a material. Researchers now present a methodology that substantially reduces these requirements, leveraging a combination of classical heuristics and partial shadow tomography to achieve a near two-order-of-magnitude decrease in the number of quantum shots – individual executions of a quantum circuit – needed to attain a specified statistical error in energy estimation. This innovative approach promises to accelerate materials discovery and refine chemical simulations by making previously intractable calculations feasible on near-term quantum devices.

The developed methodology exhibits a favourable linear scaling relationship with system size, indicating its potential applicability to increasingly complex materials and surpassing the limitations of many quantum algorithms which suffer from exponential scaling. Exponential scaling means computational effort increases dramatically with even small increases in system size, quickly becoming impossible. This allows researchers to model larger and more realistic systems, opening doors to the investigation of materials with intricate electronic structures and emergent properties – properties that arise from the collective behaviour of many interacting particles. Crucially, the developed estimators demonstrate a high degree of resilience to noise – unwanted disturbances that degrade the accuracy of quantum computations – tolerating up to an order of magnitude more noise than conventional techniques and mitigating the impact of imperfections in current quantum hardware.

Beyond simply estimating ground state energies – the lowest possible energy state of a quantum system – the methodology extends to the calculation of more complex properties, enabling a more comprehensive understanding of material behaviour and chemical reactivity. Researchers successfully map the problem onto a coupled cluster method, a technique used to approximate the solution to the Schrödinger equation for many-body systems. The Schrödinger equation describes the evolution of quantum systems over time, but finding exact solutions is often impossible for complex systems, necessitating approximation methods like coupled cluster theory.

The integration of classical heuristics with quantum algorithms is a key innovation. Classical heuristics, essentially educated guesses or rules of thumb, can be used to guide the quantum computations, reducing the number of required quantum gates – the fundamental building blocks of quantum circuits – and minimizing the impact of noise. This combination of classical and quantum techniques results in a more efficient and accurate methodology for materials modelling and chemical simulations.

The successful application of this methodology to nickel oxide demonstrates its potential to address a wide range of challenging problems in materials science and chemistry. Nickel oxide is a complex material with strong electron correlations, making it a difficult test case for many computational methods. The ability to accurately model the volume-dependence of its spin gap – a range of energies where no electron transitions are allowed – validates the methodology’s ability to handle strong correlations and provides valuable insights into the material’s electronic structure. This success opens doors to the investigation of other complex materials with intriguing properties, such as high-temperature superconductors and topological insulators – materials that exhibit unusual electronic properties due to their unique surface states.

The research team plans to further refine the methodology and explore its potential for applications in other areas of materials science and chemistry. They are also working to develop new algorithms that can take advantage of the unique capabilities of quantum computers. This work represents a significant step towards realizing the full potential of quantum computing for scientific discovery.