Neural Network-Guided Extrapolation Technique for Quantum Variational Algorithms

Summary

We propose a neural network-driven zero noise extrapolation method to increase the accuracy of VQE in a noisy quantum environment.

Abstract

In the noisy intermediate-scale quantum (NISQ) era, the Variational Quantum Eigensolver (VQE) comes out as an effective algorithm for addressing complex quantum challenges. However, the presence of noise in quantum devices frequently reduces the accuracy and reliability of VQE outcomes. This paper presents an innovative method to address this issue by using a neural network-based extrapolation technique in VQE calculation. By utilizing the Qiskit framework, we designed parameterized quantum circuits using the RY-RZ ansatz, and their performance was analyzed under different levels of depolarizing noise with bit-flip errors, phase-flip errors, and amplitude damping errors. Our inquiry involved analyzing the expected outcomes of a Hamiltonian across various levels of noise intensity with the objective of deducing the ground state energy (GSE). To connect the observed noisy outcomes with the ideal noise-free condition, a Feedforward Neural Network (FFNN) was trained using the error probabilities and their corresponding expectation values. This model accurately predicted the VQE results in an ideal noise-free scenario. Comparison of the result of simulation and real quantum hardware executions revealed noise-induced inconsistencies, highlighting the effectiveness of this neural network-based extrapolation approach in correcting them. This comprehensive method improves the accuracy of VQE calculation on NISQ devices and highlights the significant potential of blending quantum and classical methods to address the threats imposed by quantum noise. The comparison of results between FFNN, convolutional neural network (CNN), and long short-term memory (LSTM) network reveals that FFNN predicts outcomes with more accuracy but in less time.

Introduction

Quantum computing is like a mix of different subjects, blending ideas from quantum mechanics and computer theory. It could change the way we handle information completely. It can offer computational capabilities far beyond the reach of classical computations¹. Although quantum computing holds great promise, it faces significant hurdles. Quantum systems are fragile and easily influenced by noise and errors from different sources. These disturbances can greatly impact the accuracy of computations^2,3,4,5,

Protocol

All experiments were conducted using the Qiskit qasm_simulator for classical simulations and on the IBM quantum device ibm_kyoto, which was selected as the least busy backend available at the time of execution using Qiskit's least_busy() function; no human or animal subjects were involved, and thus no ethical approval was required. All software and hardware resources were used in accordance with institutional guidelines. The coding files are provided as Supplementary Coding File 1 and Supplementary Coding File 2.

Setup
The experiments were implemented in a Python-based quantum-computing....

Results

Quantum simulations under noise
We vary the noise probabilities from 0.01 to 0.05 and measure the expectation value . As noise increases, the observed expectation values deviate from their ideal (noise-free) results, reflecting the detrimental effect of decoherence and errors.

Neural network predictions
A Feed-Forward Neural Network (FFNN) is trained to predict ideal, noise-free expectation values given a noisy input. During training:
Inpu.......

Discussion

To find out the effectiveness of the neural network model described here, we started by assessing its capability to get noise-free performance depending on noisy quantum circuit outcomes. Adam optimizer is used and MSE is used as the loss function. The steady decrease in MSE values suggests that the model successfully captured the relationship between error probabilities and the associated outcomes of the quantum circuit.

The comparison is done between real quantum device result, simulation re.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Qiskit =0.39.0	IBM Quantum	https://www.ibm.com/quantum/qiskit	Primary quantum computing framework used for circuit design and simulation ((RRID:SCR_021282)
Python 3.10	Python Software Foundation	https://www.python.org/	Programming language used to implement algorithms and data analysis (RRID: SCR_008394)
Quantum Platform	IBM Quantum	https://quantum.cloud.ibm.com/computers	Quantum computing framework (RRID:SCR_021282)