End-to-end complexity for simulating the Schwinger model on quantum computers

Abstract

The Schwinger model is one of the simplest gauge theories. It is known that a topological term of the model leads to the infamous sign problem in the classical Monte Carlo method. In contrast to this, recently, quantum computing in Hamiltonian formalism has gained attention. In this work, we estimate the resources needed for quantum computers to compute physical quantities that are challenging to compute on classical computers. Specifically, we propose an efficient implementation of block-encoding of the Schwinger model Hamiltonian. Considering the structure of the Hamiltonian, this block-encoding with a normalization factor of $\mathcal{O}(N^3)$ can be implemented using $\mathcal{O}(N+{\log }^2(N/\epsilon ))$ T gates. As an end-to-end application, we compute the vacuum persistence amplitude. As a result, we found that for a system size $N=128$ and an additive error $\epsilon =0.01$, with an evolution time $t$ and a lattice spacing a satisfying $t/2a=10$, the vacuum persistence amplitude can be calculated using about $10^{13}$ T gates. Our results provide insights into predictions about the performance of quantum computers in the FTQC and early FTQC era, clarifying the challenges in solving meaningful problems within a realistic timeframe.

34 pages, 16 figures

References in corpus (17)

• Quantum Simulation for High Energy Physics
• Fixed-point quantum search with an optimal number of queries
• Finite-density lattice QCD and sign problem: current status and open problems
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Quantum simulation of non-equilibrium dynamics and thermalization in the Schwinger model
• Provably accurate simulation of gauge theories and bosonic systems
• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
• Hybridized Methods for Quantum Simulation in the Interaction Picture
• Hunting for quantum-classical crossover in condensed matter problems
• Variational thermal quantum simulation of the lattice Schwinger model
• Amplitude Estimation from Quantum Signal Processing
• Quantum computation of stopping power for inertial fusion target design
• Quench dynamics of the Schwinger model via variational quantum algorithms
• DMRG study of the higher-charge Schwinger model and its 't Hooft anomaly
• Trotter error with commutator scaling for the Fermi-Hubbard model

Cited by in corpus (1)

• Error Crafting in Mixed Quantum Gate Synthesis