Noisy quantum amplitude estimation without noise estimation

Abstract

Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory. However, this problem has an intrinsic difficulty that the system, i.e., the real quantum computing device, inevitably introduces unknown noise; the probability distribution model then has to incorporate many nuisance noise parameters, resulting that the construction of an optimal estimator becomes inefficient and difficult. For this problem, we apply the theory of nuisance parameters (more specifically, the parameter orthogonalization method) to precisely compute the maximum likelihood estimator for only the target amplitude parameter, by removing the other nuisance noise parameters. That is, we can estimate the amplitude parameter without estimating the noise parameters. We validate the parameter orthogonalization method in a numerical simulation and study the performance of the estimator in the experiment using a real superconducting quantum device.

9 pages, 6 figures

References in corpus (11)

• Quantum computing with trapped ions
• Randomized Benchmarking of Quantum Gates
• Superconducting Quantum Computing: A Review
• A Threshold for Quantum Advantage in Derivative Pricing
• Minimizing estimation runtime on noisy quantum computers
• Low depth algorithms for quantum amplitude estimation
• Variational quantum amplitude estimation
• Amplitude estimation via maximum likelihood on noisy quantum computer
• Coherent superconducting qubits from a subtractive junction fabrication process
• Modified Grover operator for amplitude estimation
• Quantum Amplitude Estimation in the Presence of Noise

Cited by in corpus (5)

• Bayesian Quantum Amplitude Estimation
• Adaptive measurement strategy for noisy quantum amplitude estimation with variational quantum circuits
• Quantum-enhanced mean value estimation via adaptive measurement
• Noise tailoring for Robust Amplitude Estimation
• On the bias in iterative quantum amplitude estimation