Digital-Analog Quantum Computing with Qudits

TL;DR

This paper extends digital-analog quantum computing from qubits to qudits, proposing a protocol for simulating complex two-body Hamiltonians using analog blocks and single-qudit gates, enhancing quantum simulation capabilities.

Contribution

It introduces a novel framework for digital-analog quantum computing with d-level systems (qudits), broadening the scope of quantum simulation methods.

Findings

Protocol for simulating arbitrary two-body Hamiltonians with O(d^4 n^2) analog blocks

Demonstration of simulating many-body qudit spin Hamiltonians including magnetic quadrupolar terms

Extension of digital-analog quantum computing to higher-dimensional systems

Abstract

Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to $d$-level systems by conjugating an analog Hamiltonian block with single-qudit gates drawn from the Weyl-Heisenberg basis, which provides a natural set of operations for qudit architectures. More specifically, we propose a protocol to simulate arbitrary two-body Hamiltonians with at most $O(d^4 n^2)$ analog blocks. The power of this approach is illustrated by the simulation of many-body qudit spin Hamiltonians including magnetic quadrupolar terms.