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Chemical reaction simulator on quantum computers by first quantization—Basic treatment: Theoretical

Tatsuya Tomaru, Hideo Takahashi, Toshiyuki Hirano, Saisei Tahara, Fumitoshi Sato

Published Dec 1, 2024• 2 citations
Publisher

Abstract

Quantum computers can potentially simulate quantum-mechanical phenomena, so chemical reactions are a potential application of them. In particular, the time evolution of the wavefunctions should be simulated because chemical reactions are accompanied by structural changes. In this study, to pave the way to achieving such wavefunction simulations, we decompose chemical reactions into their main parts and comprehensively show the minimum essential circuits for simulating each part. An antisymmetrized initial state is constructed using ancillae. Chemical reactions should be simulated in two different ways, where the difference is whether the ancillae are released or not. When they are released, the whole electronic system is simulated. When they are not released, orbital information is obtained. These ways are hence complementary.

DOI
10.1063/5.0239980

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Quantum computers can potentially simulate quantum-mechanical phenomena, so chemical reactions are a potential application of them. In particular, the time evolution of the wavefunctions should be simulated because chemical reactions are accompanied by structural changes. In this study, to pave the way to achieving such wavefunction simulations, we decompose chemical reactions into their main parts and comprehensively show the minimum essential circuits for simulating each part. An antisymmetrized initial state is constructed using ancillae. Chemical reactions should be simulated in two different ways, where the difference is whether the ancillae are released or not. When they are released, the whole electronic system is simulated. When they are not released, orbital information is obtained. These ways are hence complementary.
High Resolution Image Download MS PowerPoint Slide Chemical simulation is a key application area that can leverage the power of quantum computers. A chemical simulator that implements a grid-based first quantization method has promising characteristics, but an implementation fully in quantum circuits seems to have not been published. Here, we present “crsQ” (chemical reaction simulator Q), which is a quantum circuit generator that generates such a chemical simulator. The generated simulator is capable of antisymmetrization of the initial wave function and time-evolution of the wave function based on the Suzuki–Trotter decomposition. The potential energy term of the Hamiltonian is implemented using arithmetic gates, such as adders, subtractors, multipliers, dividers, and square roots. Circuit diagrams and output samples are shown. The number of qubits in the circuits scales on the order of O (η log η), where η is the number of electrons. Each component of the generated circuit was verified in unit tests. Along with this development, we designed frameworks to ease the development of large-scale circuits, namely, a temporary qubit allocation framework and an abstract syntax tree framework for arithmetic formulas. These frameworks are expected to be useful in large-scale quantum circuit generators.
Simulations of chemical dynamics are a powerful means for understanding chemistry. However, classical computers struggle to simulate many chemical processes, especially non-adiabatic ones, where the Born-Oppenheimer approximation breaks down. Quantum computers could simulate quantum-chemical dynamics more efficiently than classical computers, but there is currently no complete quantum algorithm for calculating dynamical observables to within a known error. Here, we develop an efficient, end-to-end quantum algorithm for simulating chemical dynamics that avoids all uncontrolled approximations (including the Born-Oppenheimer approximation) and whose error is bounded subject to mild assumptions. To do so, we treat the nuclei and the electrons on an equal footing and simulate the full molecular wavefunction on a momentum-space grid in first quantization, including all algorithmic steps: initial-state preparation, time evolution using qubitization, and measurement of chemical observables such as reaction yields and rates. Our work gives the first algorithm for quantum simulation of chemistry whose end-to-end complexity achieves sublinear scaling in the size of the grid. We achieve this by developing an exponentially faster method for initial-state-preparation. Photochemistry is a likely early application of our algorithm and we estimate resources required for end-to-end simulations of non-adiabatic dynamics of atmospherically important molecules. Classically intractable photochemical computations could be performed using resources comparable to those required for other chemical applications of quantum computing.
This paper explores the potential of quantum computing for simulating complex chemical reactions. Traditional classical computational methods often struggle with the inherent quantum mechanical nature of chemical systems, particularly when dealing with large molecules and intricate reaction pathways. This work proposes a novel quantum algorithm leveraging superposition and entanglement to directly simulate the time evolution of these systems. The core of the algorithm centers on a time-dependent Schrödinger equation (TDSE) implemented on a quantum computer. We outline the key elements, including the encoding of molecular states, the construction of a suitable Hamiltonian operator, and the execution of the quantum algorithm to obtain the final state of the system. The efficiency gains compared to classical methods, particularly for reactions involving significant quantum effects, are discussed. Furthermore, we highlight the potential impact of this technology on accelerating drug discovery, materials science, and fundamental chemical research. The algorithm's core relies on the ability of a quantum computer to perform a vast number of calculations simultaneously, offering a substantial advantage over classical computers when simulating quantum systems.
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can be applied only to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and interelectronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born-Oppenheimer approximation but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wave function is propagated on a grid with appropriately short time steps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with 100 qubits.
Quantum computing has shown promise in chemical simulation and other fields where computationally hard problems must be tackled. This research focuses on optimizing molecule structures, which is an important step in understanding the properties and activities of chemical substances. It also studies the possibility of quantum computing in this domain. The system's many-body wave function is optimized using the imaginary time evolution approach, with nuclei and electrons both being considered quantum mechanical particles. Based on numerical experiments in two-dimensional H2+ and H-C-N systems, the authors find that their suggested method may have two benefits—it can find the best nuclear positions with few observations (quantum measurements), and it can find the global minimum structure of nuclei without starting from a complex initial structure and getting stuck in local minima. It is anticipated that this approach would function admirably with quantum computers, and its advancement will pave the road for its potential application as a potent tool.
The theoretical investigation of nonadiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the unfavorable scaling of the computational resources as a function of the system size. While quantum computing exhibits proven quantum advantage for the simulation of real-time dynamics, the study of quantum algorithms for the description of nonadiabatic phenomena is still unexplored. In this Letter, we propose a quantum algorithm for the simulation of fast nonadiabatic chemical processes together with an initialization scheme for quantum hardware calculations. In particular, we introduce a first-quantization method for the time evolution of a wave packet on two coupled harmonic potential energy surfaces (Marcus model). In our approach, the computational resources scale polynomially in the system dimensions, opening up new avenues for the study of photophysical processes that are classically intractable.