Digital-Analog Quantum Simulations Using The Cross-Resonance Effect

Digital-analog quantum computation aims to reduce the resource requirements needed for quantum information processing by augmenting circuits with transformations generated from a system’s underlying Hamiltonian. We consider an extension of the cross-resonance effect, up to first order in the drive amplitude over detuning, from a pair of qubits to 1D chains and 2D lattices. In an appropriate reference frame, we find a two-local Hamiltonian comprised of non-commuting interactions. Augmenting the analog dynamics with single-qubit gates, we generate families of analog Hamiltonians. Toggling between these Hamiltonians, we design sequences simulating the dynamics of Ising, XY, and Heisenberg models. Our 1D Ising and XY sequences are Trotter error-free and 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. Our Hamiltonian toggling techniques could be extended to derive new Hamiltonians which may be of use in more complex digital-analog quantum simulations for various models.