[Paper Review] How will quantum computers provide an industrially relevant computational advantage in quantum chemistry?

Vincent E. Elfving, Benno W. Broer+5 more|arXiv (Cornell University)|Sep 25, 2020

Quantum Computing Algorithms and Architecture149 references65 citations

TL;DR

The paper analyzes the status of quantum hardware and algorithms, defines what quantum advantage would mean for quantum chemistry, and provides resource estimates (e.g., CAS sizes) for comparing quantum and classical methods, highlighting the chromium dimer as a key benchmark and discussing FeMo-co as a cautionary case for near-term industrial relevance.

ABSTRACT

Numerous reports claim that quantum advantage, which should emerge as a direct consequence of the advent of quantum computers, will herald a new era of chemical research because it will enable scientists to perform the kinds of quantum chemical simulations that have not been possible before. Such simulations on quantum computers, promising a significantly greater accuracy and speed, are projected to exert a great impact on the way we can probe reality, predict the outcomes of chemical experiments, and even drive design of drugs, catalysts, and materials. In this work we review the current status of quantum hardware and algorithm theory and examine whether such popular claims about quantum advantage are really going to be transformative. We go over subtle complications of quantum chemical research that tend to be overlooked in discussions involving quantum computers. We estimate quantum computer resources that will be required for performing calculations on quantum computers with chemical accuracy for several types of molecules. In particular, we directly compare the resources and timings associated with classical and quantum computers for the molecules H$_2$ for increasing basis set sizes, and Cr$_2$ for a variety of complete active spaces (CAS) within the scope of the CASCI and CASSCF methods. The results obtained for the chromium dimer enable us to estimate the size of the active space at which computations of non-dynamic correlation on a quantum computer should take less time than analogous computations on a classical computer. Using this result, we speculate on the types of chemical applications for which the use of quantum computers would be both beneficial and relevant to industrial applications in the short term.

Motivation & Objective

• Clarify what constitutes quantum advantage in molecular quantum chemistry and its relevance to industry.
• Estimate quantum hardware resources and runtimes needed to achieve chemical accuracy for representative systems.
• Compare quantum and classical approaches using concrete benchmarks (H2 with growing basis sets; Cr2 CAS studies).
• Discuss practical bottlenecks and realistic near-term pathways for industrial impact.

Proposed method

• Review current quantum hardware and algorithm theory in quantum chemistry.
• Translate molecular problems into qubit representations and compare qubit counts to spin-orbitals.
• Use CASCI/CASSCF-like benchmarks (e.g., Cr2) to estimate quantum vs. classical runtimes for chemical accuracy.
• Apply explicit comparisons between classical limits (e.g., CCSD(T)/CBS) and quantum resource estimates under fault-tolerant assumptions.

Experimental results

Research questions

• RQ1 What level of active-space (N,N) CAS on a quantum computer yields a meaningful speedup over classical methods for challenging multireference systems?
• RQ2 For which molecular problems and basis-set sizes can quantum computers realistically outperform state-of-the-art classical approaches to chemical accuracy?
• RQ3 What constraints (hardware, error correction, basis sets) determine the practicality of near-term quantum chemistry applications in industry?
• RQ4 How do dynamic vs. non-dynamic correlation influence the required quantum resources for achieving chemical accuracy?

Key findings

• Quantum advantage in chemistry can be sought in speed, accuracy, or molecule size, but not all forms are industrially valuable.
• The study suggests a transition CAS size of around 19 to 34 (N,N) for CAS of the type (N,N) under surface code assumptions, where quantum methods may beat classical counterparts for non-dynamic correlation energies.
• Current quantum hardware has not yet reached chemical accuracy for realistic basis-set sizes; existing qubit counts map far short of what is needed for chemical accuracy in typical problems.
• Explicitly correlated (F12-like) basis sets and density fitting may reduce quantum resource needs compared to traditional large basis sets.
• FeMo-co and related multireference problems illustrate that very large active spaces and relativistic effects pose substantial challenges for near-term quantum approaches, underscoring the need for hybrid strategies combining quantum non-dynamic with classical dynamic correlation methods.
• The authors emphasize distinguishing chemical accuracy from mere chemical precision in quantum simulations and stress the gap between reported quantum precision and true predictive chemical accuracy.