Experimental state control by fast non-Abelian holonomic gates with a superconducting qutrit

TL;DR

This paper demonstrates a non-Abelian, non-adiabatic holonomic quantum gate in a superconducting transmon, showcasing robust state control and the implementation of fundamental quantum gates in a three-level system.

Contribution

It introduces a novel non-Abelian holonomic gate in a superconducting qutrit, realized through simultaneous microwave coupling, enabling arbitrary superpositions and fundamental quantum gate operations.

Findings

Successful creation of arbitrary superpositions in the qutrit subspace

Implementation of holonomic NOT and Hadamard gates

Verification of coherence using two-photon pulses

Abstract

Quantum state manipulation with gates based on geometric phases acquired during cyclic operations promises inherent fault-tolerance and resilience to local fluctuations in the control parameters. Here we create a general non-Abelian and non-adiabatic holonomic gate acting in the $(\ket{0},\ket{2})$ subspace of a three-level transmon fabricated in a fully coplanar design. Experimentally, this is realized by simultaneously coupling the first two transitions by microwave pulses with amplitudes and phases defined such that the condition of parallel transport is fulfilled. We demonstrate the creation of arbitrary superpositions in this subspace by changing the amplitudes of the pulses and the relative phase between them. We use two-photon pulses acting in the holonomic subspace to reveal the coherence of the state created by the geometric gate pulses and to prepare different superposition states. We also test the action of holonomic NOT and Hadamard gates on superpositions in the $(\ket{0},\ket{2})$ subspace.