Benchmarking digital–analog quantum computation for the inhomogeneous two-body Ising model

Abstract Digital–analog quantum computation (DAQC) has recently been proposed as an alternative to the standard paradigm of digital quantum computation (DQC). DAQC generates entanglement through a continuous or analog evolution of the whole device, rather than by applying two-qubit gates. This manuscript describes an in-depth analysis of errors in DAQC implementing Ising Hamiltonians used for arbitrary computations, which was missing from the previous literature, revealing that, overall, DAQC errors scale less favorably compared to those in DQC. As demonstrated, for an all-to-all connectivity, the leading error source for DAQC scales like <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">Θ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>N</mml:mi> <mml:mn>4</mml:mn> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , while for the digital case, it scales like <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">O</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>N</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> for implementing an arbitrary Hamiltonian evolution. We further illustrate this result with our own simulations of the Quantum Fourier Transform, which in the previous literature were based on unrealistic parameter choices, biasing the result in favor of DAQC, and were limited to system sizes of up to only seven qubits. On the other hand, we develop a specific DAQC protocol for a star connectivity, which shows an advantage for the particular case of a GHZ state generation protocol.