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

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.

v2: Version consistent with one accepted for publication in Phys. Rev. D. v1: 1+29 pages, 4+1 figures

References in corpus (43)

• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Variational ansatz-based quantum simulation of imaginary time evolution
• A Theory of Trotter Error
• Theory of variational quantum simulation
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• Nearly optimal lattice simulation by product formulas
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits
• Quantum algorithm for simulating real time evolution of lattice Hamiltonians
• Towards Quantum Simulating QCD
• Adaptive Variational Quantum Dynamics Simulations
• Fast-forwarding of Hamiltonians and Exponentially Precise Measurements
• Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation
• Real-time chiral dynamics from a digital quantum simulation
• Provably accurate simulation of gauge theories and bosonic systems
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation
• Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters
• Quantum natural gradient generalised to noisy and non-unitary circuits
• Scalar and tensor neutrino interactions
• Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory
• How many quantum gates do gauge theories require?
• Critical flavour number of the Thirring model in three dimensions
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Sachdev-Ye-Kitaev model on a noisy quantum computer
• Identification of dynamical Lie algebras for finite-level quantum control systems
• A quantum hamiltonian simulation benchmark
• On the Scaling Limit of the 1D Hubbard Model at Half Filling
• Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations
• Lie-algebraic classical simulations for quantum computing
• Doubling Efficiency of Hamiltonian Simulation via Generalized Quantum Signal Processing
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Quantum Simulation of the N flavor Gross-Neveu Model
• Quantum Computation of the Massive Thirring Model
• Inhomogeneous phases in the 1+1 dimensional Gross-Neveu model at finite number of fermion flavors
• The phase diagram of quantum chromodynamics in one dimension on a quantum computer
• Analyzing the quantum approximate optimization algorithm: ansätze, symmetries, and Lie algebras
• Adaptive variational ground state preparation for spin-1 models on qubit-based architectures
• Quantum simulation of the phase transition of the massive Thirring model
• Hamiltonian simulation of minimal holographic sparsified SYK model
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations