Bayesian Framework for Quantum Algorithms in Qiskit: Principled Computing Amidst Noise

[ismaila-at-za-ibm]

Abstract

Bayesian Inference is a powerful tool for handling noise and uncertainty while learning from data. It leverages well-defined parameterized models (theory) of the system under study and raw observations of the system (data) to iteratively gain information about the uncertain parameters in the theory. For quantum algorithms run on quantum computing devices, the "model" of the system is the circuit itself run on the device with detailed noise models plus the variability introduced by measurement. A proper Bayesian treatment can be used to manage the noise on actual runs and piece together evidence gathered over those runs to arrive at useful answers that would otherwise be washed away. This project implements a Bayesian version of the well known iterative quantum phase estimation algorithm in such a way that the introduced primitives could be reused for other "Bayesified" algorithms:

Efficient Bayesian Phase Estimation: https://arxiv.org/pdf/1508.00869.pdf

Description

Bayesian methods can be used to learn unknown parameters, average over parameters that are not of interest and select between competing models. It is a philosophically motivated, principled treatment of knowledge with uncertainty.

However, the first problem with Bayesian methods is that it requires accurate models. Fortunately, in the field of quantum computing, the "behaviour" of the system is well understood, even though the actual noise of any one run is unknown and even though the final answer is, of course, unknown. The noise and final answer enter the theory as parameters that Bayesian methods can elegantly manage.

The second problem with Bayesian methods is that it is computationally intensive. Fortunately, there are algorithms where the classical load is manageable (small number of parameters and good approximations: rejection filtering). Furthermore, for other algorithms there is the long-term hope that quantum bayesian inference may help alleviate the computational load, leading to Quantum-Classical-Quantum Hybrid systems.

Adaptive Quantum Simulated Annealing for Bayesian Inference and Estimating Partition Functions: https://arxiv.org/abs/1907.09965

All of these considerations suggest the need for a framework to manage the "Bayesification" of algorithms.

References: QInfer: Statistical inference software for Quantum Applications: https://quantum-journal.org/papers/q-2017-04-25-5/pdf

Approximate Bayesian Inference via Rejection Filtering: https://arxiv.org/pdf/1511.06458v2.pdf

Experimentally Detecting a Quantum Change Point via Bayesian Inference: https://arxiv.org/pdf/1801.07508.pdf

Members

• @githubhandle
• @githubhandle - Slack: @slackhandle email: [email protected]
• Qiskit Coach: @ismaila-at-za-ibm
• Helpful backgrounds: Python, Pytorch, Probtorch, Qiskit, Statistics, Quantum Information, Noise modeling.

Deliverable

Aqua module, Series of papers

GitHub repo