Single-qubit rotations on a binomial code without ancillary qubits

TL;DR

This paper presents a method for performing single-qubit rotations on binomial codes in bosonic systems without the need for ancillary qubits, simplifying quantum operations for NISQ devices.

Contribution

It introduces a novel approach to implement logical qubit rotations on binomial codes without ancillary qubits, using parametric drives and detuning.

Findings

Enables $X$-axis rotations via two-frequency parametric drives.

Realizes $Z$-axis rotations through detuning.

Reduces qubit requirements for logical operations.

Abstract

Great attention has been paid to binomial codes utilizing bosonic systems as logical qubits with error correction capabilities. However, implementing single-qubit rotation operations on binomial codes has proven challenging, requiring an ancillary qubit in previous approaches. Here, we propose a method for performing logical qubit rotation on binomial codes without requiring an ancillary qubit. Specifically, we explain how to implement $X$-axis rotations by simultaneously applying two-frequency parametric drives to resonators with nonlinearity. Furthermore, we show that $Z$-axis rotations could be realized with the detuning. Due to the reduction of the need for the ancillary qubit for the logical qubit rotation, our proposed approach is advantageous for quantum computation in the NISQ era, where the number of qubits is limited.