Digital-Analog Quantum Computing

Purely digital classical computers are rather recent devices which are a consequence of the impressive technological development in miniaturization of electronics and microchips. However, until only few decades ago, digital computers had not sufficient computational power for most applications, so they usually employed analog parts for specific hard calculations. The situation nowadays in quantum computing is similar due to the small number of coherent controllable qubits allowed by current platforms. Even doubling the number of qubits yearly, a purely digital approach with error correction will not allow us to solve relevant problems in the following decades. Here, we will explore in detail a universal digital-analog approach employing the ubiquitous Ising Hamiltonian as the resource. We use this global Hamiltonian, together with local rotations, to generate an arbitrary unitary and we find efficient protocols, polynomial in the number of single-qubit rotations, to produce relevant families of Hamiltonian, such as arbitrary two-body Hamiltonians or, in general, k-body Hamiltonians. We introduce the concept of banged digital-analog quantum computing, in opposition to the stepwise, when single-qubit rotations are much faster than the natural time-scale of the Hamiltonian, which allows us to compute without switching on/off the global interaction. Employing natural models of errors, we compare the performance of digital against both stepwise and banged digital-analog protocols showing that, in general, digital-analog approaches perform better both in time and fidelity. Finally, we will also show that this emerging digital-analog approach can be applied not only to quantum simulations, but also to quantum algorithms. Indeed, we provide an efficient digital-analog description of the Quantum Fourier transform, comparing its performance against the pure digital approach in the presence of errors.