Calibrating error extrapolation for variational quantum algorithms

[michael-a-jones]

Abstract

When performing variational quantum computations on noisy quantum processors, the measured expectation values ‘drift’ as the amount of noise increases. By making use of increasingly noisy measurements, it is possible to extrapolate back to the zero-noise limit to obtain an estimate of the true value. However, this assumes knowledge of the functional form of the error dependence. By making use of classically tractable reference states, it may be possible to learn or calibrate this extrapolation method to improve reliability and/or validate the assumed form of the error dependance.

Description

Below are some notes on the key concepts, which I'm also more than happy to discuss in person or by email:

Variational Quantum Eigensolver (VQE):

• makes use of a quantum processor to simulate a quantum system (e.g. a molecule),
• allows the efficient estimation of an observable (e.g. energy),
• uses short trial states to reduce error,
• requires further error mitigation for practical circuit depths,

Zero-noise (Richardson) extrapolation:

• artificially increases the noise in the quantum processor to generate energy estimates for increasing levels of noise,
• extrapolates from the higher noise measurements to the zero-noise limit,
• assumes knowledge of the functional form of the errors (usually exponential or double-exponential),

Reference-state error mitigation:

• certain quantum states allow for efficient calculation of observables (e.g. computational basis states),
• the error (drift) in the quantum computation can be calculated at these reference states,
• near the reference-state, the drift can be assumed to be constant,
• quantum calculations for states close to the reference-state can be corrected,

Members

• Qiskit Coach: @michael-a-jones, email: jonesm3@student.unimelb.edu.au
• @jkfids
• @ccbou2

Deliverable

A report/presentation on the feasability of calibrating error extrapolation including examples on toy systems.

GitHub repo

https://github.com/michael-a-jones/Calibrating-error-extrapolation.git (Clicking the link doesn't seem to work, copy and paste into the search bar)

[michael-a-jones]

Here's a quick summary of the methods mentioned above including some references. calibrating_extrapolation_summary.pdf

[jkfids]

I'm interested in joining

[ccbou2]

I'm keen if you'll still have me Michael!

[ccbou2]

Qiskit_hackathon_22.pdf

[ccbou2]

Qiskit_hackathon_22.pdf