Quantum Simulations of Chemistry in First Quantization with any Basis Set

Abstract

Quantum computation of the energy of molecules and materials is one of the most promising applications of fault-tolerant quantum computers. Practical applications require development of quantum algorithms with reduced resource requirements. Previous work has mainly focused on quantum algorithms where the Hamiltonian is represented in second quantization with compact basis sets while existing methods in first quantization are limited to a grid-based basis. In this work, we present a new method to solve the generic ground-state chemistry problem in first quantization using any basis set. We achieve asymptotic speedup in Toffoli count for molecular orbitals, and orders of magnitude improvement using dual plane waves as compared to the second quantization counterparts. In some instances, our approach provides similar or even lower resources compared to previous first quantization plane wave algorithms that, unlike our approach, avoids the loading of the classical data. The developed methodology can be applied to variety of applications, where the matrix elements of a first quantized Hamiltonian lack simple circuit representation.

Added more detailed comparison with previous pw algo

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• The Electronic Structure of the Hydrogen Molecule: A Tutorial Exercise in Classical and Quantum Computation
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• Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations
• Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer
• Quantum-inspired dynamical models on quantum and classical annealers
• Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme
• Benchmarking Quantum Simulation of Chemical Hamiltonians using the Sorted-List Encoding
• Quantum Simulation of Nuclear Dynamics in First Quantization
• Quantum-Classical Computing for Time-Dependent Ion-Atom Collision Dynamics: Applications to Charge Transfer Cross Section Simulations