Natural parameterized quantum circuit

TL;DR

This paper introduces the natural parameterized quantum circuit (NPQC), which improves variational quantum algorithms by leveraging Euclidean quantum geometry, enabling faster training, better benchmarking, and enhanced state preparation on NISQ devices.

Contribution

The paper presents NPQC, a novel quantum circuit design that simplifies training, allows parameter estimation via sampling, and achieves minimal quantum Cramér-Rao bound for quantum metrology.

Findings

NPQC speeds up variational quantum algorithm training.

NPQC enables efficient parameter estimation and benchmarking.

NPQC achieves minimal quantum Cramér-Rao bound for quantum metrology.

Abstract

Noisy intermediate scale quantum computers are useful for various tasks such as state preparation and variational quantum algorithms. However, the non-Euclidean quantum geometry of parameterized quantum circuits is detrimental for these applications. Here, we introduce the natural parameterized quantum circuit (NPQC) that can be initialised with a Euclidean quantum geometry. The initial training of variational quantum algorithms is substantially sped up as the gradient is equivalent to the quantum natural gradient. Further, we show how to estimate the parameters of the NPQC by sampling the circuit, which could be used for benchmarking or calibrating NISQ hardware. For a general class of quantum circuits, the NPQC has the minimal quantum Cram\'er-Rao bound which highlights its potential for quantum metrology. Finally, we show how to generate arbitrary superpositions of two states with the NPQCs for state preparation tasks. Our results can be used to enhance currently available quantum processors.