# Digital-Analog Quantum Computation

## TL;DR

This paper introduces digital-analog quantum computing (DAQC), merging digital single-qubit operations with analog multi-qubit entangling blocks, demonstrating its universality, efficiency, and improved performance over purely digital schemes within NISQ device constraints.

## Contribution

It proposes a novel DAQC framework using Ising Hamiltonian unitaries, providing explicit protocols and comparing sequential and always-on approaches, showing advantages over digital-only methods.

## Key findings

- DAQC is universal and efficient for simulating spin Hamiltonians.
- Numerical tests show DAQC outperforms purely digital schemes.
- The approach combines robustness of analog with digital flexibility.

## Abstract

Digital quantum computing paradigm offers highly-desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multi-qubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. We construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and $M$-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise~DAQC) with an always-on multi-qubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.