Diabetic Retinopathy (DR) is a common complication of diabetes mellitus that causes lesions on the retina that affect vision. Late detection of DR can lead to irreversible blindness. The manual diagnosis process of DR retina fundus images by ophthalmologists is time consuming and costly. While, Classical Transfer learning models are extensively used for computer aided detection of DR; however, their maintenance costs limits detection performance rate. Therefore, Quantum Transfer learning is a better option to address this problem in an optimized manner. The significance of Hybrid quantum transfer learning approach includes that it performs heuristically. Thus, our proposed methodology aims to detect DR using a hybrid quantum transfer learning approach. To build our model we extract the APTOS 2019 Blindness Detection dataset from Kaggle and used inception-V3 pre-trained classical neural network for feature extraction and Variational Quantum classifier for stratification and trained our model on Penny Lane default device, IBM Qiskit BasicAer device and Google Cirq Simulator device. Both models are built based on PyTorch machine learning library. We bring about a contrast performance rate between classical and quantum models. Our proposed model achieves an accuracy of 93%–96% on the quantum hybrid model and 85% accuracy rate on the classical model. So, quantum computing can harness quantum machine learning to do work with power and efficiency that is not possible for classical computers.

Diabetic retinopathy (DR) is the most common form of diabetic eye disease [

In recent years, classical transfer learning approaches are used in the field of image classification, segmentation, and screening for DR. However, limited detection performance rates are hinderance to computer aided diagnostic. A breakthrough in the field of quantum computing can help in giving the ophthalmologist a second opinion to solve this problem by using hybrid quantum transfer learning approach. This quantum approach can result into more efficient detection of DR in patients as compared to the classical transfer learning [

This paper presents a hybrid approach for early detection of DR. We have compared the results of our three hybrid Quantum Transfer Learning models with one classical Transfer Learning model. We have labeled our data set into two categories i.e., no DR or DR. To build Quantum Transfer learning model, we have used inception-V3 [

Transfer learning refers to a technique for predictive modeling on a different but somehow similar problem that can be used partially or entirely to accelerate the training and improve the performance of a model. It can train deep neural network with comparatively small size of data. If a previously trained artificial neural network is successful in solving a particular problem, it can be reused with some additional training to solve a problem. Let’s consider a pre-trained deep neural network with the data set used for the solution of a problem. Transfer learning can be used to accelerates the training of neural networks as either a weight initialization scheme or feature extraction method that is retrained to solve a different or similar problem with a new dataset.

Quantum machine learning extends the concept of transfer learning, widely applied in modern machine learning algorithms, to the emerging context of hybrid neural networks composed of classical and quantum elements. In Quantum transfer learning we focus mainly on the paradigm in which a pre-trained classical network is modified and augmented by a final quantum layer. We can use any pre trained classical neural network according to our problem for feature extraction. To classify these features with the help of “dressed quantum circuit” we need to reduce output-dimensional feature vector to final dimensions with linear transformation [

In

One of the most important components in VQC is variational circuit.

In past, many works have been reported to solve DR problem by using classical machine learning approaches using different datasets. Mansour [

To avoid the time and resource consumption, Mohammadian [

It is quite evident from the majority of the work in diabetic retinopathy detection revolves around the use of various transfer learning models and performance comparison of these models. It is also observed that less emphasis has been given on improvement of quality of the diabetic retinopathy dataset which could lead to more accurate results. It is important to highlight the fact that the reliability of results generated from the transfer learning model depends on the features of the dataset. Google’s recent achievement of quantum supremacy marked the first glimpse of this promised power. This is reminiscent of how machine learning evolved towards deep learning with the advent of new computational capabilities. These new algorithms use parameterized quantum transformations called parameterized quantum circuits (PQCs), Quantum Neural Networks (QNNs), Variational quantum circuits and Dressed quantum circuits. In analogy with classical transfer learning, the parameters of a variational quantum circuits are then optimized with respect to a cost function

A tabular comparison has been outlined to discuss the limitations and contributions of the existing works.

Author | Adopted models | Experimental out-comes |
---|---|---|

DL, Mohammadian [ |
Inception-V3 and Xception pre-trained models | Accuracy score of 87.12% and 74.49% achieved |

Wan et al. [ |
Pre-trained models AlexNet, VggNet-s, VggNet-16, VggNet-19, GoogleNet and RestNet | Highest accuracy score was that of VggNet-s model, which reached 95.68% |

Dutta et al. [ |
Shallow feed forward neural network, deep neural network and VggNet-16 model. | Accuracy of 42%, and 86.3% 78.3% accuracy achieved |

The dataset we used in our study is a publicly available retinal fundus images database from Kaggle (APTOS 2019 Blindness Detection) [

The Quantum Computing device used in our study is Penny-lane default device, IBM QiskitBasicaer and Google Cirq Simulator device. These simulators are noiseless to avoid any error.

In current work, APTOS 2019 Blindness Detection dataset is taken from Kaggle and labelled into two categories with the help of provided file in Kaggle documentation. Furthermore, resizing of imbalance images is done to 350 by 350. These images are further processed to remove extra black pixel part to covert image as input in our inception V3 pre-trained neural network. After this we have converted our images into tensor vector because machine learning model always input data in the form of vectors. We have done some normalization of parameters like ( [0.485,0.456,0.406]) to remove any misbalancing during resizing of images [

We have proposed hybrid Quantum transfer learning model, in which we have used inception-v3 pre trained neural network for feature extraction. Inception-v3 is a pre-trained convolutional neural network model that is 48 layers deep that is used to reduce images to 2048-dimensional feature vector [

To classify these features with the help of 4-qubit “dressed quantum circuit” we have reduced 2048-dimensional feature vector to 4 dimensions with linear transformation [

Following steps are performed to build quantum classifier

1. Firstly, we have initialized 4 qubits in |0) state and then apply Hadamard (H) gate on these 4 qubits to make them in superposition state of zero and one [

2. Then we have applied, additional transformation to encode our classical data with unitary circuit. To perform this operation, we encoded our 4-dimensional feature vector as a parameters or weights into our circuit consisting of Ry(fi) gates and U (α, β, θ, γ) circuit.

3. We have a sequence of trainable variational layers having an entanglement layer and a data encoding circuit. We have 3 CNOT gates in the entanglement layer which makes all qubits, entangled

4. In the end we have done measurements on each 4-qubits to get the expected value along the z-operator.

We have trained two models, first is classical model using classical transfer learning and second is quantum model using quantum transfer learning with the same training data set and parameters. We have setup learning rate 0.0004 which is same for both models and used Adam optimization algorithm and Cross Entropy function as activation function. Online google Colab notebook is being used to run our model.

We have evaluated our model with five basic standards: Accuracy, Precision, Recall, f1-score and specificity with the following formulas.

Where 𝑇_{𝑝} = True Positive, 𝐹_{𝑃} = False Positive, 𝑇_{𝑁} = True Negative, 𝐹_{𝑁} = False Negative.

Performance of classical and hybrid quantum models on 5 epochs are presented in

Sr | Evaluation | PannyLane | BasicAer Qiskit | Cirq simulator | Classical computer |

1 | Accuracy rate | 91.48% | 93.25% | 94.11% | 85.14% |

2 | Precision rate | 94.74% | 97.43% | 95.59% | 97.43% |

3 | Recall | 87.96% | 89.14% | 92.10% | 76.93% |

4 | F1 Score | 91.22% | 93.09% | 93.80% | 85.95% |

5 | Specificity | 88.62% | 89.59% | 92.81% | 74.35% |

In

Sr | Evaluation | PannyLane | BasicAer Qiskit | Cirq simulator | Classical computer |

1 | 0-No DR | 95% | 96% | 95% | 97% |

2 | 1-DR | 88% | 89% | 92% | 76% |

The probability distributions are used in Statistics to make the detection of any change in the trend of the data. If a probability distribution is fitted accurately to the data, then it will be helpful to detect the change in data at early stage. In this section we tried to fit five different probability distributions such as Reflected Power function distribution, Kumarswamy Lehmann-2 Power function distribution (KL2PFD), Beta Lehmann-2 Power function distribution (BL2PFD), Weighted Power function distribution(WPFD) and Exponentiated Generalized Power function distribution (EGPFD) which are generated and used in medical diagnosis in literature [

The probability density function (pdf) of the proposed Reflected Power function distribution (RPDF) for the diabetic retinopathy are given as

The probability density function (pdf) of Kumarswamy Lehmann-2 Power function distribution (KL2PFD) are given as

Where “γ” and

The probability density function (pdf) of Beta Lehmann-2 Power function distribution (BL2PFD) are given as

The probability density function (pdf) Weighted Power function distribution (WPFD) is given as

The probability density function (pdf) Exponentiated Generalized Power function distribution (EGPFD) is given as

In this section, we have analyzed diabetic retinopathy data using statistical modeling. We have derived the estimates and their standard errors of the parameters of distributions using modified maximum likelihood method. The results are presented in

Distribution | Estimates | |||
---|---|---|---|---|

RPFD | 8.271522 |
– | – | – |

KL2PFD | 0.3475206 |
2.4412303 |
4.2730098 |
2.1817279 |

BL2PFD | 0.3678653, |
5.0156976 |
1.7911449 |
2.8191529 |

WPFD | 0.1895936 |
– | – | – |

EGPFD | 0.4088129 |
4.9477360 |
4.6112238 |
– |

The TTT-plot is presented in

In

Distribution | AIC | CAIC | BIC | HQIC | -logL |
---|---|---|---|---|---|

RPFD | 798.6368 | 798.6688 | 801.481 | 799.7923 | 398.3184 |

EGPFD | 808.0444 | 808.2395 | 816.577 | 811.5111 | 400.0222 |

KL2PFD | 810.2859 | 810.6137 | 821.6626 | 814.9081 | 400.6429 |

BL2PFD | 810.5365 | 810.8644 | 821.9133 | 815.1588 | 401.2683 |

WPFD | 942.4546 | 942.4866 | 945.2988 | 943.6102 | 470.2273 |

A hybrid quantum transfer learning approach is adopted to model early DR detection. From our results we clearly see that Google Cirq simulator shows higher efficiency in terms of model accuracy. Moreover, already used Classical training model have presented large gap in accuracy rate. We report superiority of Quantum models in terms of performance and speed. During training of our models, we see Pannylane default device takes very less time as compared to other models. Overall performance of Pannylane default device is very good in term of time. This work suggests that there might be some variation in performance of these quantum devices but these show high performance rate when compared with classical model and is verified by statistical methods as well. This performance analysis shows that computer aided technique can be used in mobile applications for timely detection of DR in rural areas.

The authors would like to thank Pannylane, IBM Qiskit, Google Cirq for providing access to their resources and quantum devices that are used to simulate our models.