Further quantum-gate methods using selective displacement of trapped ions

TL;DR

This paper presents advanced quantum gate techniques for trapped ions using state-selective displacement, demonstrating high-fidelity operations across various trap configurations and enabling complex multi-qubit gates like Toffoli.

Contribution

It generalizes previous methods to arbitrary trap separations, analyzes anharmonic effects, and proposes implementations for logical qubits and multi-qubit gates in ion traps.

Findings

High-fidelity gates for arbitrary trap separations

Implementation of non-neighbour ion gates and Toffoli gate

Effective suppression of unwanted evolution terms

Abstract

We consider quantum gates for trapped ions using state-selective displacement of the ions. We generalize earlier work in order to treat arbitrary separations between the traps. This requires the impact of anharmonicity arising from the Coulomb interaction to be estimated. We show that its effects are always small enough to allow high fidelity. In particular, the method can be applied to two ions in the same trap. We also show that gates between non-neighbour ions, and hence a Toffoli (three-qubit controlled-NOT) gate, can be achieved. We discuss how the gate can be applied to logical qubits encoded in the decoherence-free-subspace {|01>,|10>}, where each pair of ions stores a single qubit. We also suggest alternatives to the spin-echo method to suppress unwanted terms in the evolution.