2 research outputs found
Digital-Analog Quantum Simulations Using The Cross-Resonance Effect
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 1D chains and 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, , and Heisenberg
spin models. Our dynamics simulations are Trotter error-free for the Ising and
models in 1D. We also show that the Trotter errors for 2D 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 Hamiltonians which may be of use in more complex
digital-analog quantum simulations for various models of interacting spins