Benchmarking the Impact of Active Space Selection on the VQE Pipeline for Quantum Drug Discovery

TL;DR

This work addresses the challenge of applying VQE to drug-like molecules on near-term quantum hardware by establishing the first systematic benchmark for active-space selection. It combines chemically grounded multi-reference diagnostics with end-to-end VQE evaluations (UCCSD and HEA) across a diverse seven-molecule suite, using both simulators and physical QPUs to quantify chemistry and architecture metrics. Key findings reveal substantial energy gains from expanding active spaces but also steep resource scaling, with hardware validation showing VQE viability for small spaces and highlighting measurement overhead as a bottleneck. The study offers actionable guidance for hardware–algorithm co-design and provides open benchmark data to accelerate progress in quantum drug discovery.

Abstract

Quantum computers promise scalable treatments of electronic structure, yet applying variational quantum eigensolvers (VQE) on realistic drug-like molecules remains constrained by the performance limitations of near-term quantum hardwares. A key strategy for addressing this challenge which effectively leverages current Noisy Intermediate-Scale Quantum (NISQ) hardwares yet remains under-benchmarked is active space selection. We introduce a benchmark that heuristically proposes criteria based on chemically grounded metrics to classify the suitability of a molecule for using quantum computing and then quantifies the impact of active space choices across the VQE pipeline for quantum drug discovery. The suite covers several representative drug-like molecules (e.g., lovastatin, oseltamivir, morphine) and uses chemically motivated active spaces. Our VQE evaluations employ both simulation and quantum processing unit (QPU) execution using unitary coupled-cluster with singles and doubles (UCCSD) and hardware-efficient ansatz (HEA). We adopt a more comprehensive evaluation, including chemistry metrics and architecture-centric metrics. For accuracy, we compare them with classical quantum chemistry methods. This work establishes the first systematic benchmark for active space driven VQE and lays the groundwork for future hardware-algorithm co-design studies in quantum drug discovery.

Figures (5)

• Figure 1: Variational Quantum Eigensolver schematic: parameterized quantum circuit $U(\theta)$ generates trial states, measurement outcomes define the energy objective, and classical optimization refines $\theta$ iteratively until convergence.
• Figure 2: Active space approximation for molecular orbital partitioning. Virtual orbitals (top, gray) and inactive orbitals (bottom, gray) remain frozen at Hartree-Fock occupation, while electrons in the active space (middle, dashed box) explore all possible configurations $C_1, C_2, \ldots, C_n$ via quantum computation. Red lines indicate chemically relevant orbitals treated variationally; arrows represent electron occupations.
• Figure 3: Our VQE benchmark workflow. Molecules undergo heuristic classification for quantum computing suitability, followed by active space selection(left: multiscale framework for molecules calculation, QM=quantum mechanics, MM=molecualr mechanics). VQE calculations execute on simulators and QPUs, with evaluation via chemistry metrics (energy accuracy) and architecture metrics (circuit resources). This systematic pipeline enables cross-platform assessment of VQE performance for drug-like molecules.
• Figure 4: Molecular suitability spectrum for quantum computing. Seven molecules arranged from unsuitable (left) to hardware-limited (right) based on quantum computing applicability. Upper gradient: H$_2$O (single-reference benchmark) $\rightarrow$ oseltamivir/morphine (optimal candidates with manageable multi-reference character) $\rightarrow$ lovastatin/imatinib (hardware-limited by large active space requirements). Lower annotations indicate molecular properties—single-reference nature, $\pi$-system complexity, multi-reference character, active space size—that determine VQE suitability. This gradient captures the practical window where quantum advantage emerges for drug-like molecules.
• Figure 5: VQE energy convergence on superconducting quantum processors.All runs successfully converge despite hardware noise.