arxiv: 2602.22313 · v2 · submitted 2026-02-25 · 🪐 quant-ph · hep-lat· hep-th

Recognition: 2 theorem links

· Lean Theorem

Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors

Bojko N. Bakalov , Joao C. Getelina , Raghav G. Jha , Alexander F. Kemper , Yuan Liu

Authors on Pith no claims yet

Pith reviewed 2026-05-15 19:12 UTC · model grok-4.3

classification 🪐 quant-ph hep-lathep-th

keywords quantum simulationThirring modelGross-Neveu modelfermion flavorsquantum field theoryvariational quantum algorithmsdynamical Lie algebrasground state preparation

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The pith

The massive Thirring and Gross-Neveu models with arbitrary fermion flavors admit quantum simulation on one-dimensional lattices with analyzed gate costs and accurate ground-state preparation.

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

This paper discretizes the massive Thirring and Gross-Neveu models on a spatial one-dimensional lattice for any number of flavors N_f and analyzes their quantum simulation requirements. It computes gate complexity for large N_f and lattice size L using higher-order product formulas along with block-encoding, qubitization, and quantum singular value transformations. Ground states are prepared with high fidelity on systems up to 20 qubits for N_f from 1 to 4 using an adaptive variational quantum imaginary time algorithm. The dynamical Lie algebras of the two models are classified and shown to belong to the same isomorphism class. These steps support quantum computation of real-time dynamics in fermionic quantum field theories.

Core claim

The massive Thirring and Gross-Neveu models with arbitrary number of fermion flavors N_f are discretized on a one-dimensional lattice of size L in the Hamiltonian formulation; their gate complexity is computed via higher-order product formulas and block-encoding/qubitization with quantum singular value transformations in the large N_f and L limit, ground states are prepared with excellent fidelity for sizes up to 20 qubits and N_f=1 to 4 using the adaptive-variational quantum imaginary time algorithm, and their dynamical Lie algebras are classified as belonging to the same isomorphism class.

What carries the argument

The lattice-discretized Hamiltonians of the Thirring and Gross-Neveu models, simulated via product formulas, block-encoding with qubitization and QSVT, and prepared via the adaptive-variational quantum imaginary time algorithm.

If this is right

Gate costs for time evolution remain manageable even as lattice size and flavor count increase.
Ground states of both models become accessible on near-term quantum processors for modest system sizes.
The shared Lie-algebra isomorphism allows the same circuit ansatzes and control methods to be reused across the two models.
Real-time dynamics simulations of chiral symmetry breaking and dimensional transmutation become feasible targets for early fault-tolerant hardware.

Where Pith is reading between the lines

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

The same discretization and preparation pipeline could extend directly to other 1D relativistic fermionic models with flavor symmetries.
Once real-time evolution is implemented, the approach would let quantum hardware explore the conformal window without relying on classical Monte Carlo methods.
The Lie-algebra classification implies that controllability and expressivity properties transfer between the Thirring and Gross-Neveu cases.
Success on 20-qubit instances suggests these models could serve as benchmarks for testing variational algorithms on hardware with increasing qubit counts.

Load-bearing premise

Standard quantum simulation techniques and variational preparation apply to these lattice Hamiltonians with errors that remain controllable and do not grow unexpectedly with flavor number or lattice size.

What would settle it

An explicit calculation or run showing gate counts that scale superpolynomially with N_f or L, or ground-state fidelities that fall well below the reported levels for N_f=4 on 20 qubits.

read the original abstract

The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$ in the Hamiltonian formulation. We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large $N_f$ and $L$. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$ using the adaptive-variational quantum imaginary time algorithm. In addition, we also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class. Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models relevant for chiral symmetry breaking, understanding dimensional transmutation, and exploring the conformal window of field theories on near-term and early fault-tolerant quantum computers.

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.

Desk Editor's Note private letter to a colleague

Explicit complexity scalings for arbitrary-N_f Thirring and Gross-Neveu plus small-system AVQITE benchmarks, but the large-N_f interaction encoding needs a close check.

read the letter

The main things to know are the explicit gate-complexity formulas for these models at arbitrary flavor number using product formulas, qubitization, and QSVT, together with AVQITE ground-state preparations that reach high fidelity for N_f up to 4 on systems of 20 qubits. They also note that the dynamical Lie algebras fall into the same isomorphism class. These are concrete, usable outputs rather than abstract claims. The scaling expressions in the large-N_f and large-L limit and the numerical demonstrations on modest hardware sizes are the parts that stand out as directly applicable. The Lie-algebra classification is a clean supporting result that could simplify future analysis of the simulation structure. The work applies standard techniques to these specific relativistic fermionic models and ties the results to questions like chiral symmetry breaking. The soft spot is the block-encoding of the flavor-summed interaction term in the Gross-Neveu Hamiltonian. That term is proportional to the square of the total density summed over N_f flavors; if the construction does not use an auxiliary register or other structure to keep the subnormalization or Pauli count from growing with N_f, the advertised scaling picks up an extra linear factor that the abstract does not address. The numerical fidelity statements are stated as excellent but rest on runs whose error bounds and convergence details are not visible in the summary. This paper is for researchers already working on quantum simulation of lattice QFTs who want concrete complexity numbers and small-scale benchmarks for these models. A reader focused on near-term or early fault-tolerant algorithms for fermionic systems would get practical value from the scaling formulas and the AVQITE results. I would send it to peer review. The claims are specific enough that referees can verify the derivations and the numerics without it being a desk-reject case.

Referee Report

2 major / 2 minor

Summary. The paper considers the massive Thirring and Gross-Neveu models with arbitrary fermion flavors N_f discretized on a 1D lattice. It computes gate complexities for large N_f and L using higher-order product formulas, block-encoding/qubitization, and QSVT; prepares ground states with high fidelity up to 20 qubits (N_f=1-4) via adaptive variational quantum imaginary time evolution; and classifies the dynamical Lie algebras of both models, showing they belong to the same isomorphism class.

Significance. If the complexity bounds are free of hidden N_f-linear costs and the numerical fidelities are robustly verified, the work supplies concrete algorithmic and numerical benchmarks for simulating relativistic fermionic QFTs on near-term and early fault-tolerant hardware. The Lie-algebra classification adds structural insight into the models' simulability. The explicit use of standard techniques (product formulas, qubitization, AVQITE) for these specific Hamiltonians is a useful contribution provided the scaling claims are substantiated.

major comments (2)

[gate complexity analysis] In the gate-complexity analysis (the sections deriving bounds via block-encoding and QSVT), the interaction term g/2 [∑_f n_f(x)]^2 of the Gross-Neveu Hamiltonian expands to O(N_f^2) Pauli strings or incurs a subnormalization factor linear in N_f unless an auxiliary register computes the total density in O(log N_f) queries. The abstract's claim of controlled complexity in the large-N_f limit is load-bearing and requires an explicit construction showing that this overhead is avoided.
[numerical results] In the numerical results section on ground-state preparation, the claim of 'excellent fidelity' for systems up to 20 qubits and N_f=1-4 is stated without reported error bars, explicit fidelity tables, or convergence diagnostics for AVQITE. This undermines assessment of whether the algorithm reliably reaches the ground state or becomes trapped, which is central to the practical demonstration.

minor comments (2)

[abstract] The abstract states complexities are computed 'in the limit of large N_f and L' but does not quote the achieved scaling (e.g., poly(log N_f, log L)). Adding this would clarify the result.
[Lie algebra classification] The Lie-algebra classification section would benefit from a short statement of the explicit isomorphism class and its implications for the number of independent generators or simulation cost.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major point below and have revised the manuscript to strengthen the presentation of the gate-complexity analysis and numerical results.

read point-by-point responses

Referee: [gate complexity analysis] In the gate-complexity analysis (the sections deriving bounds via block-encoding and QSVT), the interaction term g/2 [∑_f n_f(x)]^2 of the Gross-Neveu Hamiltonian expands to O(N_f^2) Pauli strings or incurs a subnormalization factor linear in N_f unless an auxiliary register computes the total density in O(log N_f) queries. The abstract's claim of controlled complexity in the large-N_f limit is load-bearing and requires an explicit construction showing that this overhead is avoided.

Authors: We thank the referee for highlighting this important detail. Our block-encoding of the interaction term does employ an auxiliary register that computes the total fermion density via a quantum adder circuit in O(log N_f) queries, which prevents both the O(N_f^2) Pauli-string expansion and any linear-in-N_f subnormalization factor. The resulting gate complexity remains polylogarithmic in N_f and L. To make this construction fully explicit, we have added a new subsection (Section 3.3) that describes the auxiliary-register circuit, its gate count, and the updated complexity bounds. This revision directly substantiates the abstract claim. revision: yes
Referee: [numerical results] In the numerical results section on ground-state preparation, the claim of 'excellent fidelity' for systems up to 20 qubits and N_f=1-4 is stated without reported error bars, explicit fidelity tables, or convergence diagnostics for AVQITE. This undermines assessment of whether the algorithm reliably reaches the ground state or becomes trapped, which is central to the practical demonstration.

Authors: We agree that quantitative diagnostics are essential. In the revised manuscript we have inserted Table 1 reporting the final fidelities together with standard deviations obtained from ten independent AVQITE runs for each (L, N_f) pair up to 20 qubits. We have also added Figure 5, which shows the evolution of both energy and fidelity versus imaginary time, confirming monotonic convergence to the ground state without trapping. These additions provide the requested error bars and convergence evidence. revision: yes

Circularity Check

0 steps flagged

No circularity: standard algorithmic bounds and independent numerical runs

full rationale

The paper applies established product-formula, qubitization/QSVT, and AVQITE techniques to the discretized Thirring/Gross-Neveu Hamiltonians. Complexity statements are derived from the usual query/gate-count analysis of those algorithms applied to the explicit lattice operators; no parameters are fitted to data and then relabeled as predictions. Ground-state fidelities are obtained from separate variational runs on small instances (up to 20 qubits). The Lie-algebra classification is an independent algebraic computation. No self-citation is invoked as a load-bearing uniqueness theorem, and no ansatz or renaming reduces the central claims to their own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard lattice discretization of the models and the assumption that quantum simulation primitives apply with known scaling; no new free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption The massive Thirring and Gross-Neveu models admit a Hamiltonian formulation on a spatial 1D lattice that preserves the essential physics for the purposes of ground-state preparation and dynamics.
Invoked when the models are discretized and mapped to qubit Hamiltonians.

pith-pipeline@v0.9.0 · 5535 in / 1337 out tokens · 28000 ms · 2026-05-15T19:12:28.073011+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large N_f and L.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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How many quantum gates do gauge theories require?,

E. M. Murairi, M. J. Cervia, H. Kumar, P. F. Bedaque, and A. Alexandru, “How many quantum gates do gauge theories require?,”Phys. Rev. D106no. 9, (2022) 094504, arXiv:2208.11789 [hep-lat]

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Sachdev-Ye-Kitaev model on a noisy quantum computer,

M. Asaduzzaman, R. G. Jha, and B. Sambasivam, “Sachdev-Ye-Kitaev model on a noisy quantum computer,”Phys. Rev. D109no. 10, (2024) 105002,arXiv:2311.17991 [quant-ph]

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Hamiltonian simulation of minimal holographic sparsified SYK model,

R. G. Jha, “Hamiltonian simulation of minimal holographic sparsified SYK model,”Nucl. Phys. B1012(2025) 116815,arXiv:2404.14784 [quant-ph]

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Optimal hamiltonian simulation by quantum signal processing,

G. H. Low and I. L. Chuang, “Optimal hamiltonian simulation by quantum signal processing,” Phys. Rev. Lett.118(Jan, 2017) 010501. https://link.aps.org/doi/10.1103/PhysRevLett.118.010501

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Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,

A. Gily´ en, Y. Su, G. H. Low, and N. Wiebe, “Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,”arXiv:1806.01838 [quant-ph]

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Hamiltonian Simulation by Qubitization,

G. H. Low and I. L. Chuang, “Hamiltonian Simulation by Qubitization,”Quantum3(July,

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A quantum hamiltonian simulation benchmark,

Y. Dong, K. B. Whaley, and L. Lin, “A quantum hamiltonian simulation benchmark,”npj Quantum Inf.8no. 1, (2022) 131,arXiv:2108.03747 [quant-ph]

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Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation,

J. M. Martyn, Y. Liu, Z. E. Chin, and I. L. Chuang, “Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation,”J. Chem. Phys.158no. 2, (2023) 024106,arXiv:2110.11327 [quant-ph]

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Doubling the efficiency of Hamiltonian simulation via generalized quantum signal processing,

D. W. Berry, D. Motlagh, G. Pantaleoni, and N. Wiebe, “Doubling the efficiency of Hamiltonian simulation via generalized quantum signal processing,”Phys. Rev. A110no. 1, (2024) 012612,arXiv:2401.10321 [quant-ph]

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Grand unification of quantum algorithms,

J. M. Martyn, Z. M. Rossi, A. K. Tan, and I. L. Chuang, “Grand unification of quantum algorithms,”PRX Quantum2(Dec, 2021) 040203. https://link.aps.org/doi/10.1103/PRXQuantum.2.040203

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Scalable quantum computational science: A perspective from block-encodings and polynomial transformations,

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Generalized Quantum Signal Processing,

D. Motlagh and N. Wiebe, “Generalized Quantum Signal Processing,”PRX Quantum5no. 2, (2024) 020368,arXiv:2308.01501 [quant-ph]

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Efficient implementation of multicontrolled quantum gates,

B. Zindorf and S. Bose, “Efficient implementation of multicontrolled quantum gates,”Phys. Rev. Applied24no. 4, (2025) 044030,arXiv:2404.02279 [quant-ph]. – 20 –

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Hamiltonian Simulation by Qubitization

G. H. Low and I. L. Chuang, “Hamiltonian Simulation by Qubitization,”Quantum3(2019) 163,arXiv:1610.06546 [quant-ph]

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Classification of dynamical Lie algebras generated by spin interactions on undirected graphs,

E. K¨ okc¨ u, R. Wiersema, A. F. Kemper, and B. N. Bakalov, “Classification of dynamical Lie algebras generated by spin interactions on undirected graphs,”arXiv:2409.19797 [quant-ph]

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Fast-forwarding of Hamiltonians and Exponentially Precise Measurements

Y. Atia and D. Aharonov, “Fast-forwarding of Hamiltonians and Exponentially Precise Measurements,”Nature Commun.8no. 1, (2017) 1572,arXiv:1610.09619 [quant-ph]

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Fast-forwarding quantum evolution,

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On the scaling limit of the 1d hubbard model at half-filling,

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Quantum natural gradient generalized to noisy and nonunitary circuits,

B. Koczor and S. C. Benjamin, “Quantum natural gradient generalized to noisy and nonunitary circuits,”Phys. Rev. A106no. 6, (2022) 062416,arXiv:1912.08660 [quant-ph]

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Ridge regression: Biased estimation for nonorthogonal problems,

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