A regularized function inserted into Carleman linearization, derived from a Möbius conformal map, removes the long-time divergence for logistic, KPP-Fisher, and phase-field models and supports an LCU quantum implementation.
Theory of Trotter Error with Commutator Scaling
9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, $k$-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a byproduct. Our analysis reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of $5$, and is close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and constant prefactor.
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background 1representative citing papers
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Quantum algorithm for GPDs in Schwinger model using Wilson fermions, with polynomial resource scaling and exact-diagonalization benchmarks matching theory.
Linear-programming method for conjugating local fermionic unitaries with free evolution realizes arbitrary complex tunneling coefficients in fermionic lattice models constrained only by connectivity.
The Projector Variational Ansatz (PVA) is a new VQE ansatz that can match ISQ-QSP or ADAPT-VQE structures and converges with shallower circuits than standard ADAPT-VQE in experiments.
An algorithm is presented for estimating distribution complexity of electronic structure Hamiltonians, with O(N^3) entanglement estimation per fragment and quadratic/exponential reductions in distribution cost for quantum and classical interconnects.
In a neutrino-gas model, the many-body Hamiltonian yields different evolution timescales and asymptotics than the quantum kinetic approach with collisions, while quantum resources for the full case sit at the low end for HEP problems and mid-to-high for quantum chemistry.
New analytic and Monte Carlo-assisted method tightens energy-based boson truncation bounds, reducing volume dependence in (1+1)D scalar and (2+1)D U(1) gauge theories.
Quantum simulation methods for Thirring and Gross-Neveu fermionic models with arbitrary flavors, including gate complexity bounds and ground-state preparation up to 20 qubits.
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Fast and Parallel High-Rate STAR Architecture for Megaquop Quantum Simulation
A symmetry-co-designed high-rate QEC architecture with parallel STAR injection on bivariate bicycle codes achieves ~5.5x space savings for TFIM and Fermi-Hubbard simulations versus surface-code STAR.
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Distribution Complexity of Electronic Structure Simulations on Quantum Supercomputers
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