Non-Clifford gate on optical qubits by nonlinear feedforward

Shunya Konno,Kosuke Fukui,Atsushi Sakaguchi,Petr Marek,Warit Asavanant,Radim Filip,Akira Furusawa,Fumiya Hanamura,Jun-Ichi Yoshikawa

doi:10.1103/physrevresearch.3.043026

Shunya Konno, Kosuke Fukui + Show 7 more

Open Access

https://doi.org/10.1103/physrevresearch.3.043026

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Abstract

In a continuous-variable optical system, the Gottesman-Kitaev-Preskill (GKP) qubit is a promising candidate for fault-tolerant quantum computation. To implement non-Clifford operations on GKP qubits, non-Gaussian operations are required. In this context, the implementation of a cubic phase gate by combining nonlinear feedforward with ancillary states has been widely researched. Recently, however, it is pointed out that the cubic phase gate is not the most suitable for non-Clifford operations on GKP qubits. In this work, we show that we can achieve linear optical implementation of non-Clifford operations on GKP qubit with high fidelity by applying the nonlinear feedforward originally developed for the cubic phase gate and using a GKP-encoded ancillary state. Our work shows the versatility of nonlinear feedforward technique important for optical implementation of the fault-tolerant continuous-variable quantum computation.

Highlights

Quantum computation holds a key to a computational power that supersedes current classical computers [1]
Our proposal shows that nonlinear feedforward is versatile and can be used for the cubic phase gate and for the T gate
In addition to the logical gates on GKP qubits, nonlinear feedforward is an important component of other types of non-Gaussian operations [41]

Summary

INTRODUCTION

Quantum computation holds a key to a computational power that supersedes current classical computers [1]. By combining nonlinear feedforward with appropriate ancillary states, we can implement one of the non-Gaussian operations called a cubic phase gate [10]. There is a large experimental loss because of low coupling efficiency between the input modes and an optical parametric oscillator, which enhances the nonlinear effect To avoid this problem, a measurement-induced QND gate has been widely studied and demonstrated in experiments recently [31,32,33]. By using offline ancillary states and feedforwards, we can apply nonlinear effects on the input modes indirectly without coupling loss This implementation of the QND gate is subject to another problem: the intrinsic noise in the measurement and feedforward due to the ancillary states, which is equal to quantum duty in the context of quantum teleportation [34]. Our paper shows the versatility of nonlinear feedforward important for optical realizations of quantum computing and is a crucial step toward the realization of the fault-tolerant optical universal quantum computer

NOTATION

IMPLEMENTATION OF T GATE

ACTUAL SETUP

NUMERICAL EVALUATION FOR FINITE SQUEEZING

DISCUSSION AND CONCLUSION