[论文解读] Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors

Bojko Bakalov, Joao C. Getelina+3 more|arXiv (Cornell University)|Feb 25, 2026

Quantum Computing Algorithms and Architecture被引用 0

一句话总结

该论文展示了在一维晶格上对于任意费米子风格数的巨大Thirring和Gross–Neveu模型的量子模拟，分析通过AVQITE进行基态制备，并使用高阶积近似和QSVT估算门复杂度，同时给出动力 Lie 代数分类。

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.

研究动机与目标

• Motivate the study of fermionic quantum field theories on quantum computers, focusing on massive Thirring and Gross–Neveu models with arbitrary flavor number.
• Discretize these 1+1D models on a lattice and formulate a qubit-amenable Hamiltonian for simulation.
• Evaluate ground-state preparation fidelity and energy error for varying lattice size and flavor number.
• Provide gate-count estimates for Hamiltonian simulation using higher-order product formulas and QSVT.
• Classify the dynamical Lie algebras of these relativistic fermionic models to understand controllability and trainability.

提出的方法

• Formulate massive Thirring and Gross–Neveu models with Nf flavors on a 1D lattice and map to qubits via Jordan–Wigner.
• Use AVQITE to adaptively build a variational circuit that approximates the imaginary-time evolution to ground states.
• Compute equal-time fermion bilinear correlators from AVQITE-prepared ground states and compare with exact results.
• Analyze gate complexity for Hamiltonian simulation using higher-order product formulas (Suzuki–Trotter) with clustering of commuting Pauli strings.
• Analyze gate complexity for Hamiltonian simulation via block-encoding and quantum singular value transformation (QSVT).
• Classify the dynamical Lie algebras generated by Pauli terms of the fermionic Hamiltonians.

Figure 1 : Five-site lattice ( $L=5$ ) with three flavors ( $N_{f}=3$ ) of fermions (different colors) at each physical lattice site. Each blob (i.e., Dirac spinor) is represented by two qubits. The lattice spacing is denoted as $a$ .

实验结果

研究问题

• RQ1 What is the ground-state energy and fidelity achievable for the Thirring and GN models with various L and Nf using AVQITE?
• RQ2 What are the resource requirements (gates, depth) to simulate these four-fermion models on quantum processors using higher-order Trotter and QSVT?
• RQ3 How does the four-fermion interaction affect the dynamical Lie algebra and controllability of these models?
• RQ4 How well do static fermion correlators computed from AVQITE-prepared states match exact results?
• RQ5 What is the scaling of complexity with lattice size L and flavors Nf in the large-Nf limit?

主要发现

• AVQITE achieves ground-state preparation with fidelity around 0.99 and energy errors below 1% across tested cases up to L=5, Nf=4, m=0.5, g up to 0.2.
• Ground-state preparation for up to 20 qubits (n=2 Nf L) requires final ansatz with on the order of hundreds of two- and three-qubit operators, often ~O(n^2) despite starting from an O(n^3) pool.
• Static equal-time fermion bilinear correlators computed from AVQITE-prepared ground states match exact results to about three digits for the tested parameters, indicating correct mass-gap behavior.
• For large L and Nf, the four-fermion models have Hamiltonian blocks that can be efficiently block-encoded; QSVT offers favorable scaling relative to higher-order product formulas in these regimes.
• Product-formula costs scale as O(L^2 Nf^4 t^2/ε) for first-order, and as O(L^2 Nf^4 t^{1+1/p} ε^{-1/p}) for order-p; QSVT costs scale as O(L Nf^2 t (Nf + log(L Nf^2)) + (Nf + log(L Nf^2)) log(1/ε)).
• Dynamical Lie algebra classification shows these models belong to the same isomorphism class, aiding understanding of reachable states and trainability.

Figure 2 : Convergence of the AVQITE algorithm compared to the exact ground state energy (dashed lines) and fidelity (inset) for two representative examples from the set of simulations detailed in Table 1 .