The family of n-bit Toffoli gates, with the 2-bit Toffoli gate as the figurehead, are of great interest in quantum information as they can be used as universal gates and in quantum error correction, among other things. We present a single-step implementation of arbitrary n-bit Toffoli gates (up to a local change of basis), based on resonantly driving a single qubit that has a strong Ising coupling to n other qubits. The setup in the 2-qubit case turns out to be identical to the universal Barenco gate. The gate time and error are, in theory, independent of the number of control qubits, scaling better than conventional circuit decompositions. We note that our assumptions, namely strongly coupling n + 1 qubits and a driving frequency that scales with n, may break down for large systems. Still, our protocol could enhance the capabilities of intermediate scale quantum computers, and we discuss the prospects of implementing our protocol on trapped ions, Rydberg atoms, and on superconducting circuits. Simulations of the latter platform show that the Toffoli gate with two control bits attains fidelities of above 0.98 even in the presence of decoherence. We also show how similar ideas can be used to make a series of CNOT-gates in a single step. Lastly, we show how these can speed up the implementation of quantum error correcting codes, and simulate the encoding steps of the three-qubit bit flip code and the seven-qubit Steane code. arXiv:1910.07548v2 [quant-ph]

Quantum logic gates with many control qubits are essential in many quantum algorithms, but remain challenging to perform in current experiments. Trapped ion quantum computers natively feature the Mølmer–Sørensen (MS) entangling operation, which effectively applies an Ising interaction to all pairs of qubits at the same time. We consider a sequence of equal all-to-all MS operations, interleaved with single-qubit gates that act only on one special qubit. Using a connection with quantum signal processing techniques, we find that it is possible to perform an arbitray SU(2) rotation on the special qubit if and only if all other qubits are in the state 1 . Such controlled rotation gates with N − 1 control qubits require 2N applications of the MS gate, and can be mapped to a conventional Toffoli gate by demoting a single qubit to ancilla.