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arxiv: 2306.02620 · v4 · submitted 2023-06-05 · 🪐 quant-ph · cond-mat.str-el

Feasibility of performing quantum chemistry calculations on quantum computers

Thibaud Louvet , Thomas Ayral , Xavier Waintal This is my paper

Pith reviewed 2026-05-24 08:05 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords quantum chemistryvariational quantum eigensolverquantum phase estimationdecoherenceorthogonality catastrophefault-tolerant quantum computingmolecular ground state
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The pith

Decoherence makes VQE unusable for chemistry on noisy hardware while QPE success probability falls exponentially with system size.

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

The paper develops two criteria to test whether leading quantum algorithms can compute molecular ground states. The first bounds the decoherence tolerable by the variational quantum eigensolver and shows that the required hardware performance exceeds noisy devices even after error mitigation. The second estimates the ground-state overlap needed by quantum phase estimation from the input state's energy and variance, revealing exponential decay with molecule size for states prepared by classical methods. These results matter because quantum chemistry is widely viewed as an early target application for quantum computers. A sympathetic reader therefore sees concrete quantitative obstacles rather than generic difficulty.

Core claim

The authors establish that the variational quantum eigensolver cannot tolerate realistic decoherence because the molecular spectrum bears no relation to the hardware spectrum, so the algorithm demands fault-tolerant performance levels. They further show that the overlap between classical variational input states and the true ground state obeys the orthogonality catastrophe, producing an exponential drop in quantum phase estimation success probability as system size grows.

What carries the argument

Two evaluation criteria: an upper bound on imprecision and decoherence for VQE derived from targeted precision, gate count and energy contributions of decohered states; an overlap estimate for QPE obtained from the input state's energy and energy variance.

If this is right

  • Relevant quantum chemistry calculations with VQE require fault-tolerant quantum computers rather than noisy intermediate-scale hardware.
  • Advanced error mitigation techniques remain insufficient to restore VQE accuracy for chemistry on present devices.
  • Quantum phase estimation success probability is suppressed exponentially by system size when using input states from state-of-the-art classical methods.
  • The orthogonality catastrophe in overlap scaling applies across a variety of classical preparation techniques.

Where Pith is reading between the lines

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

  • Other quantum algorithms or improved state-preparation techniques may be required to circumvent the identified scaling barriers.
  • The two criteria could be applied to additional molecules to delineate which systems remain feasible on early fault-tolerant hardware.
  • Hybrid classical-quantum workflows might need to target better initial-state quality to avoid the exponential QPE penalty.

Load-bearing premise

The molecular energy spectrum is uncorrelated with the hardware spectrum used for VQE, and input states from current classical methods give representative overlaps for estimating QPE performance.

What would settle it

Perform VQE on a small molecule while deliberately adding controlled decoherence at the level predicted by the bound and measure whether the energy error exceeds the target precision; or compute the exact ground-state overlap for a molecule large enough that the predicted exponential suppression can be checked numerically.

Figures

Figures reproduced from arXiv: 2306.02620 by Thibaud Louvet, Thomas Ayral, Xavier Waintal.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic of the difference between the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Difference between the energy of the infinite [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Different energy scales of a chain of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (a) Sketch of the energy [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Scaling of the Hartree-Fock energy (a) and the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

Quantum chemistry is envisioned as an early and disruptive application for quantum computers. Yet, closer scrutiny of the proposed algorithms shows that there are considerable difficulties along the way. Here, we propose two criteria for evaluating two leading quantum approaches for finding the ground state of molecules. The first criterion applies to the variational quantum eigensolver (VQE) algorithm. It sets an upper bound to the level of imprecision/decoherence that can be tolerated in quantum hardware as a function of the targeted precision, the number of gates and the typical energy contribution from states populated by decoherence processes. We find that decoherence is highly detrimental to the accuracy of VQE and performing relevant chemistry calculations would require performances that are expected for fault-tolerant quantum computers, not mere noisy hardware, even with advanced error mitigation techniques. Physically, the sensitivity of VQE to decoherence originates from the fact that, in VQE, the spectrum of the studied molecule has no correlation with the spectrum of the quantum hardware used to perform the computation. The second criterion applies to the quantum phase estimation (QPE) algorithm, which is often presented as the go-to replacement of VQE upon availability of (noiseless) fault-tolerant quantum computers. QPE requires an input state with a large enough overlap with the sought-after ground state. We provide a criterion to estimate quantitatively this overlap based on the energy and the energy variance of said input state. Using input states from a variety of state-of-the-art classical methods, we show that the scaling of this overlap with system size does display the standard orthogonality catastrophe, namely an exponential suppression with system size. This in turns leads to an exponentially reduced QPE success probability.

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 / 3 minor

Summary. The manuscript proposes two criteria for assessing the feasibility of the variational quantum eigensolver (VQE) and quantum phase estimation (QPE) for ground-state quantum chemistry calculations. For VQE it derives an upper bound on tolerable decoherence (as a function of target precision, gate count, and typical energy contribution from decohered states) and concludes that relevant calculations require fault-tolerant hardware even with error mitigation; the physical origin is stated to be the lack of correlation between the molecular spectrum and the hardware spectrum. For QPE it supplies a quantitative overlap estimator based on the energy and energy variance of classical input states and shows that this overlap exhibits the standard orthogonality-catastrophe exponential suppression with system size, thereby exponentially reducing QPE success probability.

Significance. If the derivations hold, the work supplies concrete, quantitative feasibility criteria that reproduce the expected orthogonality-catastrophe scaling and highlight the stringent requirements on decoherence for VQE. The arguments rest on standard Markovian noise and variance-based overlap bounds, are parameter-free in the sense described, and directly address two leading algorithmic approaches, thereby providing a useful benchmark for the community.

major comments (2)
  1. [§2] §2 (VQE decoherence bound): the central claim that 'the spectrum of the studied molecule has no correlation with the spectrum of the quantum hardware' is used to derive the bound; a short explicit justification or reference to the Markovian model employed would be needed to confirm that the bound is not sensitive to this modeling choice.
  2. [§3] §3 (QPE overlap criterion): the quantitative estimator relating overlap to energy and variance is load-bearing for the exponential-suppression conclusion; the precise inequality or Chebyshev-type bound invoked should be stated explicitly so that the scaling result can be reproduced from the given classical input-state data.
minor comments (3)
  1. [Abstract / Introduction] The abstract and introduction would benefit from a brief citation to the original orthogonality-catastrophe literature (e.g., Anderson 1967) when the exponential suppression is first mentioned.
  2. [Figures] Figure captions for any numerical overlap plots should explicitly list the classical methods used to generate the input states and the system sizes examined.
  3. [§3] Notation for the energy variance in the QPE overlap formula should be defined once at first use to avoid ambiguity with the molecular Hamiltonian variance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment, and constructive suggestions. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§2] §2 (VQE decoherence bound): the central claim that 'the spectrum of the studied molecule has no correlation with the spectrum of the quantum hardware' is used to derive the bound; a short explicit justification or reference to the Markovian model employed would be needed to confirm that the bound is not sensitive to this modeling choice.

    Authors: The derivation assumes standard Markovian decoherence acting in the hardware's native basis (typically the computational basis), which is uncorrelated with the eigenbasis of the molecular Hamiltonian for a general-purpose device. This modeling choice is standard in the literature on open quantum systems for NISQ hardware. In the revised manuscript we will insert a short clarifying paragraph with this justification and a reference to the Markovian master-equation framework. revision: yes

  2. Referee: [§3] §3 (QPE overlap criterion): the quantitative estimator relating overlap to energy and variance is load-bearing for the exponential-suppression conclusion; the precise inequality or Chebyshev-type bound invoked should be stated explicitly so that the scaling result can be reproduced from the given classical input-state data.

    Authors: We agree that explicit statement of the bound will improve reproducibility. The estimator applies a one-sided Chebyshev inequality to the energy variance of the classical input state to lower-bound the overlap with the ground state. In the revised manuscript we will state the precise inequality and its application to the classical data. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's two central criteria are derived directly from standard quantum mechanics and information theory. The VQE decoherence bound follows from a Markovian noise model and the assumption of uncorrelated hardware/molecular spectra (explicitly stated as a physical origin, not a fitted parameter). The QPE overlap estimator follows from a variance-based or Chebyshev-type bound on the ground-state projection, reproducing the known orthogonality catastrophe scaling without any reduction to self-referential inputs, fitted parameters renamed as predictions, or load-bearing self-citations. No equations or steps reduce by construction to the paper's own outputs; both derivations remain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard quantum mechanics and established models of decoherence and state preparation without introducing new free parameters or postulated entities.

axioms (2)
  • standard math Standard quantum mechanics and decoherence models apply to the quantum hardware and molecular systems.
    Invoked to derive the VQE imprecision bound and model error effects.
  • domain assumption Input states from classical methods have computable energies and variances that allow overlap estimation.
    Used for the QPE overlap criterion and scaling analysis.

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Forward citations

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