[Paper Review] Is there evidence for exponential quantum advantage in quantum chemistry?

Seunghoon Lee, Joonho Lee+16 more|arXiv (Cornell University)|Aug 3, 2022

Quantum Computing Algorithms and Architecture20 citations

TL;DR

The paper argues that there is no current evidence for exponential quantum advantage in ground-state quantum chemistry and discusses how classical heuristics often scale polynomially, challenging the expectation of generic exponential speedups.

ABSTRACT

The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through quantum computation, as a potential ``killer application''. Indications of potential exponential quantum advantage in artificial tasks have increased interest in this application, thus, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation. We conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for quantum chemistry, it may be prudent to assume exponential speedups are not generically available for this problem.

Motivation & Objective

• Evaluate whether generic chemistry problems exhibit exponential quantum speedups for ground-state energy estimation.
• Analyze the cost components of fault-tolerant quantum algorithms for quantum chemistry, especially QPE.
• Investigate how state preparation affects the practicality of quantum advantage in chemistry.
• Examine how classical heuristic methods scale with system size and accuracy in comparison to quantum approaches.
• Provide guidance on the realistic prospects of exponential quantum advantage in quantum chemistry.

Proposed method

• Analyze fault-tolerant quantum algorithms for ground-state energy estimation, focusing on quantum phase estimation (QPE).
• Decompose the total cost into state preparation, phase estimation circuit, and repetitions related to state overlap S.
• Study ansatz-based and adiabatic state preparation to assess overlap and scaling with system size.
• Examine classical heuristics (e.g., CC methods, tensor networks) and their observed scaling with system size and accuracy.
• Use Fe-S clusters and model Hamiltonians to empirically evaluate overlap, adiabatic costs, and classical scaling.
• Present numerical experiments and theoretical arguments to compare quantum and classical costs across chemical space.

Experimental results

Research questions

• RQ1 Does ground-state energy estimation in generic chemistry problems admit exponential quantum speedups over classical heuristics?
• RQ2 How do state preparation and overlap affect the practical cost of quantum phase estimation for chemistry problems?
• RQ3 Do classical heuristics for quantum chemistry scale exponentially with system size or remain polynomial under realistic error controls?
• RQ4 Under what conditions could adiabatic state preparation yield a protected gap and polynomial versus exponential costs?
• RQ5 What evidence from model and real chemical systems supports or refutes the exponential quantum advantage hypothesis?

Key findings

• There is no strong evidence that exponential quantum speedups are generic for ground-state quantum chemistry in the studied problems.
• Quantum state preparation costs depend on the overlap between initial and ground states and can be prohibitively large if overlap decays with system size.
• Adiabatic state preparation costs vary widely and can be worse than QPE depending on the initial Hamiltonian and path, highlighting the challenge of a universally good starting point.
• Classical heuristics often show polynomial scaling with system size for fixed accuracy or density, challenging the assumption of exponential hardness.
• Tensor network and local coupling methods demonstrate poly(L) scaling in several model and material systems, suggesting substantial classical tractability for many problems.
• The overall conclusion is that exponential quantum advantage in ground-state quantum chemistry remains unproven and likely not generic, though polynomial quantum speedups could still provide meaningful advantages.