Quantum Algorithm Simulates Molecular Reactions with Tenfold Cost Reduction

Researchers are tackling the complex challenge of simulating molecular dynamics with a new quantum algorithm. Matthew Pocrnic and Ignacio Loaiza, both from Xanadu, University of Toronto, alongside Juan Miguel Arrazola from Xanadu, and Nathan Wiebe working with colleagues at University of Toronto, Pacific Northwest National Laboratory, and the Canadian Institute for Advanced Research, detail a method for efficiently simulating pre-Born-Oppenheimer dynamics on a quantum computer. Their work presents a best-in-class approach to block-encoding the molecular Hamiltonian, achieving a significant reduction, over an order of magnitude, in computational costs compared to previous methods, ultimately lowering the resource requirements for simulating crucial photochemical reactions and establishing foundational algorithmic primitives for future quantum chemistry applications.

Scientists present a quantum algorithm for direct first-principles simulation of electron-nuclear dynamics on a first-quantized real-space grid, achieving best-in-class efficiency for block-encoding the pre-Born-Oppenheimer molecular Hamiltonian. It harnesses the linear scaling of swap networks for implementing the quadratic number of particle interactions inherent in molecular dynamics simulations. A novel alternating sign implementation of the Coulomb interaction exploits highly optimised arithmetic routines, approximating 1/r with an accuracy scaling as O(1/M), where M represents the number of values used in an auxiliary register. Researchers benchmark their approach for a series of scientifically and industrially relevant chemical reactions, demonstrating over an order-of-magnitude reduction in costs compared to previous methods. The study’s algorithm is designed for first-principles simulations, bypassing the need for pre-calculated electronic structure models when constructing the Hamiltonian, which is advantageous for systems where the Born-Oppenheimer approximation breaks down. By directly simulating electron-nuclear dynamics, the work provides a foundational set of algorithmic primitives applicable to a wider range of quantum algorithms. The research demonstrates a Toffoli cost of 8.7 × 109 per femtosecond for simulating the NH3 + BF3 reaction, utilising 1362 logical qubits encompassing both the system and ancilla qubits. This represents over an order-of-magnitude reduction in computational cost compared to previously established state-of-the-art methods for the same reaction. The algorithm encodes the amplitudes of the many-body wavefunction directly onto a Cartesian grid, treating both electrons and nuclei equally without relying on periodic boundary conditions, making it well-suited for organic and photo-organic systems. As hardware developments bring fault-tolerant quantum computing closer to reality, the need for expanding the pool of useful applications of quantum computers intensifies, with quantum chemistry offering a rich landscape of industrially relevant problems. However, algorithmic development has overwhelmingly focused on solving the electronic structure problem within the Born-Oppenheimer approximation, with limited attention given to quantum algorithms for dynamical problems. Cases where the Born-Oppenheimer approximation breaks down are pervasive in chemistry, particularly in photochemistry and reactions involving highly reactive radical species, where multiple electronic states are closely coupled and non-adiabatic effects become dominant. Simulating pre-Born-Oppenheimer chemistry classically is a formidable challenge, resulting in a wide array of approximations that trade accuracy for computational efficiency. Despite the successes of many methods, no single, efficient classical method exists that is applicable to general systems, potentially mishandling critical quantum phenomena such as electronic decoherence and zero-point leakage. Exact classical methods suffer from the curse of dimensionality, exhibiting exponential cost scaling with the number of particles, making comprehensive classical methods computationally intractable for all but the smallest systems. Quantum algorithms that go beyond the Born-Oppenheimer approximation have been proposed, such as the simulation of vibronic Hamiltonians, but these require prior knowledge of the relevant chemical space and rely on complex fitting procedures. First-principles simulations of molecular dynamics bypass the need for electronic structure calculations when building a model Hamiltonian, as presented in a previous work which provided the first full resource estimates for such simulations using a plane-wave basis. While attractive for periodic systems, this approach has drawbacks, including resource requirements beyond the reach of early fault-tolerant quantum computers and an ill-suited basis for non-periodic chemistry, especially for systems with a non-neutral electric charge. This work presents a first-principles algorithm for simulating chemical dynamics on a first-quantized real-space grid, treating electrons and nuclei on equal footing. The amplitudes of the many-body wavefunction are encoded in a Cartesian grid, while the electrostatic Coulomb interaction is directly implemented in Cartesian coordinates, ideal for organic and photo-organic systems. A key technical contribution is a “swap network” block-encoding architecture, which generalizes the “swap up” technique, allowing recursive building of block-encodings of multi-particle operators with linear complexity in the number of particles. Specifically, the algorithm evaluates all O(η2) pairwise electrostatic interactions with only O(η) cost and reduces the required quantum Fourier transform (QFT) applications for kinetic terms. To address the 1/r Coulomb bottleneck, an efficient linear combination of unitaries (LCU)-based approach utilising an alternating sign technique for block-encoding diagonal operators is implemented, bypassing the need for costly evaluation of inverse functions. Spectral shifting and saturation techniques further minimise the 1-norm, achieving over an order-of-magnitude reduction in Toffoli counts for the NH3 + BF3 reaction compared to previous benchmarks, while maintaining a small ancilla footprint. Overall, these results bring the first-principles simulation of organic chemistry closer to the reach of first-generation fault-tolerant quantum computers. The relentless pursuit of simulating molecular dynamics with ever-increasing accuracy has long been hampered by computational bottlenecks, but this algorithm represents a significant step forward by fundamentally altering the scaling of these calculations. For decades, modelling chemical reactions at a fundamental level demanded resources that grew exponentially with system size, whereas this work demonstrates a pathway towards linear scaling, potentially unlocking simulations of far more complex and realistic systems. The implications extend beyond academic chemistry, with accurate modelling of photochemical reactions vital for designing more efficient solar cells, developing novel catalysts, and understanding atmospheric processes. However, it is important to acknowledge that this is still a computational algorithm, and the promise of practical quantum devices remains some distance away. Error correction, and the associated overhead, remains a formidable challenge, and future work will focus on translating these algorithmic gains into demonstrable advantages on actual quantum computers. The true test will be whether this algorithm can bridge the gap between theoretical possibility and practical utility.