Full-quantum variational dynamics simulation for time-dependent Hamiltonians with global spectral discretization

TL;DR

This paper introduces a fully quantum algorithm for simulating time-dependent Hamiltonian dynamics using spectral discretization and quantum singular value transformation, eliminating classical feedback and enabling efficient, scalable quantum simulations.

Contribution

It presents a novel full-quantum approach transforming variational differential equations into static linear equations solved via quantum algorithms, advancing beyond hybrid methods.

Findings

Achieves exponential convergence for smooth Hamiltonians

Provides quantum circuit depth independent of time steps

Validated through numerical simulations of quantum chemistry dynamics

Abstract

The most widely used approach for simulating the dynamics of time-dependent Hamiltonians via quantum computation depends on the quantum-classical hybrid variational quantum time evolution algorithm, in which ordinary differential equations of the variational coefficients for determining time evolution are solved via classical simulations with a time discretization method. We here present a full-quantum approach, in which ordinary differential equations of the variational coefficients are transformed into static linear equations via the Chebyshev spectral discretization method and then solved via the quantum singular value transformation algorithm. Our full quantum algorithm avoids classical feedback, achieves exponential convergence for smooth Hamiltonians, and yields a quantum circuit depth that is independent of the number of time steps. We demonstrate two implementation strategies, with a global formulation designed for fault-tolerant architectures and a sequential formulation tailored to near-term devices, and validate the approach through numerical simulations of proton-hydrogen charge-transfer dynamics, a prototypical time-dependent quantum chemistry problem. This work establishes a systematic pathway from quantum-classical hybrid variational quantum algorithms to full-quantum solvers for general time-dependent Hamiltonians, particularly those whose dynamics admit compact variational descriptions, opening a route toward full quantum computational advantages in time-dependent simulations.