Effective nonlocal parity-dependent couplings in qubit chains

For the efficient implementation of quantum algorithms, practical ways to generate many-body entanglement are a basic requirement. Specifically, coupling multiple qubit pairs at once can be advantageous and may provide multiqubit operations useful in the construction of hardware-tailored algorithms. Here we extend the theory of fractional state transfer and harness the simultaneous coupling of qubits on a chain to engineer a set of nonlocal parity-dependent quantum operations suitable for a wide range of applications. The resulting effective long-range couplings directly implement a parametrizable Trotter-step for Jordan-Wigner fermions, and they can be used for simulations of quantum dynamics, efficient state generation in variational quantum eigensolvers, parity measurements for error-correction schemes, and the generation of efficient multiqubit gates. Moreover, we present numerical simulations of the gate operation in a superconducting quantum circuit architecture, which show a high gate fidelity for realistic experimental parameters.