Internal:Quantum Machine Learning

Quantum Classifiers

Scalable Quantum Neural Networks for Classification

Jindi Wu, Zeyi Tao, Qun Li https://arxiv.org/abs/2208.07719

Relies on a hybrid classical-quantum architecture. Each subdomain has the following:

1. Encoding Unit

• Authors utilize angle encoding (N qubits for N features) because it can support gradient calculations
• Amplitude encoding not used due to error rate and difficulty in computing gradients

2. VQC

• They follow the VQC introduced in https://www.tensorflow.org/quantum/tutorials/mnist#21_build_the_model_circuit

3. Measurement

• Calculation of the expectation value, seemingly Pauli-Z operator giving [-1, 1]

4. The measurement of the sub domain is then encoded into a qubit in the next layer.

Seemingly, this process combines both convolutional and pooling layers in the same way that Iris Cong et al. performs calculations. Advantageous over the qiskit implementation in that the "pooling layers" are not parameterized since the pooling is the measurement itself. Additionally, we can run circuits in parallel.

Quantum convolutional neural networks

Iris Cong et al., Nature Physics https://doi.org/10.1038/s41567-019-0648-8

N qubit input requires O(log(N)) variational parameters. "This corresponds to a double exponential reduction compared with a generic quantum circuit-based classifier..." hopefully leading to faster training times?

Quantum convolutional neural networks for high energy physics data analysis

Chen et al., Brookhaven National Labs https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.4.013231

The (SIMULATED) QCNN follows the following protocol:

1. Feature mapped (Amplitude encoded?) particle images of size 30x30 are implemented in the encoding layer.

2. A VQC acts as a convolutional layer. Convolutional outputs are calculated via the expectation value of the Pauli-Z operator acting on the first qubit.

3. Pooling is done classically with nonlinear activation functions in between convolutional layers (look deeper into this).

4. Categorical Cross Entropy Loss Function is applied to the final output.

5. Back Prop to adjust the parameters in the VQC's (convolutional layers).

We can implement this "by hand" in qiskit using their approximate expectation function on a Wahab GPU node using simulator.set_options(device='GPU'). This is considerable because it may be a faster process (also for larger circuits) than available public access QML methods.

Quantum machine learning for particle physics using a variational quantum classifier

Andrew Blancea and Michael Spannowsky https://link.springer.com/article/10.1007/JHEP02(2021)212

This method follows the same methodology as many others.

1. Angle Encoding the data 2. Generic VQC using universal single qubit gates and CNOTs producing layers of two entangled qubits 3. Measurement is performed by experimental repetitions to determine the expectation value of the Pauli-Z operator, not calculated deterministically

Rudimentary introduction to QNN classification.

Challenges and opportunities in quantum machine learning for high-energy physics

Sau Lan Wu and Shinjae Yoo2 https://www.nature.com/articles/s42254-022-00425-7

"Overall, the greatest challenge in using quantum computer hardware for machine learning at present... is the size of the event samples and the effective use of large num- bers of qubits... analyses will need to manage large event sample size and large data dimensionality...

... advanced quantum computers with large numbers of qubits, reduced noise and improved running time may outperform classical machine learn- ing in both classification power and in speed. QML may well be a new computational paradigm for big data analyses in HEP. For this reason, the HEP community should stay aware of what is happening in quantum technologies — improvements in the hardware, software ecosystem and algorithms — to bring a quantum advan- tage to the HEP data challenge. Conversely, the develop- ment of solutions for unique HEP data challenges could also lead to contributions to the development of quantum technologies."

Quantum machine learning in high energy physics

Guan et al. https://iopscience.iop.org/article/10.1088/2632-2153/abc17d/pdf

Uses adiabatic quantum annealing as an optimizer. This methodology also uses angle encoding for particle track data, a general VQC, with different optimizers such as ADAM and COBYLA.