Parity-based mirror inversion for efficient quantum state transfer and computation in nearest-neighbor arrays

Abstract

We introduce an efficient scheme for quantum state transfer that uses a parity-based mirror inversion technique. We design efficient circuits for implementing mirror inversion in Ising ${\mathbit{\ensuremath{\sigma}}}_{\mathbf{X}}{\mathbit{\ensuremath{\sigma}}}_{\mathbf{X}}$ and ${\mathbit{\ensuremath{\sigma}}}_{\mathbf{Y}}{\mathbit{\ensuremath{\sigma}}}_{\mathbf{Y}}$ coupled systems and show how to analytically solve for system parameters to implement the operation in these systems. The key feature of our scheme is a three-qubit parity gate, which we design as a two-control one-target qubit gate. The parity gate operation is implemented by only varying a single control parameter of the system Hamiltonian and the difficulty of implementing this gate is equivalent to that of a controlled-not gate in a two-qubit system. By applying a sequence of $N+1$ parity-based controlled-unitary operations between nearest-neighbor qubits, where all qubits in an $N$-qubit chain function either as controls or targets, we are able to reverse the order of all qubits along the array. These operations are accomplished by varying only a single control parameter per data qubit. The control parameter depends on the physical system under consideration and on the choice of the designer. Since every qubit participates in the mirror-inversion process functioning either as a control or target, all nearest-neighbor couplings are used. Therefore, we do not need additional measures to cancel the effect of any unwanted interactions and the quantum cost of our scheme does not increase in systems that do not have the ability shut off couplings. Moreover, our scheme does not require additional ancillas, nor does it use a pre-engineered mirror-periodic Hamiltonian to govern the evolution of the system. Using our mirror inversion scheme, we also show how to implement a swap gate between two arbitrary remote qubits, move a block of qubits, and implement efficient computing between two remote qubits in nearest-neighbor layouts.