This project is to demonstrate variational quantum autoregressive (VQAR) model as a quantum machine learning (QML) method to forecast data trends (such as foreign exchange and COVID-19 cases), submitted under an open hackathon in QHack 2022.
VQAR is a variational quancum circuit (VQC)-based autoregressive (AR) model, also related to nonlinear autoregressive exogenous (NARX) to predict future trend.
A schematic is illustrated below.
A time-series vector input is time-delayed to feed into VQC, and the output of VQC is a prediction of future data.
The input data is optionally pre-scaled as an angle value to embed into VQC gates, while the quantum measurement is also optionally post-scaled.
The VQC uses variational parameters to be trained such that the prediction loss is minimized.
We may use a VQC ansatz, e.g., based on 2-design and data reuploading.
An option with skip connection will model residual nonlinear VAR.
Use the package manager pip for python=3.9. We build VQAR model using Pennylane.
pip install pennylane=0.21.0
pip install matplotlib=3.5.1
pip install pandas=1.4.1
pip install scikit-learn=1.0.2
pip install tqdm=4.62.3
pip install argparseOther versions should work.
The first demo is to predict a financial trend, focusing on foreign exchange (a.k.a. forex or FX).
We use a submodule exchange-rates licensed under the PDDL.
To update the data, run as
pip install dataflows
git submodule update --remote exchange-rates
python exchange-rates/exchange_rates_flow.pyThere are 'annual', 'monthly', and 'daily' datasets from 1971 to 2018 for some countries:
- exchange-rates/data/annual.csv
- exchange-rates/data/monthly.csv
- exchange-rates/data/daily.csv
A wrapper to load the data is forex_loader.py. E.g., select 'monthly' data for Australia and Canada for dates from 1980 to 2011/05:
python forex_loader.py --data monthly --country Australia Canada --dates 1980 2011/05
For example, to predict Denmark and Sweden currencies from USD, you may run quforex.py as
python quforex.py --data annual --country Denmark Sweden --memory 2 --epoch 100To sweep memory, layer, and reuploading parameters of VQAR, you may run quforex_sweep.py as
python quforex_sweep.py --target memory --sweep 1 2 3 4 5 6 --reup 3It will save results in plots/annual_sweep-memory_6_1_2.png.
Example performance for Canada/US rate, you may run
python quforex_sweep.py --target memory --sweep 1 2 3 4 5 6 7 --reup 3 --layer 1 --data annual --country CanadaThe prediction performance in mean-square error (MSE) improves with the VQAR memory:
Optimized VQC may look like:
0: ──RY(2.06)────╭C──RY(1.62)─────RY(2.06)──────────────────────────╭C──RY(-0.322)───RY(2.06)──────────────────────────╭C──RY(0.901)────────────────────┤ ⟨Z⟩
1: ──RY(0.0649)──╰Z──RY(-0.612)──╭C─────────RY(1.74)────RY(0.0649)──╰Z──RY(-0.384)──╭C─────────RY(0.0422)──RY(0.0649)──╰Z──RY(-0.684)──╭C──RY(-0.692)───┤ ⟨Z⟩
2: ──RY(-1.61)───╭C──RY(-0.528)──╰Z─────────RY(-0.761)──RY(-1.61)───╭C──RY(1.13)────╰Z─────────RY(0.583)───RY(-1.61)───╭C──RY(-0.123)──╰Z──RY(-0.397)───┤ ⟨Z⟩
3: ──RY(0.939)───╰Z──RY(-1.07)───╭C─────────RY(0.319)───RY(0.939)───╰Z──RY(-1.1)────╭C─────────RY(-1.1)────RY(0.939)───╰Z──RY(-0.936)──╭C──RY(-0.687)───┤ ⟨Z⟩
4: ──RY(0.196)───╭C──RY(0.865)───╰Z─────────RY(-0.249)──RY(0.196)───╭C──RY(-0.172)──╰Z─────────RY(1.14)────RY(0.196)───╭C──RY(-0.268)──╰Z──RY(-0.845)───┤ ⟨Z⟩
5: ──RY(0.264)───╰Z──RY(-2.3)────╭C─────────RY(1.46)────RY(0.264)───╰Z──RY(-0.878)──╭C─────────RY(0.902)───RY(0.264)───╰Z──RY(0.53)────╭C──RY(-0.671)───┤ ⟨Z⟩
6: ──RY(-0.641)──────────────────╰Z─────────RY(-2.06)───RY(-0.641)──────────────────╰Z─────────RY(0.502)───RY(-0.641)──────────────────╰Z──RY(-0.0127)──┤ ⟨Z⟩ The second demo is to predict COVID-19 cases.
We use a submodule nytimes/covid-19-data licensed under the CC-BY NC. There are data from The New York Times, based on reports from state and local health agencies
To update the data, run as
git submodule update --remote covid-19-dataWe use CSV files:
- covid-19-data/us.csv: daily US-nationwide cases
- covid-19-data/us-states.csv: daily US state-wise cases
Note that the data are cummurative sum. A wrapper to load the data is covid_loader.py, which may convert to daily/weekley diff (with --periods and --decimate):
python covid_loader.py --periods 7 --decimate 7 --states Massachusetts Maine 'New Hampshire' 'New York' Connecticut
You may run qucovid.py as
python qucovid.py --memory 2 --states MassachusettsExample results when running qucovid_sweep.py as
python qucovid_sweep.py --verb --target memory --reup 1 --memory 2 --layer 1 --sweep 1 2 3 4 5 6 7 --states Connecticut --lr 1e-2may look like as below. Training MSE improves with memory size, whereas testing MSE is not improved.
Optimized VQC circuits:
0: ──RY(-0.997)──╭C──RY(1.62)────────────────────┤ ⟨Z⟩
1: ──RY(-0.107)──╰Z──RY(-0.612)──╭C──RY(1.74)────┤ ⟨Z⟩
2: ──RY(1.45)────╭C──RY(-0.528)──╰Z──RY(-0.761)──┤ ⟨Z⟩
3: ──RY(-0.618)──╰Z──RY(-1.07)───╭C──RY(0.319)───┤ ⟨Z⟩
4: ──RY(-2.04)───╭C──RY(0.865)───╰Z──RY(-0.249)──┤ ⟨Z⟩
5: ──RY(-1.94)───╰Z──RY(-2.3)────╭C──RY(1.46)────┤ ⟨Z⟩
6: ──RY(-2.51)───────────────────╰Z──RY(-2.06)───┤ ⟨Z⟩ It is straightforward to use a real quantum processing unit (QPU) for testing our VQAR. For example, we may use IBM Q Experience. You may specify the account token via Pennylane configulation file, and a scpecific backend of real QPU, such as 'ibmq_london'. To run our vqar.py on a real quantum computer, you just need to change the device as follows:
pip install pennylane-qiskit=0.21.0 # qiskit plugin
python vqar.py --dev qiskit.ibmqWe can use different backends such as Amazon braket. For example, we may run as
pip install amazon-braket-pennylane-plugin=1.5.6 # AWS plugin
python vqar.py --dev braket.aws.qubitFurther examples and tutorials are found at amazon-braket-example and README.
Note that we do not guarantee to achieve quantum advantage. We do not intend to maintain this project for future.
MIT. Copyright (c) 2022 Toshi Koike-Akino. This project is provided 'as-is', without warranty of any kind. In no event shall the authors be liable for any claims, damages, or other such variants.