Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis

  title={Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis},
  author={Sharu Theresa Jose and Osvaldo Simeone},
—Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy intermediate-scale quantum (NISQ) processors. Such systems leverage classical optimization to tune the parameters of a parameterized quantum circuit (PQC). The goal is minimizing a cost function that depends on measurement outputs obtained from the PQC. Optimization is typically implemented via stochastic gradient descent (SGD). On NISQ computers, gate noise due to imperfections and… 

Figures and Tables from this paper



Filtering variational quantum algorithms for combinatorial optimization

The filtering variational quantum eigensolver is introduced which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution and the use of causal cones to reduce the number of qubits required on a quantum computer.

Error mitigation for shortdepth quantum circuits

  • Physical review letters, vol. 119, no. 18, p. 180509, 2017.
  • 1805

Noise-resilient variational hybrid quantum-classical optimization

This work considers a minimization problem with respect to a variational state, iteratively obtained via a parametric quantum circuit, taking into account both the role of noise and the stochastic nature of quantum measurement outcomes, and shows the robustness of the algorithm against different noise strengths.

Quantum Information Theory

In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory.

An Introduction to Quantum Machine Learning for Engineers

  • O. Simeone
  • Computer Science, Physics
    Found. Trends Signal Process.
  • 2022
This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra and describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements.

Quantum error mitigation by hidden inverses protocol in superconducting quantum devices

We present a method to improve the convergence of variational algorithms based on hidden inverses (HIs) to mitigate coherent errors. In the context of error mitigation, this means replacing the

The Accuracy vs. Sampling Overhead Trade-off in Quantum Error Mitigation Using Monte Carlo-Based Channel Inversion

This treatise considers a practical channel inversion strategy based on Monte Carlo sampling, which introduces additional computational error that in turn may be eliminated at the cost of an extra sampling overhead and shows that when the computational error is small compared to the dynamic range of the error-free results, it scales with the square root of the number of gates.

Qubit noise deconvolution

We present a noise deconvolution technique to remove a wide class of noises when performing arbitrary measurements on qubit systems. In particular, we derive the inverse map of the most common single

Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

This work shows that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere, and finds numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe.

Quantum Noise Sensing by Generating Fake Noise

The SuperQGAN protocol, proposed, is a very promising framework to characterize noise in a realistic quantum device, even in the case of spatially and temporally correlated noise (memory channels) affecting quantum circuits.