Variational Quantum Approximate Support Vector Machine (VQASVM)

Related Preprints:

1. Variational Quantum Approximate Support Vector Machine With Inference Transfer https://arxiv.org/abs/2206.14507

Version Information

Qiskit Software Version

• Qiskit 0.25.4
• Terra 0.17.2
• Aer 0.8.2
• Ignis 0.6.0
• Aqua 0.9.1
• IBM Q Provider 0.12.3

System information

• Python 3.9.2 (default, Mar 3 2021, 20:02:32) [GCC 7.3.0]
• OS Linux
• CPUs 8
• Memory (Gb) 15.561397552490234
• Mon Nov 01 09:49:13 2021 KST

Environment setting

Create new conda enviroment with the command.

conda env create --name `YOUR_ENV_NAME` --file environment.yaml

If you have created new environment already, install proper packages

pip install -r run_requirements.txt

Notice

After setting environments, run ibmq_device_run.ipynb. Please check lines with # TODO: for they are configuration controllers. The experiement result will be stored at default directory ibmq_device_run_results.

Config. in ibmq_device_run.ipynb

• I_HAVE_ACCESS: Boolean. Set to True if have vaild IBMQ access.
• DATA_TYPE : Str. Either 'balanced' or 'unbalanced'
• DEVICE : Str. Either 'montreal' or 'toronto'
• TEST_SIZE : Int. Size of test dataset. Choose suitable value in terms of experiment time.
• MAXITER : Int. Maximum number of iteration. default = 2**10
• LAST_AVG : Int. Number of last samples to average. default = 2**4
• DIR_NAME : Str. Directory to save results. default = 'ibmq_device_run_results'
• provider : Your IBMQ provider.
• layout : Mapping between virtual and physical qubits.

How to choose layout

The hardware-noise-robustness of QASVM heavily depends on layout.

Decision Rule

Priority 1. Should be one of four

• (yi - i1 - i0 - xi - a - xj - j0 - j1 - yj) connection
• (i1 - i0 - xi - a - xj - j0 - j1) + (i0 - yi) + (j0 - yj) connection
• (yi - i0 - i1 - xi - a - xj - j1 - j0 - yj) connection
• (i0 - i1 - xi - a - xj - j1 - j0) + (i1 - yi) + (j1 - yj) connection

Priority 2. Should minimize TwoQubit (gate) error of possible connections in layout

Priority 3. Should minimize SingleQubit (gate) error of qubits in layoyt

Priority 4. Overall error on *i register should be lower than error on *j register

Examples

from classifiers.quantum import Qasvm_Mapping_4x2

layout = Qasvm_Mapping_4x2(backend, a=3, i0=8, i1=11, xi=5, yi=14, j0=1, j1=4, xj=2, yj=7)
layout = Qasvm_Mapping_4x2(backend, a=16, i0=11, i1=8, xi=14, yi=5, j0=22, j1=25, xj=19, yj=24)
layout = Qasvm_Mapping_4x2(backend, a=3, i0=9, i1=11, xi=5, yi=8, j0=0, j1=4, xj=2, yj=1)
layout = Qasvm_Mapping_4x2(backend, a=13, i0=10, i1=7, xi=12, yi=6, j0=11, j1=8, xj=14, yj=9)

IBM Quantum Processor Results

If dataset is unbalanced, QASVM performs better than uniform weight STC. Below figures summarize classification result on quantum processor ibmq_montreal

1. When training dataset is balanced
2. When training dataset is unbalanced

Numerical Analysis on Iris Dataset

Number of optimization parameter can be lower than training dataset size $M$. Refer to our paper https://arxiv.org/abs/2206.14507