Digital-analog quantum computation

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, establishing an avenue for achieving quantum advantage with near-term quantum hardware. arXiv:1812.03637v1 [quant-ph]

Digital-analog quantum algorithm for the quantum Fourier transform

“…Merging these two approaches, leads to a paradigm known as digital-analog quantum computation [7,[30][31][32]. A digitalanalog protocol, built combining analog blocks with digital steps, shows the flexibility of the digital gate model [33] and the robustness of the analog simulation model.…”

“…A formal definition of these elements could be found in Ref. [7]. Here, we give a practical definition: a digital step is constituted by single-qubit unitary operations whereas an analog block is constituted by the time evolution of a known interaction Hamiltonian.…”

“…The problem reduces to find an appropriate map between t F g j,k and gt nm by slicing the homogeneous time evolution U zz (t) into N(N − 1)/2 analog blocks of different time lengths t nm , sandwiched by the local rotations X (n) X (m) , as explained in Ref. [7] and depicted in Fig. 1.…”

“…This case is discussed in detail in Ref. [7]. The method aforementioned is called stepwise DAQC (sDAQC) and, under ideal circumstances, i.e.…”

“…A possible approach to bypass the NISQ-era hardware limitations and solve relevant problems was introduced by A. Parra-Rodriguez et al [7]. They proposed a universal paradigm to perform quantum computation, inspired in the evolution of classical computation, called digital-analog quantum computation (DAQC).…”