Towards quantum simulation of lower-dimensional supersymmetric lattice models

David Schaich; Emanuele Mendicelli

REVIEW 2 major objections 5 minor 22 references

Towards quantum simulation of lower-dimensional supersymmetric lattice models

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Sampling noise from a fixed number of shots can make a supersymmetry-preserving model appear to spontaneously break supersymmetry.

desk verdict A modest but honest proceedings paper: the shot-noise caution is plausible and useful, but underquantified; the statevector baselines are solid and reproducible. read the letter →

arxiv 2411.15083 v1 pith:2CHAWXMC submitted 2024-11-22 hep-lat quant-ph

Emanuele Mendicelli , David Schaich This is my paper · ORCID

classification hep-latquant-ph

keywords supersymmetricquantummechanicsvariationaleigensolvershotnoisespontaneoussupersymmetrybreakingqubitencodinglatticesimulationsignproblem

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This proceedings article tests a quantum-computing route to a classic problem: deciding whether supersymmetric quantum mechanics preserves or spontaneously breaks supersymmetry, which is read off from whether the ground-state energy is zero or nonzero. The authors encode a 0+1-dimensional boson-fermion system on qubits and run the variational quantum eigensolver (VQE) on an exact noiseless simulator and on a simulator that includes the sampling noise of 10,000 shots. Their central finding is a caution: for the harmonic-oscillator superpotential, which exactly preserves supersymmetry and has zero ground-state energy, the shot-noise runs produce a median energy that is nonzero and grows with the bosonic truncation level, so a researcher looking only at the noisy results could wrongly report spontaneous supersymmetry breaking. They conclude that shot noise must be accounted for in future VQE studies, and they point to repeating runs at different shot counts and using variational quantum deflation as next steps.

What carries the argument

The object carrying the argument is the supersymmetric quantum-mechanics Hamiltonian $H=\frac{1}{2}(\hat{p}^2+[W'(\hat{q})]^2-W''(\hat{q})\,[\hat{b}^\dagger,\hat{b}])$, whose supercharges satisfy $2H=\{Q,Q^\dagger\}$; because every eigenenergy is non-negative, a zero-energy ground state exists exactly when both supercharges annihilate it, making the ground-state energy the order parameter for spontaneous supersymmetry breaking. The numerical machinery is VQE with a RealAmplitude ansatz, single-qubit rotations plus a reverse-linear chain of CNOT entanglers, minimized by the gradient-free COBYLA optimizer and run 100 times per superpotential and truncation level. The diagnostic that makes the noise visible is the boxplot of those 100 runs placed against the exact diagonalization value: the median, quartiles, and outliers turn a collection of noisy energy measurements into a clear visual statement that the noisy distribution is biased away from zero.

What would settle it

Repeat the harmonic-oscillator VQE on real quantum hardware, or on a simulator that adds gate errors and decoherence, at shot counts from $10^3$ to $10^6$, and record the median ground-state energy as a function of $\Lambda$. If the nonzero median disappears or does not grow with $\Lambda$ when hardware noise is included, the paper's claim that shot noise alone can create a spurious supersymmetry-breaking signal would not hold on actual devices; if the bias persists and shrinks with increasing shots, the shot-noise explanation is confirmed.

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Extended reading notes

Core claim

The paper's central claim is that sampling noise, not physics, can masquerade as spontaneous supersymmetry breaking in current quantum-simulation workflows. For the harmonic-oscillator superpotential, exact diagonalization and a noiseless state-vector VQE both give ground-state energy zero for every truncation level $\Lambda$, matching the expectation that supersymmetry is preserved. The VQE runs with 10,000 shots instead give a distribution of energies whose median is positive and increases with $\Lambda$; by the model's standard criterion, nonzero ground-state energy means supersymmetry is spontaneously broken, so this looks like breaking. The authors state directly that this illustrates how noise from a fixed number of shots might be misinterpreted as evidence of spontaneous supersymmetry breaking. In the double-well case, where supersymmetry is genuinely broken, the larger energy scale makes the breaking signal survive the noise, while in the anharmonic-oscillator case bosonic truncation effects already make even the noiseless results deviate beyond $\Lambda=8$.

Load-bearing premise

The warning depends on the assumption that a simulator with 10,000 random samples and the chosen classical optimizer behaves like real quantum hardware; the paper explicitly leaves gate errors and decoherence for future work, so the caution has not yet been demonstrated on actual devices.

Editorial extensions

If this is right

VQE studies that search for spontaneous supersymmetry breaking should report shot-count dependence, repeating runs at different numbers of shots, before interpreting a nonzero ground-state energy as breaking.
For the harmonic-oscillator superpotential, shot noise biases the median energy upward with increasing bosonic truncation $\Lambda$, so noiseless-versus-noisy comparisons are needed to separate algorithmic bias from physical signals.
The double-well superpotential's spontaneous breaking signal is large enough to survive shot noise, so not all supersymmetry-breaking conclusions from VQE are suspect.
The general-purpose ansatz used here reproduces exact results only for modest $\Lambda$, so reaching the untruncated limit will require a problem-tailored ansatz.
A more robust route is to compute the low-energy spectrum, for example with variational quantum deflation, rather than only the ground-state energy, since the pairing of excited states is a cleaner supersymmetry diagnostic.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same spurious-breaking mechanism should apply to any VQE order parameter measured with finite shots and a noisy optimizer, so the caution generalizes beyond supersymmetry to symmetry-breaking searches in other lattice models.
A testable extension is to quantify how the median bias scales with shot count and truncation level for the harmonic oscillator; if the bias falls as the inverse square root of the shot count, it is purely sampling noise, while a plateau would indicate optimizer bias.
Comparing noiseless and shot-noise distributions, as the boxplots do, could become a standard low-cost diagnostic for detecting optimizer-versus-noise artifacts before moving to real hardware.
The truncation-plus-noise interplay seen in the anharmonic-oscillator model suggests that digitization errors and sampling noise may compound, motivating studies that vary both $\Lambda$ and shot count simultaneously.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a modest proceedings paper from an established program. The only genuinely new result is the observation that finite-shot sampling noise shifts VQE medians away from the exact zero energy in the harmonic oscillator, potentially mimicking spontaneous SUSY breaking. The statevector results match exact diagonalization across the board, and the code is public, so the baseline is solid. But the headline shot-noise claim is supported only by boxplots; no medians, errors, or significance tests are reported, and the authors themselves attribute the discrepancy to COBYLA's behavior under noise, which weakens the generality of the caution.

What's new: prior papers by the same group [6,8,9] used noiseless statevector simulation. This one adds shot noise at 10,000 shots per run across 100 runs and shows the effect. That is a legitimate extension. The resource table with Pauli-string counts is a useful community service. I also credit the paper for its careful phrasing: it says noise "might be misinterpreted," not that it definitively invalidates VQE, and Section 6 explicitly defers hardware noise.

Soft spots, in proportion: the central claim lacks quantification. For the HO, the exact energy is zero, so a symmetric sampling error should center near zero. The assertion that the median is non-zero and grows with Lambda is a real empirical effect that needs numbers. A bootstrap confidence interval on the medians, or even a simple sign test, would settle it. This is the load-bearing result, and it is currently visual inspection of Fig. 4. I agree with the stress-test note that the mechanism is also ambiguous: the authors say COBYLA struggles in the presence of noise, which suggests the spurious signal may be optimizer-specific rather than a generic property of finite-shot VQE. Testing a second optimizer or at least adding a caveat would make the warning more robust. Minor: the AHO statevector results fail beyond Lambda=8, which they acknowledge; the DW shot-noise results are order-of-magnitude larger than the HO case, which supports their interpretation but is again not statistically formalized.

Overall: this is what it claims to be, a preliminary study with an important caution for a niche community. The caution, if correct, affects how VQE results for SUSY models should be interpreted. The fix is straightforward: report numbers with confidence intervals, and ideally run a different optimizer. I would send it to peer review rather than desk-reject, expecting a moderate revision.

Referee Report

2 major / 5 minor

Summary. This proceedings paper explores the use of the variational quantum eigensolver (VQE) to detect spontaneous supersymmetry breaking in 0+1-dimensional supersymmetric quantum mechanics. The authors encode the model on qubits using one fermionic qubit and B bosonic qubits for Λ=2^B bosonic modes, and study three superpotentials (harmonic oscillator, double well, anharmonic oscillator). For each case they perform 100 VQE runs on Qiskit statevector and shot-noise simulators using the RealAmplitude ansatz and the COBYLA optimizer, comparing the resulting ground-state energy distributions with exact diagonalization. The paper's main observation is that in the presence of shot noise the harmonic-oscillator median ground-state energy appears positive and increases with Λ, which could be misinterpreted as evidence of spontaneous supersymmetry breaking. The authors also provide a tabulation of the Pauli-string resources required for various truncations.

Significance. If the shot-noise caution is quantitatively established, it is a valuable practical warning for VQE-based studies of supersymmetry breaking on near-term quantum hardware, and the paper offers a clean, explicit qubit encoding and resource estimates for the SQM models. The statevector results benchmarked against exact diagonalization support the basic validity of the encoding and the VQE setup. However, the central claim about shot noise currently rests on qualitative inspection of boxplots without numerical values, confidence intervals, or significance tests, and the attribution to the COBYLA optimizer is not tested. The manuscript is explicitly preliminary, and the authors appropriately scope out hardware noise, but the evidentiary basis for the headline finding needs strengthening before it can be considered established.

major comments (2)

[Section 5, Fig. 4] The central claim that shot noise produces a spurious positive median ground-state energy for the harmonic oscillator is not quantified. The text states that "the median is consistent with a non-zero energy value, which tends to increase with larger Λ," but no numerical medians, interquartile ranges, confidence intervals, or significance tests are reported for the 100 runs. Without these, the reader cannot determine whether the positive median is statistically significant or within the expected finite-sample fluctuation around the true value E0=0, and the Λ-trend is asserted without a fit or a correlation measure. Please report the numerical values and a simple statistical test (e.g., a bootstrap confidence interval for the median or a sign test against zero), and quantify the trend, for example with a rank correlation or a linear fit.
[Section 5, Fig. 4 and Section 6] The paper attributes the shot-noise discrepancy to the statement that "the COBYLA optimizer struggles to find the minimum in presence of noise." This leaves open the possibility that the positive median is an artifact of the specific interaction between COBYLA and a noisy objective rather than a generic property of finite-shot VQE. To support the general caution, please compare with at least one alternative optimizer (e.g., SPSA or a gradient-based method) under the same shot-noise conditions, or demonstrate the same positive shift with a fixed ansatz parameter set. If the effect is optimizer-specific, the conclusion should be reframed accordingly.

minor comments (5)

[Section 5, Fig. 4] Please clarify whether the vertical lines for the harmonic oscillator represent the exact diagonalization energy of the truncated Hamiltonian or the continuum result E0=0. Section 3 states that the bosonic truncation explicitly breaks supersymmetry, so it would be helpful to state explicitly how the truncated ED energy behaves for HO as Λ increases.
[Section 5] The description of the shot-noise simulations is ambiguous: "10000 shot executions for each of the 100 VQE runs" could mean 10,000 shots per Pauli string per energy evaluation or 10,000 shots total per run. Please specify the measurement budget, since the effective shot noise depends on this.
[Section 5, AHO results] For the anharmonic oscillator, the statevector VQE agrees with exact diagonalization only up to Λ=8, and the text acknowledges this. Please state explicitly in the conclusions that the current ansatz does not scale to larger bosonic truncations for the AHO, and clarify whether the failure is due to optimizer convergence or ansatz expressibility.
[Figure 4 caption] The caption contains a typo: "different superpontentials" should be "different superpotentials."
[Section 3] The text says "the Λ states require B qubits, where Λ=2^B"; the notation is correct, but consider adding a brief explanation of why B qubits are sufficient for Λ=2^B bosonic modes.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the VQE ground-state energies are benchmarked against exact diagonalization, and the shot-noise caution is an empirical observation rather than a fitted or self-cited prediction.

full rationale

The paper's central derivation chain is self-contained. The target quantity, the ground-state energy, is defined directly by the supersymmetric Hamiltonian in Eq. (1), and the VQE algorithm minimizes that same Hamiltonian to produce an estimate that is then compared against exact diagonalization. This is the intended use of VQE, not a circular reduction: the variational parameters are optimized, but the reported observable (the energy) is an independent quantity defined by the model, and the exact result is computed by a separate classical method. The shot-noise caution in Section 5 is an empirical observation from 100 Qiskit simulator runs with 10,000 shots, presented as boxplots relative to the exact values; it does not rest on any fitted parameter being renamed as a prediction, nor does it invoke a uniqueness theorem. The self-citations to Refs. [6, 8, 9] are contextual: they identify prior efforts, note that prior work did not account for shot noise, and suggest VQD as future work. None of these citations supplies a load-bearing premise for the paper's own results. The skeptical concern about the lack of quantitative significance testing for the median offset is a matter of evidence strength and correctness risk, not circularity, because the observation is not defined in terms of the conclusion. No equation in the paper reduces to its own input, and no known empirical result is merely renamed. Accordingly, the paper exhibits no significant circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central calculations rest on standard SQM, a Jordan-Wigner mapping, a specific bosonic digitization, simulator fidelity, and ansatz expressivity. The model couplings m, g, mu and the truncation Lambda are chosen by hand rather than fitted to the target results. No new physical entities are introduced.

free parameters (4)

m (boson mass) = 1
Set to 1 for simplicity (Section 2). The results are demonstrated only at this point in parameter space.
g (interaction strength) = 1
Set to 1 for simplicity (Section 2). The results are demonstrated only at this point in parameter space.
mu (double-well parameter) = 1
Set to 1 for simplicity (Section 2). The results are demonstrated only at this point in parameter space.
Bosonic truncation Lambda = 2, 4, 8, 16, 32, 64
Number of harmonic-oscillator modes retained in the digitization (Section 3). Varied to study convergence to the untruncated limit; truncation explicitly breaks supersymmetry for general superpotentials.

assumptions (5)

domain assumption Supersymmetric quantum mechanics: the Hamiltonian is H = (1/2){Q, Q-dagger}, and supersymmetry is preserved iff the ground state energy is zero.
Standard SQM framework from Cooper, Khare and Sukhatme [10], used throughout Section 2.
standard math Jordan-Wigner transformation maps fermionic operators to Pauli matrices (Eq. 4).
Standard encoding used in Section 3 to map the fermion to one qubit.
domain assumption Truncated harmonic-oscillator basis with Lambda modes provides a valid finite-dimensional regularization of the bosonic operators (Eq. 5).
Digitization scheme taken from Macridin et al. [11]; the paper relies on it for the qubit Hamiltonian.
domain assumption The Qiskit statevector and shot-noise simulators correctly implement the circuits and sampling statistics.
All VQE results in Section 5 are produced with Qiskit [12]; simulator fidelity is not independently verified.
domain assumption The RealAmplitude reverse-linear ansatz is expressive enough to approximate the ground state of the truncated Hamiltonian.
Ansatz used for all VQE runs (Section 4). The paper finds it fails for the anharmonic oscillator with Lambda > 8 (Section 5), so this assumption only holds for the simpler cases.

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Cite this review

Pith. "Pith review of Towards quantum simulation of lower-dimensional supersymmetric lattice models." pith.science (2026). https://pith.science/paper/2CHAWXMC

@misc{pith2026241115083,
  author       = {Pith},
  title        = {Pith review of: Towards quantum simulation of lower-dimensional supersymmetric lattice models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2CHAWXMC}},
  note         = {Machine review of arXiv:2411.15083}
}

read the original abstract

Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle physics and fostering connections to theories of quantum gravity. However, lattice studies exploring the non-perturbative features of these models, such as spontaneous supersymmetry breaking and real-time evolution encounter significant challenges, particularly due to the infamous sign problem. The sign problem obstructs simulations on classical computers, especially when dealing with high-dimensional lattice systems. While one potential solution is to adopt the Hamiltonian formalism, this approach necessitates an exponential increase in classical resources with the number of lattice sites and degrees of freedom, rendering it impractical for large systems. In contrast, quantum hardware offers a promising alternative, as it requires in principle a polynomial amount of resources, making the study of these models more accessible. In this context, we explore the encoding of lower-dimensional supersymmetric quantum mechanics onto qubits. We also highlight our ongoing efforts to implement and check the model supersymmetry breaking on an IBM gate-based quantum simulator with and without shot noise, addressing the technical challenges we face and the potential implications of our findings for advancing our understanding of supersymmetry.

Figures

Figures reproduced from arXiv: 2411.15083 by the authors.

**Figure 1.** Graphical representation of the qubitization of the model. Left: The untruncated model, where the fermion is represented by 𝜓 while the boson by 𝜙. Right: The model qubitization, where the symbol made by a circle with two lines inside represents a qubit as a two-level system. The fermion needs one qubit while the boson with Λ = 2 𝐵 bosonic modes requires 𝐵 qubits. To finally encode the model on a quantum hardware, t… view at source ↗

**Figure 2.** The circuit representation of the ‘reverse-linear’ Realamplitude ansatz for the case of a system requiring 4 qubits. The ansatz is made by combining an initial and final layer of rotation gates around the y-axis, individually represented by a square. In the middle there is a layer of entangling gates, CNOTs represented by an elongated cross-like symbol, in reversed order, starting from the last two up to the first t… view at source ↗

**Figure 3.** Graphical representation of a boxplot with labels for its main components. falls outside this range is considered an outlier and individually labelled with a symbol. For a thorough presentation of boxplot and its use to analyze the periodic trends and properties of chemical elements see [19]. Furthermore, an interested reader may find it useful to see how boxplots were used in the field of quantum chemistry by [20],… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: VQE results for the ground state energy of a system with different superpontentials for a growing number of bosonic modes Λ presented using boxplots. All the results are obtained using the quantum simulator. Left: The calculation using the exact Qiskit statevector simu…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Recent progress in lattice supersymmetry: from lattice gauge theory to black holes

D. Kadoh,Recent progress in lattice supersymmetry: from lattice gauge theory to black holes, PoS LATTICE2015(2016) 017 [1607.01170]

work page Pith review arXiv 2016

[2] [2]

Bergner and S

G. Bergner and S. Catterall,Supersymmetry on the lattice,Int. J. Mod. Phys. A31 (2016) 1643005 [1603.04478]

arXiv 2016

[3] [3]

Schaich,Lattice studies of supersymmetric gauge theories, Eur

D. Schaich,Lattice studies of supersymmetric gauge theories, Eur. Phys. J. ST232 (2023) 305 [2208.03580]

arXiv 2023

[4] [4]

Preskill,Quantum Computing in the NISQ era and beyond,Quantum 2 (2018) 79 [1801.00862]

J. Preskill,Quantum Computing in the NISQ era and beyond,Quantum 2 (2018) 79 [1801.00862]

arXiv 2018

[5] [5]

Peruzzo, J

A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P.J. Love et al.,A variational eigenvalue solver on a photonic quantum processor, Nature Commun.5 (2014) 4213 [1304.3061]

arXiv 2014

[6] [6]

Quantum computing for lattice supersymmetry

C. Culver and D. Schaich,Quantum computing for lattice supersymmetry,PoS LATTICE2021(2022) 153 [2112.07651]

work page Pith review arXiv 2022

[7] [7]

Observation of Supersymmetry and its Spontaneous Breaking in a Trapped Ion Quantum Simulator

M.L. Cai, Y.K. Wu, Q.X. Mei, W.D. Zhao, Y. Jiang, L. Yao et al.,Observation of supersymmetry and its spontaneous breaking in a trapped ion quantum simulator,Nature Commun. 13 (2022) 3412 [2205.14860]

work page Pith review arXiv 2022

[8] [8]

Quantum Computing for the Wess-Zumino Model

C. Culver and D. Schaich,Quantum Computing for the Wess–Zumino Model, PoS LATTICE2022(2023) 008 [2301.02230]

work page Pith review arXiv 2023