Near-Optimal Quantum Time Evolution Circuits via Provably Convergent Compression

TL;DR

This paper introduces a method for variational quantum circuit compression that guarantees near-optimal gate complexity for simulating Hamiltonian time evolution, demonstrated on complex lattice models.

Contribution

It provides a convergent initialization strategy for variational compression, achieving near-optimal quantum circuits for local Hamiltonians with practical implementation insights.

Findings

Achieves gate complexity of O(N t polylog(N t/ε)) for local Hamiltonians.

Demonstrates encoding of Heisenberg antiferromagnet evolution on Kagome lattice.

Proposes implementation scheme for ion-trap quantum computers.

Abstract

Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior. In this work, we provide a recipe for choosing the initial point of such variational optimizations that guarantees convergence to a quantum circuit with near-optimal gate complexity $\mathcal{O}\left( N \, t \, \text{polylog}(N \, t/\epsilon) \right)$ for all local and translationally invariant Hamiltonians. We demonstrate our method by encoding the globally controlled time evolution of a Heisenberg antiferromagnet on a Kagome lattice. For $N = 48$ sites, evolution time $t=0.1$ and infidelity $\epsilon\approx1\%$, the controlled time-evolution circuit requires 960 two-qubit B gates, for which we propose a straightforward implementation scheme for ion-trap setups. Thereby, our recipe extends digital quantum simulators toward system sizes and geometries that are challenging for classical computation.