Multi-qubit gates in a trapped-ion quantum computer

Quantum computers promise to solve computational problems more efficiently than classical computers ever could. Trapped 171Yb+ ions in a linear Paul trap exposed to a magnetic field gradient have already been used to demonstrate quantum computing. The qubits are encoded in hyperfine states of the electronic ground state of 171Yb+ ions. The susceptibility of the qubit levels to magnetic fields by a linear Zeeman effect generates the coupling of the qubits and allows for individual addressing in frequency space.
In a register of qubits stored in a linear Paul trap, the coupling generated by the magnetic field gradient is an inherent all-to-all coupling. Implementing a given quantum circuit on a register of qubits requires tuning the coupling strength. Here tuning the coupling with up to four qubits is demonstrated using a pulsed dynamical decoupling sequence, which protects the qubits from dephasing while the coupling can be chosen.
Direct implementation of quantum gates with three or more qubits is necessary to exploit the full capabilities of a trapped-ion quantum computer. An example is the Toffoli gate implemented here. A driving field, applied to the target qubit, is used to perform a conditional rotation based on the control qubits state, while a dynamical decoupling sequence protects the coherence of the qubits. The Toffoli gate is then applied in a half-adder and is used to generate a three-qubit Greenberger Horne Zeilinger state.
Half-adders, which are used as elementary units in classical computer science, form the basis of classical arithmetic units. In a quantum computer, they can be realized using the Toffoli gate and a CNOT gate.
Perceptrons are a part of neural networks, a fundamental building block in modern computer science. Here a Perceptron gate is demonstrated on a register of three qubits where two qubits serve as control qubits and one as a perceptron. The characteristic tunable sigmoid excitation of the perceptron is shown using an adiabatic driving field interleaved with a dynamical decoupling sequence to prolong coherence times and tune the interaction strength between the qubits. The perceptron is then applied in a two-layer neural network to implement an XNOR operation.
In addition to its use as a qubit, the dependence of the qubit resonance on the magnetic field allows an ion qubit to be used as a quantum sensor for magnetic fields and thus, using a magnetic field gradient, to measure forces in the 10^(-23) N range.