Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing

TL;DR

The paper addresses the challenge of identifying molecular resonances in open quantum systems by introducing qDRIVE, a hybrid quantum-classical workflow that combines the complex absorbing potential formalism with asynchronous high-throughput computing. The method builds a non-Hermitian Hamiltonian $H_{ ext{N}}=H_{ ext{H}}+iV_{ ext{CAP}}$ and identifies Siegert states by first solving Hermitian eigenstates of $H_{ ext{H}}$ via a deflated VQE (VQD) and then refining to non-Hermitian eigenstates by minimizing the pseudovariance $oldsymbol{\sigma_{ ext{pseudo}}^{2}}$, all executed as a directed acyclic graph on HTC. Key contributions include a detailed algorithmic framework, error-mitigation strategies for near-term devices, and a proof-of-concept demonstration on a benchmark predissociation model where energies $E_b$, $E_{r1}$, and $E_{r2}$ are recovered with relative errors $oldsymbol{\\mathcal{E}}$ below 1% in noiseless and shot-noise simulations, with realistic degradation under hardware-like noise. The results establish a scalable, heterogeneous computing approach that leverages quantum resources for eigenstate preparation alongside classical HTC to accelerate resonance identification, offering a practical path toward applying quantum computation in computational chemistry and related quantum-control problems.

Abstract

Recent advancements in quantum algorithms have reached a state where we can consider how to capitalize on quantum and classical computational resources to accelerate molecular resonance state identification. Here we identify molecular resonances with a method that combines quantum computing with classical high-throughput computing (HTC). This algorithm, which we term qDRIVE (the quantum deflation resonance identification variational eigensolver) exploits the complex absorbing potential formalism to distill the problem of molecular resonance identification into a network of hybrid quantum-classical variational quantum eigensolver tasks, and harnesses HTC resources to execute these interconnected but independent tasks both asynchronously and in parallel, a strategy that minimizes wall time to completion. We show qDRIVE successfully identifies resonance energies and wavefunctions in simulated quantum processors with current and planned specifications, which bodes well for qDRIVE's ultimate application in disciplines ranging from photocatalysis to quantum control and places a spotlight on the potential offered by integrated heterogenous quantum computing/HTC approaches in computational chemistry.

Figures (10)

• Figure 1: Schematic of the qDRIVE algorithm.
• Figure 2: Quantum circuits for (a) the three-layer efficient SU(2) Ansatz, (b) the Hadamard test for estimation of the expectation value of Pauli code word components of the Hermitian Hamiltonian $\text{Re}\left(\left\langle U\left(H_{\text{H}}\right)\right\rangle \right)$, (c) the overlap between two states $\left\langle \psi\left(\mathbf{\theta}_{j}\right)\middle|\psi\left(\mathbf{\theta}_{i}\right)\right\rangle =\left\langle \bar{0}\left|U^{\dagger}\left(\mathbf{\theta}_{j}\right)U\left(\mathbf{\theta}_{i}\right)\right|\bar{0}\right\rangle$, and (d) the Hadamard test for estimation of the expectation value Pauli code word components of the non-Hermitian Hamiltonian $\text{Re}\left(\left\langle U\left(H_{\text{N}}\right)\right\rangle \right)$.
• Figure 3: Schematic for implementation of qDRIVE with HTC resources. Each batch (blue rectangles) begins with identification of the ground state of the Hermitian Hamiltonian on an individual classical processor), which spawns both identification of a corresponding eigenstate of the non-Hermitian Hamiltonian on another classical processor and identification of the next excited state on yet another classical processor (yellow rectangles). For each batch, upon completion all resonances are pooled to a single file (lime rectangles), and finally sorted among all batches to identify the result for each resonance with the lowest pseudovariance (green rectangle).
• Figure 4: Benchmark potential energy surface $V_{0}$ (solid gray line), which supports a bound state $\psi_{b}$ and two resonances $\psi_{r_{1}}$ and $\psi_{r_{2}}$ (solid green, blue, and red lines, probability density shown), here termed the bound state, first resonance, and second resonance, respectively, shown as computed via exact diagonalization where purely outgoing boundary conditions are imposed by a complex absorbing potential $V_{\text{CAP}}$ (dashed gray line, shown as $-V_{\text{CAP}}$). Each state's probability density is vertically shifted by the value of the real part of its energy $\text{Re}\left(E\right)$.
• Figure 5: Probability probability $\left|\psi\right|^{2}$ visualized in position space corresponding to the qDRIVE-optimized three-qubit Ansatz for the statevector (dashed lines), Aer (dotted lines), and Torino (dashed-dotted lines) simulators as compared to exact diagonalization (solid lines) for the (left) bound state (green lines), (center) first resonance (blue lines), and (right) second resonance (red lines).