Natural parameterized quantum circuit

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 Cramér-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.

14 pages, 10 figures

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• Quantum machine learning of large datasets using randomized measurements
• Symmetry enhanced variational quantum spin eigensolver
• Solving Fractional Differential Equations on a Quantum Computer: A Variational Approach
• Random Natural Gradient
• Variational quantum simulation of long-range interacting systems
• Variational simulation of higher-spin systems on qubit-based quantum simulators