Realizing quantum linear regression with auxiliary qumodes

TL;DR

This paper proposes a hybrid quantum linear regression algorithm that combines discrete qubits and continuous qumodes, enhancing efficiency and feasibility while maintaining exponential speed-up.

Contribution

It introduces a novel hybrid approach using qubits and qumodes for quantum linear regression, improving practicality over all-qubit methods.

Findings

Hybrid approach is more efficient than all-qubit methods.

Finite squeezing improves algorithm efficiency in realistic setups.

Exponential quantum speed-up is retained with the hybrid method.

Abstract

In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear regression, which utilizes both discrete and continuous quantum variables, in contrast to existing wisdoms based solely upon discrete qubits. In our framework, data information is encoded in a qubit system, while information processing is tackled using auxiliary continuous qumodes via qubit-qumode interactions. Moreover, it is also elaborated that finite squeezing is quite helpful for efficiently running the quantum algorithms in realistic setup. Comparing with an all-qubit approach, the present hybrid approach is more efficient and feasible for implementing quantum algorithms, still retaining exponential quantum speed-up.