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Activity Number: 300 - The Appeal of Quantum Computing in Statistical Science
Type: Topic Contributed
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
Sponsor: Quantum Computing in Statistics and Machine Learning
Abstract #312465
Title: Quantum Amplitude Estimation in the Presence of Noise
Author(s): Eric Brown* and Weng Kian Tham and Oktay Goktas
Companies: Agnostiq Inc. and University of Toronto and Agnostiq Inc
Keywords: Quantum amplitude estimation; Quantum Monte-Carlo; Grover search; Maximum likelihood estimation

Quantum Amplitude Estimation (QAE) - a technique by which the amplitude of a given quantum state can be estimated with quadratically fewer queries than by standard sampling - is a key sub-routine in several important quantum algorithms, including Grover search and Quantum Monte-Carlo methods. An obstacle to implementing QAE in near-term noisy intermediate-scale quantum (NISQ) devices has been the need to perform Quantum Phase Estimation (QPE) - a costly procedure - as a sub-routine. This impediment was lifted with various QPE-free methods of QAE, wherein Grover queries of varying depths / powers (often according to a “schedule") are followed immediately by measurements and classical post-processing techniques like maximum likelihood estimation (MLE). Existing analyses as to the optimality of various query schedules in these QPE-free QAE schemes have hitherto assumed noise-free systems. In this work, we analyse QPE-free QAE under common noise models that may afflict NISQ devices and report on the optimality of various query schedules in the noisy regime. We demonstrate that, given an accurate noise characterization of one's system, one must choose a schedule that balances the trade-off between the greater ideal performance achieved by higher-depth circuits, and the correspondingly greater accumulation of noise-induced error.

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