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arxiv: 2606.29547 · v1 · pith:XK5QAQXVnew · submitted 2026-06-28 · 🪐 quant-ph · physics.chem-ph

Quantum simulation of molecular excited-state manifolds and energies using the TEPID-ADAPT-VQE algorithm

Jason Saroni , Bharath Sambasivam , Ayush Asthana , Edwin Barnes This is my paper

Pith reviewed 2026-06-30 07:22 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-ph
keywords excited statesvariational quantum eigensolvermolecular potential energy surfacesGibbs stateADAPT-VQEquantum chemistry simulationnear-term quantum devices
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The pith

TEPID-ADAPT-VQE prepares multiple molecular excited states by variationally diagonalizing one truncated low-temperature Gibbs state.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents TEPID-ADAPT-VQE as a method to compute low-lying excited states of molecules on quantum computers. It works by variationally finding the eigenstates of a single truncated low-temperature Gibbs state rather than optimizing separate states one by one. Tests on H2, LiH, and linear H4 show that the resulting energies and potential energy curves match exact results within chemical accuracy in both weakly and strongly correlated regimes. The adaptive circuit construction keeps the quantum resources modest. The approach needs only one physically motivated hyperparameter, temperature, in contrast to methods that require multiple tunable parameters.

Core claim

TEPID-ADAPT variationally diagonalizes a truncated low-temperature Gibbs state, enabling the simultaneous preparation of multiple excited states within a single optimization. Applied to H2, LiH, and linear H4 across bond lengths that span weakly and strongly correlated regimes, the algorithm reproduces excited-state spectra and potential energy curves to within chemical accuracy. A modified MORE-ADAPT-VQE achieves similar accuracy but requires several hyperparameters whose best values depend on the specific molecule and geometry.

What carries the argument

The truncated low-temperature Gibbs state, which is diagonalized variationally to obtain the manifold of low-lying excited states in one run.

If this is right

  • Multiple excited states become available after one variational optimization instead of separate runs for each state.
  • The method maintains accuracy across both weak and strong electron correlation regimes for small molecules.
  • Only a single temperature parameter sets the energy window for the targeted states.
  • Adaptive ansatz growth produces circuits short enough for near-term quantum hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The single-hyperparameter design may reduce the difficulty of variational optimization landscapes compared with multi-parameter alternatives.
  • If the truncation of the Gibbs state remains valid for larger systems, the same framework could address excited states in photochemistry or catalysis.
  • The approach could be combined with other density-matrix techniques to target states at different energy scales without redesigning the ansatz.

Load-bearing premise

The truncated low-temperature Gibbs state must capture the low-lying excited states without significant mixing from higher states, and the adaptive variational circuit must approximate that state closely enough for the tested molecules.

What would settle it

If the computed excited-state energies for any of the studied molecules at any tested geometry deviate from exact diagonalization results by more than chemical accuracy (roughly 1.6 millihartree), the accuracy claim would be falsified.

Figures

Figures reproduced from arXiv: 2606.29547 by Ayush Asthana, Bharath Sambasivam, Edwin Barnes, Jason Saroni.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Energies of the lowest excited states of H [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The energy spectrum of H [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Average energy error as a function of the pa [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Energy error versus adaptation number for TEPID-ADAPT applied to (a) H [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Absolute energy errors for the energy eigenstates of H [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Absolute energy errors for the energy eigenstates of H [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

The simulation of molecular excited states is a key challenge in quantum chemistry and a promising application for quantum computing. In this work, we investigate the efficacy of the truncated eigenvalue parametrized initial density adaptive variational algorithm (TEPID-ADAPT-VQE) for computing low-lying excited states and potential energy surfaces. TEPID-ADAPT variationally diagonalizes a truncated low-temperature Gibbs state, enabling the simultaneous preparation of multiple excited states within a single optimization. We apply the method to H$_2$, LiH, and linear H$_4$ across bond lengths spanning weakly and strongly correlated regimes. The adaptive derivative-assembled problem-tailored (ADAPT) ansatz construction yields compact circuits suitable for near-term hardware. We also implement a modified version of the MORE-ADAPT-VQE algorithm for comparison with TEPID-ADAPT. We find that both algorithms accurately reproduce excited-state spectra and potential energy curves within chemical accuracy for all the molecules and geometries studied. However, TEPID-ADAPT has the advantage of utilizing only a single, physically motivated hyperparameter (temperature) that controls the energy scale at which excited states are targeted, while MORE-ADAPT utilizes multiple hyperparameters whose optimal values depend sensitively on the target problem. These results demonstrate that combining adaptive ansatz construction with density-matrix-based formulations provides an efficient framework for excited-state quantum chemistry on near-term devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces the TEPID-ADAPT-VQE algorithm, which variationally diagonalizes a truncated low-temperature Gibbs state to prepare multiple low-lying excited states simultaneously within a single optimization using an adaptive ADAPT ansatz. It benchmarks the method on H2, LiH, and linear H4 across weakly and strongly correlated bond lengths, claiming reproduction of excited-state spectra and potential energy curves to chemical accuracy, and compares it favorably to a modified MORE-ADAPT-VQE on the basis of having only a single physically motivated hyperparameter (temperature).

Significance. If the numerical results hold under the stated assumptions, the work supplies a density-matrix-based route to excited-state manifolds that requires fewer tunable parameters than subspace-expansion alternatives and produces compact circuits, which would be a useful addition to the near-term quantum chemistry toolkit.

major comments (2)
  1. [Abstract and § on TEPID-ADAPT formulation] The central claim that the eigenstates of the truncated low-T Gibbs state coincide with the target low-lying manifold rests on the unverified assumption of negligible higher-state contamination. For linear H4 at stretched geometries the spectrum is dense; no overlap, fidelity, or trace-norm data between the variationally obtained states and the exact eigenstates of the truncated operator are supplied, leaving open whether reported chemical accuracy reflects faithful diagonalization or cancellation.
  2. [Abstract] The abstract states that both TEPID-ADAPT and MORE-ADAPT reproduce spectra 'within chemical accuracy for all the molecules and geometries studied,' yet the supplied text contains no tables of absolute or relative errors, no error bars, no circuit-depth metrics, and no explicit exclusion criteria for the temperature cutoff. Without these data the quantitative claim cannot be assessed.
minor comments (1)
  1. [Abstract] The expansion of the TEPID acronym is given only in the abstract; repeating it once in the methods section would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to incorporate additional data and clarifications as needed.

read point-by-point responses

  1. Referee: [Abstract and § on TEPID-ADAPT formulation] The central claim that the eigenstates of the truncated low-T Gibbs state coincide with the target low-lying manifold rests on the unverified assumption of negligible higher-state contamination. For linear H4 at stretched geometries the spectrum is dense; no overlap, fidelity, or trace-norm data between the variationally obtained states and the exact eigenstates of the truncated operator are supplied, leaving open whether reported chemical accuracy reflects faithful diagonalization or cancellation.

    Authors: We agree that explicit verification of state fidelity would strengthen the manuscript. While the chemical accuracy in energies provides indirect support, we will add overlap and fidelity metrics (and trace-norm distances where relevant) between the variationally obtained states and the exact eigenstates of the truncated Gibbs operator, with particular attention to the linear H4 stretched geometries. These will be included in a new subsection or appendix in the revised version. revision: yes

  2. Referee: [Abstract] The abstract states that both TEPID-ADAPT and MORE-ADAPT reproduce spectra 'within chemical accuracy for all the molecules and geometries studied,' yet the supplied text contains no tables of absolute or relative errors, no error bars, no circuit-depth metrics, and no explicit exclusion criteria for the temperature cutoff. Without these data the quantitative claim cannot be assessed.

    Authors: We acknowledge that the abstract claim would be better supported by explicit quantitative summaries. In the revised manuscript we will add a table of absolute and relative errors (with error bars where applicable) for all reported energies, include circuit-depth metrics for the final ADAPT ansatze, and provide explicit criteria used to select the temperature cutoff (including how the truncation threshold was determined). These additions will allow direct assessment of the chemical-accuracy claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity; method is self-contained with external benchmarks

full rationale

The TEPID-ADAPT-VQE approach defines a variational optimization over a truncated low-temperature Gibbs state whose eigenstates are targeted for excited-state preparation. All reported accuracies are obtained by direct numerical comparison against exact diagonalization or established reference values for H2, LiH, and H4 at multiple bond lengths. No equation in the derivation reduces to a fitted parameter renamed as a prediction, no load-bearing premise rests on self-citation, and the single temperature hyperparameter is chosen on physical grounds rather than tuned to reproduce the target spectra. The derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum-chemistry and variational-algorithm assumptions plus one tunable parameter; no new particles or forces are introduced.

free parameters (1)
  • temperature
    Single physically motivated hyperparameter that sets the energy scale for the truncated Gibbs state.
axioms (1)
  • domain assumption A variational optimization over an adaptive ansatz can accurately approximate the truncated low-temperature Gibbs state for the studied molecules.
    Invoked when claiming that TEPID-ADAPT simultaneously prepares multiple excited states.

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    TheL 2 andL ∞ energy errors are shown

    Temperature dependence Figure 4 examines the accuracy of excited states ob- tained via TEPID-ADAPT as a function of inverse tem- peratureβfor H 4. TheL 2 andL ∞ energy errors are shown. Asβincreases, corresponding to lower effec- tive temperatures, both theL2 andL ∞ errors increase. Errors in higher excited states grow because a circuit trained on a low-t...

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    Figure 5 shows results from weighted MORE-ADAPT for the average energy error for H2 and H4 as a func- tion of a parameterαthat controls the distribution of weights viaw k = e−αλk N

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