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arXiv:2208.05906 · Physical review. D/Physical review. D.

Quantum simulation of the N -flavor Gross-Neveu model

Muhammad Asaduzzaman, Goksu Can Toga, Simon M. Catterall, Yannick Meurice, Ryo Sakai

Published Dec 30, 2022• 14 citations
arXivHTMLPDF

Abstract

We discuss the use of quantum simulation to study an $N$-flavor theory of interacting relativistic fermions in ($1+1$) dimensions on noisy intermediate-scale quantum (NISQ)-era machines. The case of two flavors is particularly interesting as it can be mapped to the Hubbard model. We derive the appropriate qubit Hamiltonians and associated quantum circuits. We compare classical simulation and density matrix renormalization group/time-evolving blocked decimation calculations with the results of quantum simulation on various platforms for $N=2$ and 4-flavors. We demonstrate that the four steps needed for calculations of real-time scattering can be implemented using current NISQ devices.

DOI
10.1103/physrevd.106.114515

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We discuss the use of quantum simulation to study an NNN-flavor theory of interacting relativistic fermions in (1+11+11+1) dimensions on noisy intermediate-scale quantum (NISQ)-era machines. The case of two flavors is particularly interesting as it can be mapped to the Hubbard model. We derive the appropriate qubit Hamiltonians and associated quantum circuits. We compare classical simulation and density matrix renormalization group/time-evolving blocked decimation calculations with the results of quantum simulation on various platforms for N=2N=2N=2 and 4-flavors. We demonstrate that the four steps needed for calculations of real-time scattering can be implemented using current NISQ devices.
We present a scalable quantum simulation framework for real-time dynamics of the multi-flavor Gross-Neveu model in 1+1 dimensions. Using superconducting quantum processors at utility scale, we develop a hardware-efficient Trotterization whose per-step circuit depth scales with fermion flavor number rather than total system size, enabling simulations beyond 100 qubits. A central contribution of this work is the Localized Diagonal Operator Approximation (LDOA), which systematically reduces the overhead associated with quartic interactions. We formulate diagonal unitary synthesis as a structured least-squares problem in phase space and obtain analytic solutions via the Moore-Penrose pseudoinverse. This formulation provides a principled and quantitatively controlled approximation: in the small Trotter-step regime, the unitary error is directly linked to the phase reconstruction error and vanishes asymptotically as the Trotter step size decreases. This establishes a clear mathematical foundation for the LDOA while significantly reducing two-qubit gate counts and circuit depth, and is broadly applicable to diagonal quantum operators with long-range structure, making it particularly well suited for quantum hardware with limited qubit connectivity. Using these techniques, we run large-scale simulations on IBM superconducting processors and study real-time observables, including density-density correlators. We benchmark against exact diagonalization and tensor network-based methods, finding strong agreement across system sizes. These results show that combining hardware-aware circuit design with rigorous approximations enables practical near-term simulation of interacting fermionic field theories and provides a scalable pathway toward more complex quantum field theory simulations.
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, NfN_fNf​, discretized on a spatial one-dimensional lattice of size LLL 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 NfN_fNf​ and LLL. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with Nf=1,2,3,4N_f = 1,2,3,4Nf​=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 NfN_fNf​ 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.
The quantum simulation of fermionic gauge field theories is one of the anticipated uses of quantum computers in the noisy intermediate-scale quantum (NISQ) era. Recently work has been done to simulate properties of the fermionic Z2{\mathbb{Z}}_{2}Z2​ gauge field theory in (1+1)D(1+1)\mathrm{D}(1+1)D and the pure gauge theory in (2+1)D(2+1)\mathrm{D}(2+1)D. In this work, we investigate various options for simulating the fermionic Z2{\mathbb{Z}}_{2}Z2​ gauge field theory in (2+1)D(2+1)\mathrm{D}(2+1)D. To simulate the theory on a NISQ device it is vital to minimize both the number of qubits used and the circuit depth. In this work we propose ways to optimize both criteria for simulating time dynamics. In particular, we develop a new way to simulate this theory on a quantum computer, with minimal qubit requirements. We provide a quantum circuit for simulating a single first-order Trotter step that minimizes the number of 2-qubit gates needed and gives comparable results to methods requiring more qubits. Furthermore, we investigate variational Trotterization approaches that allow us to further decrease the circuit depth.
In this study, we investigate Trotter evolution in the Gross-Neveu and hyperbolic Ising models in two spacetime dimensions, using quantum computers. We identify different sources of errors prevalent in various quantum processing units and discuss challenges to scale up the size of the computation. We present benchmark results obtained on a variety of platforms and employ a range of error mitigation techniques to address coherent and incoherent noise. By comparing these mitigated outcomes with exact diagonalization results and density matrix renormalization group calculations, we assess the effectiveness of our approaches. Moreover, we demonstrate the implementation of an out-of-time-ordered correlator (OTOC) protocol using IBM's quantum computers.
A quantum algorithm to simulate the real time dynamics of two-flavor massive Gross-Neveu model is presented in Schrodinger picture. We implement the simulation on a classic computer by applying the matrix product state representation. The real time evolutions of up to four particles on a site in initial state are figured out in space-time coordinate. The state evolutions are effectively affected by fermion mass and coupling constant of the model. Especially when the mass of fermion is small enough and the coupling is strong enough, the fundamental fermions evolve synchronistically in space from the two-fermion and four-fermion initial states. These are also the conditions on which the bound states made up of fundamental fermion pairs were found to arise automatically in the literatures.
Quantum computing has long been an experimental technology with the potential to simulate, at scale, phenomena which on classical devices would be too expensive to simulate at any but the smallest scales. Over the last several years, however, it has entered the NISQ era, where the number of qubits are sufficient for quantum advantage but substantial noise on hardware stands in the way of this achievement. This thesis details NISQ device-centered improvements to techniques of quantum simulation of the out-of-equilbrium real-time dynamics of lattice quantum chromodynamics (LQCD) and of dense 3-flavor neutrino systems on digital quantum devices. The first project concerning LQCD is a comparison of methods for implementing the variational quantum eigensolver (VQE) that initializes the ground state of an SU(3) plaquette-chain. The thesis then pivots to a 1+1D lattice of quarks interacting with an SU(3) gauge-field. A VQE-based state-preparation for the vacua and a Trotterized time-evolution circuit is designed and applied to the problems of simulating beta and neutrinoless double beta decay. Finally, these circuits are adapted to a version useable on quantum devices with nearest-neighbor connectivity with minimal overhead, with an eye towards utilizing the higher qubit count of such devices for hadron dynamics and scattering. This thesis covers two projects that concern dense 3-flavor neutrino systems. The first details design and testing of Trotterized time-evolution circuits on state-of-the-art quantum devices. The second, motivated by the Gottesman-Knill theorem's result that deviation from stabilizer states ("magic") is necessary for a problem to exhibit quantum advantage, details results with implications for the Standard Model in general that the 3 flavor ultradense neutrino systems with the highest, most-persistent magic are those that start with neutrinos in all 3 flavors.