Generating arbitrary interaction patterns for multi-qubit quantum gates

An all-to-all interaction between qubits can significantly speed up quantum algorithms and enable the efficient encoding of fault-tolerant logical qubits. Here, we present a novel method for tuning the interaction between qubits that are coupled via an all-to-all Ising-type interaction. Specifically, we synthesise an arbitrary interaction matrix within a four-qubit quantum register and generate non-interacting subregisters. This method opens up a new path for the efficient synthesis of quantum algorithms for all-to-all coupled qubits.

This generally applicable method is demonstrated using laser cooled trapped ¹⁷¹Yb⁺ ions with qubits encoded into hyperfine states of their electronic ground states. An all-to-all Ising-type interaction between qubits in a quantum register of four ions is provided by magnetic gradient induced coupling (MAGIC). The interaction strength between radio frequency-controlled qubits is thus determined by the trapping potential and the magnetic field gradient. We demonstrate how to tune the interaction between the qubits using a novel pulsed dynamical decoupling scheme, without altering the physical parameters that characterise the trapping potential and the magnetic field, while simultaneously preserving the coherence of the qubits.