Single-step implementation of high fidelity \(n\)-bit Toffoli gate

Abstract

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. Here we present a simple single-step implementation of arbitrary \(n\)-bit Toffoli gates. The gate time of the implementation is independent of the number of control qubits, and the fidelities of our systems are well above 0.98 for up to five control qubits, with the major contribution to error coming from the qubit decoherence time. We discuss an implementation of the gates using superconducting circuits, however, the ideas presented in this paper is not limited to such implementation. We also show how these ideas can be used to make a series of CNOT-gates more efficient by performing all CNOT-gates in a single time step. Lastly we combine all of the above to create efficient quantum error correction codes. Specifically we simulate the three-qubit bit flip code and the Steane seven-qubit encoding, both with high fidelity.