Hamiltonian simulation with explicit formulas for Digital-Analog Quantum Computing

TL;DR

This paper introduces an efficient method for digital-analog quantum simulation that expresses arbitrary two-body Hamiltonians as sums of local unitaries of Ising Hamiltonians, reducing classical computational complexity.

Contribution

It provides an exact polynomial-time solution for decomposing two-body Hamiltonians into local unitaries of Ising Hamiltonians, enabling scalable digital-analog quantum simulations.

Findings

Exact solution for Hamiltonian decomposition with quadratic terms

Reduced classical computational resources for circuit design

Facilitates scalable digital-analog quantum computing

Abstract

Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its digital gate-based counterpart, designing digital-analog circuits that employ optimal quantum resources often requires an exceedingly large classical computational time. In this work we find a suboptimal solution to this exponentially large problem, showing that it can be solved within polynomial computational time. In particular, we provide an exact solution for the problem of expressing arbitrary two-body Hamiltonians as the sum of local unitary transformations of an arbitrary Ising Hamiltonian, with the total number of required terms being at most quadratic in system size. This allows us to design a digital-analog simulation protocol that avoids employing numerical optimization over a large parameter space at the preprocessing stage, minimizing computational resources and allowing for further scaling.