Hamiltonian simulation in Zeno subspaces

TL;DR

This paper explores using the quantum Zeno effect with frequent measurements to simulate Hamiltonian dynamics efficiently, connecting it to existing algorithms and improving scaling through novel sequences.

Contribution

It introduces a Zeno-based approach for Hamiltonian simulation that reduces classical sampling overhead and links it to post-Trotter methods, with improved scaling techniques.

Findings

Zeno-based simulation matches randomized approach complexity

Second-order Zeno sequences enhance scaling

Connections established between Zeno and post-Trotter algorithms

Abstract

We investigate the quantum Zeno effect as a framework for designing and analyzing quantum algorithms for Hamiltonian simulation. We show that frequent projective measurements of an ancilla qubit register can be used to simulate quantum dynamics on a target qubit register with a circuit complexity similar to randomized approaches. The classical sampling overhead in the latter approaches is traded for ancilla qubit overhead in Zeno-based approaches. A second-order Zeno sequence is developed to improve scaling and implementations through unitary kicks are discussed. We show that the circuits over the combined register can be identified as a subroutine commonly used in post-Trotter Hamiltonian simulation methods. We build on this observation to reveal connections between different Hamiltonian simulation algorithms.