A team of researchers from various institutions, including the University of Toronto and Harvard University, have proposed a new approach to solving chemical simulation problems using quantum computers. The team’s method involves using quantum circuits of size scaling polynomially in relevant system parameters to find good initial states for dynamical simulation in a scattering tree. This approach could potentially overcome the computational challenges of simulating chemical systems, which currently increase exponentially with system size. The team’s framework also allows for the modeling of complex chemical reactions by hierarchically operating the scattering with 𝑁 atoms to create 𝑀 reactants.
Quantum Computing and Chemical Simulations
A team of researchers from various institutions including the University of Toronto, Vector Institute of Artificial Intelligence, St Jude Children’s Research Hospital, Harvard University, Horizon Quantum Computing, and the Canadian Institute for Advanced Research have proposed an efficient approach for solving chemical simulation problems using quantum computers. The team includes Philipp Schleich, Lasse Bjørn Kristensen, Jorge A Campos Gonzalez Angulo, Davide Avagliano, Mohsen Bagherimehrab, Abdulrahman Aldossary, Christoph Gorgulla, Joe Fitzsimons, and Alán AspuruGuzik.
The Challenge of Chemical Simulations
Simulating chemical systems is a computationally challenging task as the simulation cost exponentially increases with the system size. Quantum computers have been proposed as a computational means to overcome this bottleneck. However, most efforts recently have been spent on determining the ground states of chemical systems. The lack of efficient heuristics for initial state generation has cast doubt on the feasibility of this approach.
A New Approach to Chemical Simulations
The team proposes an inherently efficient approach for solving chemical simulation problems. This approach requires quantum circuits of size scaling polynomially in relevant system parameters. If a set of assumptions can be satisfied, the approach finds good initial states by assembling initial states for dynamical simulation in a scattering tree. A variety of quantities of chemical interest can be measured based on quantum simulation.
Quantum Computing and Quantum Simulations
The idea of using quantum computers for the simulation of quantum systems has generated substantial effort towards the application of quantum computing to chemical problems. Quantum many-body simulations for chemistry are inherently limited by the curse of dimensionality and constitute a significant portion of current supercomputing usage. The team proposes a departure from how a majority of the quantum computing community approaches chemistry, moving from a computational chemist’s way of thinking to a new era.
The Role of Dynamical Simulation
With fault-tolerant quantum computers, dynamical simulation of quantities that a practicing chemist might directly care about is within reach. Most relevant quantum chemistry problems are inherently addressable through dynamical evolution alone, leading to efficient quantum algorithms for these problems. The team proposes a framework that makes use of a limited set of preparable atomic initial states and then builds input states for a reaction of interest through a scattering process dynamically.
The Scattering Process and Quantum Simulation
The scattering process dynamically builds input states for a reaction of interest. Then, time evolution embodies the reaction and a wide set of relevant quantities can be measured. This yields an algorithm that is not limited by the QMA hardness of preparing ground states and thermal states. The team’s framework facilitates the modeling of complex chemical reactions by hierarchically operating the scattering with 𝑁 atoms to create 𝑀 reactants, which then can undergo a quantum simulation corresponding to a reaction.
Complexity Considerations in Quantum Computing
The complexity class BQP (bounded-error quantum polynomial-time) is often considered the quantum generalization of the complexity class P (polynomial time) or more precisely its probabilistic extension BPP (bounded-error probabilistic polynomial-time). Polynomial complexity is usually considered efficient as the increase in cost when scaling relevant parameters is somewhat moderate. However, problems from QMA (Quantum Merlin Arthur) are believed to not be efficiently solvable even on a quantum computer.
In computational complexity theory, polynomial time problems are a class of problems that are solvable by an algorithm whose running time grows at most polynomially with the size of the input. Specifically, a problem is said to be in polynomial time if there exists an algorithm that can solve any instance of the problem in time O(n^k), where n is the size of the input and k is a constant. This class is significant because it is considered to represent the set of problems that are efficiently solvable in practice. Problems in this class are often contrasted with NP (nondeterministic polynomial time) problems, which are verifiable in polynomial time but not necessarily solvable in polynomial time. The distinction between polynomial and super-polynomial (like exponential) time problems is central to the P vs NP question, one of the most fundamental unsolved questions in computer science.
The article titled “Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer” was published on arXiv (Cornell University) on January 17, 2024. The authors of the article are Philipp Schleich, Lasse Bjørn Kristensen, Davide Avagliano, Mohsen Bagherimehrab, Abdulrahman Aldossary, Christoph Gorgulla, Joe Fitzsimons, and Alán Aspuru‐Guzik. The article can be accessed through the DOI reference https://doi.org/10.48550/arxiv.2401.09268.
