Scalable uniform construction of highly-conditional quantum gates

TL;DR

This paper introduces a scalable, uniform method for constructing highly conditional quantum gates in trapped ion systems, reducing complexity and improving selectivity without extensive ancillary resources.

Contribution

The authors develop a novel composite pulse technique that simplifies the implementation of C^n-NOT gates, avoiding complex circuits and ancillary qubits, applicable across different regimes.

Findings

Efficient construction of C^n-NOT gates without ancillas.

Enhanced spatial addressing through narrowband composite pulses.

Applicable both inside and outside the Lamb-Dicke regime.

Abstract

We present a scalable uniform technique for construction of highly conditional C$^n$-NOT quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.