Digital-Analog quantum simulations using the cross-resonance effect
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Date
2021-05-27Author
González Raya, Tasio
Asensio Perea, Rodrigo
Céleri, Lucas C.
Lougovski, Pavel
Dumitrescu, Eugene F.
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PRX Quantum 2(2) : (2021) // Article ID 020328
Abstract
[EN] Digital-analog quantum computation aims to reduce the currently infeasible resource requirements
needed for near-term quantum information processing by replacing sequences of one- and two-qubit
gates with a unitary transformation generated by the systems’ underlying Hamiltonian. Inspired by this
paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first
order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on one-
dimensional (1D) chains and two-dimensional (2D) square lattices, which, in an appropriate reference
frame, results in a purely two-local Hamiltonian. By augmenting the analog Hamiltonian dynamics with
single-qubit gates we show how one may generate a larger variety of distinct analog Hamiltonians. We
then synthesize unitary sequences, in which we toggle between the various analog Hamiltonians as needed,
simulating the dynamics of Ising, XY, and Heisenberg spin models. Our dynamics simulations are Trotter
error-free for the Ising and XY models in 1D. We also show that the Trotter errors for 2D XY and 1D
Heisenberg chains are reduced, with respect to a digital decomposition, by a constant factor. In order to
realize these important near-term speedups, we discuss the practical considerations needed to accurately
characterize and calibrate our analog Hamiltonians for use in quantum simulations. We conclude with a
discussion of how the Hamiltonian toggling techniques could be extended to derive new analog Hamil-
tonians, which may be of use in more complex digital-analog quantum simulations for various models of
interacting spins.
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