Quantum Machine Learning for FinTech and Time Series Data
Quantum Neural Networks for FinTech Time Series Function Fitting
This repository is for developing quantum neural network models for fitting one-dimensional time series data and noisy signals. It is modified from the model presented in PennyLane Function fitting with a quantum neural network. We modify the code presented in the default notebook downloaded from PennyLane so that it works using synthetic data created by the user, and we train a model on several years worth of drug sales data.
In this very basic setup, there were only 4-layers in the quantum neural network, initialized with random weights. The model went through 50 iterations and had the following training data:
Iter: 1 | Cost: 0.4366430 Iter: 2 | Cost: 0.4130995 Iter: 3 | Cost: 0.4401763 Iter: 4 | Cost: 0.4843044 Iter: 5 | Cost: 0.5272264 Iter: 6 | Cost: 0.5590949 Iter: 7 | Cost: 0.5756194 Iter: 8 | Cost: 0.5762956 Iter: 9 | Cost: 0.5631025 Iter: 10 | Cost: 0.5394853 Iter: 11 | Cost: 0.5095363 Iter: 12 | Cost: 0.4773198 Iter: 13 | Cost: 0.4463337 Iter: 14 | Cost: 0.4191397 Iter: 15 | Cost: 0.3972019 Iter: 16 | Cost: 0.3809405 Iter: 17 | Cost: 0.3699549 Iter: 18 | Cost: 0.3633300 Iter: 19 | Cost: 0.3599337 Iter: 20 | Cost: 0.3586456 Iter: 21 | Cost: 0.3584964 Iter: 22 | Cost: 0.3587285 Iter: 23 | Cost: 0.3588033 Iter: 24 | Cost: 0.3583769 Iter: 25 | Cost: 0.3572647 Iter: 26 | Cost: 0.3554029 Iter: 27 | Cost: 0.3528146 Iter: 28 | Cost: 0.3495813 Iter: 29 | Cost: 0.3458197 Iter: 30 | Cost: 0.3416648 Iter: 31 | Cost: 0.3372562 Iter: 32 | Cost: 0.3327294 Iter: 33 | Cost: 0.3282081 Iter: 34 | Cost: 0.3238007 Iter: 35 | Cost: 0.3195972 Iter: 36 | Cost: 0.3156676 Iter: 37 | Cost: 0.3120615 Iter: 38 | Cost: 0.3088088 Iter: 39 | Cost: 0.3059200 Iter: 40 | Cost: 0.3033888 Iter: 41 | Cost: 0.3011936 Iter: 42 | Cost: 0.2993004 Iter: 43 | Cost: 0.2976666 Iter: 44 | Cost: 0.2962437 Iter: 45 | Cost: 0.2949811 Iter: 46 | Cost: 0.2938298 Iter: 47 | Cost: 0.2927447 Iter: 48 | Cost: 0.2916878 Iter: 49 | Cost: 0.2906292 Iter: 50 | Cost: 0.2895481 Iter: 51 | Cost: 0.2884328 Iter: 52 | Cost: 0.2872799 Iter: 53 | Cost: 0.2860931 Iter: 54 | Cost: 0.2848812 Iter: 55 | Cost: 0.2836566 Iter: 56 | Cost: 0.2824333 Iter: 57 | Cost: 0.2812253 Iter: 58 | Cost: 0.2800452 Iter: 59 | Cost: 0.2789039 Iter: 60 | Cost: 0.2778094 Iter: 61 | Cost: 0.2767668 Iter: 62 | Cost: 0.2757787 Iter: 63 | Cost: 0.2748451 Iter: 64 | Cost: 0.2739643 Iter: 65 | Cost: 0.2731328 Iter: 66 | Cost: 0.2723465 Iter: 67 | Cost: 0.2716004 Iter: 68 | Cost: 0.2708895 Iter: 69 | Cost: 0.2702092 Iter: 70 | Cost: 0.2695549 Iter: 71 | Cost: 0.2689228 Iter: 72 | Cost: 0.2683099 Iter: 73 | Cost: 0.2677134 Iter: 74 | Cost: 0.2671316 Iter: 75 | Cost: 0.2665631 Iter: 76 | Cost: 0.2660070 Iter: 77 | Cost: 0.2654630 Iter: 78 | Cost: 0.2649310 Iter: 79 | Cost: 0.2644110 Iter: 80 | Cost: 0.2639034 Iter: 81 | Cost: 0.2634083 Iter: 82 | Cost: 0.2629260 Iter: 83 | Cost: 0.2624569 Iter: 84 | Cost: 0.2620009 Iter: 85 | Cost: 0.2615582 Iter: 86 | Cost: 0.2611285 Iter: 87 | Cost: 0.2607117 Iter: 88 | Cost: 0.2603074 Iter: 89 | Cost: 0.2599152 Iter: 90 | Cost: 0.2595346 Iter: 91 | Cost: 0.2591651 Iter: 92 | Cost: 0.2588059 Iter: 93 | Cost: 0.2584567 Iter: 94 | Cost: 0.2581168 Iter: 95 | Cost: 0.2577857 Iter: 96 | Cost: 0.2574629 Iter: 97 | Cost: 0.2571479 Iter: 98 | Cost: 0.2568405 Iter: 99 | Cost: 0.2565402 Iter: 100 | Cost: 0.2562468 After training the quantum neural network learns to smooth the noisy sine function as can be seen in the red plots:
This example illustrates an implementation of optical quantum computing and training an optical based quantum neural network. For more information on photonic quantum computing see the Strawberry Fields documentation. Strawberry Fields is a full-stack library for design, simulation, optimization, and quantum machine learning of continuous-variable circuits that is fully integrated into PennyLane. For more information on more general quantum nodes, see the PennyLane documentation.
In later examples of applications of quantum machine learning to FinTech, we will also be investigating quantum walks. Quantum walks are a quantum analogue to random walks and have substantially reduced the time-consumption in Monte Carlo simulations for mixing of Markov chains as reported by Ashley Montanaro (2015). These quantum algorithms are applied for investment strategies in wealth management and trading.