{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Multibody formulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Device: Dirac-3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importance\n", "\n", "The polynomial models we use in our Dirac-3 device are continuous rather than discrete models. While perhaps not the most common setting in optimization, they are very powerful, and the multibody terms make them even more powerful. Formally, even a simple quadratic-only version of our quadratic model is already NP-hard \n", " minimize $X^TQX$ where $X\\ge 0$.\n", "This fact was shown in [this paper](https://deepblue.lib.umich.edu/bitstream/handle/2027.42/6740/bam7058.0001.001.pdf?sequence=5) (and section 2.9.3 of [this book](https://public.websites.umich.edu/~murty/books/linear_complementarity_webbook/lcp-complete.pdf)), this essentially means that it is a rich enough optimization problem that all other hard optimization can be mapped to it. The details of the theory are explained in this lesson. Being NP-hard is important because it shows that even a more limited (quadratic only) version of our model is already rich enough to map interesting problems to. The restricted range plays a key role in the richness of the model. In particular, the version with unrestricted values of $X$\n", " minimize $X^TQX$ where $X$ can take any real values, is not NP-hard. In other words, it is not rich enough to represent hard optimization problems. In fact, this is essentially matrix diagonalization, which is performed efficiently by the ARPACK and LAPACK linear algebra libraries that are commonly used in Python. Even without the restricted range, adding fourth-order terms would also render the problem NP-hard, as discussed in [this paper](https://web.mit.edu/~a_a_a/Public/Publications/convexity_nphard.pdf).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Applications" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Optimization over polynomials is a less explored topic than more traditional binary optimization. However, such problems are very important and arise naturally. One example discussed in [this paper](https://arxiv.org/abs/1504.06002) and [this paper](https://groups.csail.mit.edu/robotics-center/public_papers/Majumdar12a.pdf) considers the problem of optimizing drone paths while avoiding danger. In this example, the parameters that are optimized are the continuous control inputs at all points, requiring good-quality solutions to polynomial optimization problems in real time. Problems related to wireless coverage, as discussed in [this paper](https://arxiv.org/abs/1504.06002) also naturally involve polynomial terms. In this case, the expression for electromagnetic power being delivered to each location in a space becomes a polynomial constraint, which could be enforced using lagrange multipliers and a polynomial with a degree which is twice as large. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tutorial preparation\n", "Multi-body support was added to `qci-client` in version 3.2.0, but in order to utilize this tutorial, a version of `qci-client` of at least 4.0 is required." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "!pip install --quiet \"qci-client>=4.0\"\n", "import numpy as np\n", "from matplotlib import cm\n", "import matplotlib.pyplot as plt\n", "import qci_client as qc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multi-body Tutorial\n", "Multi-body problems are polynomials where the total degree of at least one term in the polynomial is higher than 2. For instance \n", "$$\n", "f(x,y)=xy^2-x^2y+x+y\n", "$$ \n", "is a two variable, cubic problem.\n", "\n", "## Optimization\n", "\n", "Dirac-3 is a purpose-built device for finding global minima of a polynomial function. As demonstrated in the [Dirac-3 Quick Start](https://quantumcomputinginc.com/learn/tutorials-and-use-cases/dirac-3-quick-start), it optimizes a multi-variate polynomial over a domain $x_i\\in[0,R]\\, i\\in[0,1,\\ldots,N-1]$ where $R$ is a positive value all $x_i$ must sum to.\n", "\n", "## Example\n", "Observe the following visualization of the function. The surface with the jet color scale describes the function across the entire domain $0\\leq x\\leq 10, 0\\leq y\\leq 10$, while the surface in semi transparent blue shows the domain of the optimization problem with the sum constraint of $x+y=10$. Notice the cross section with two extrema due to the cubic curvature indicates the function range Dirac-3 samples." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.linspace(0, 10, 100)\n", "Y = np.linspace(0, 10, 100)\n", "X, Y = np.meshgrid(X, Y)\n", "Z = X*Y**2 - X**2*Y - X*X - 2*X +Y*Y\n", "fig, ax = plt.subplots(subplot_kw={\"projection\": \"3d\"})\n", "surface = ax.plot_surface(X, Y, Z, cmap=cm.jet)\n", "\n", "# Add a color bar which maps values to colors.\n", "fig.colorbar(surface, shrink=0.5, aspect=5)\n", "X2 = np.linspace(0, 10, 20)\n", "Y2 = 10 - X2\n", "Z2 = X2 * Y2 ** 2 - X2 ** 2 * Y2 - X2 ** 2 - 2 * X2 + Y2 ** 2\n", "ax.plot3D(X2, Y2, Z2, \"k-\")\n", "X3 = X2 * np.ones((20, 20))\n", "Y3 = 10 - X3\n", "Z3 = np.linspace(np.min(Z), np.max(Z), 20) * np.ones((20, 20))\n", "sum_surface = ax.plot_surface(X3, Y3, Z3.T, alpha=0.2)\n", "ax.view_init(azim=15, elev=20)\n", "ax.set_xlabel(\"$x$\")\n", "ax.set_ylabel(\"$y$\")\n", "ax.set_zlabel(\"$f(x,y)$\")\n", "ax.zaxis.set_label_position(\"upper\")\n", "ax.zaxis.set_ticks_position(\"upper\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Running the Problem\n", "We will prepare data in a list and a list of lists, upload the polynomial file to Qatalyst and submit a job.\n", "\n", "### QciClient Instantiation\n", "This call to `QciClient` uses the environment variables `QCI_TOKEN` and `QCI_API_URL` to configure the API connection. It may also be called with `api_token` and `url` parameters to configure it explicitly. See the [Quick Start on Cloud](https://quantumcomputinginc.com/learn/tutorials-and-use-cases/quick-start-on-cloud) tutorial for a deeper explanation on this configuration.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "client = qc.QciClient()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Polynomial Format\n", "The ability to support higher order terms efficiently for the majority of problems requires a sparse format. That format is inspired by polynomials themselves. Two different arrays are required. The first is a coefficient array. Each term in the function has an entry in the coefficient array. The second array, the indices array, is where to indicate which term the corresponding coefficient is for. The second polynomial from above is presented here.\n", "\n", "$$\n", "f(x,y)=xy^2-x^2y+x+y\n", "$$ \n", "is represented in polynomial format\n", "```\n", "poly_coefficients = [1, -1, 1, 1]\n", "poly_indices = [[1, 2, 2], [1, 1, 2], [0, 0, 1], [0, 0, 2]]\n", "```\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'6672ed6798263204a365ddc1'" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "poly_coefficients = [1, -1, 1, 1]\n", "poly_indices = [[1, 2, 2], [1, 1, 2], [0, 0, 1], [0, 0, 2]]\n", "data = []\n", "for i in range(len(poly_coefficients)):\n", " data.append({\n", " \"val\": poly_coefficients[i],\n", " \"idx\": poly_indices[i]\n", " })\n", "poly_file = {\"file_name\": \"test-polynomial\",\n", " \"file_config\": {\"polynomial\": {\n", " \"min_degree\": 1,\n", " \"max_degree\": 3,\n", " \"num_variables\": 2,\n", " \"data\": data\n", " }}}\n", "file_id = client.upload_file(file=poly_file)[\"file_id\"]\n", "file_id" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'file_name': 'test-polynomial',\n", " 'file_config': {'polynomial': {'min_degree': 1,\n", " 'max_degree': 3,\n", " 'num_variables': 2,\n", " 'data': [{'val': 1, 'idx': [1, 2, 2]},\n", " {'val': -1, 'idx': [1, 1, 2]},\n", " {'val': 1, 'idx': [0, 0, 1]},\n", " {'val': 1, 'idx': [0, 0, 2]}]}}}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "poly_file" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'job_submission': {'problem_config': {'normalized_qudit_hamiltonian_optimization': {'polynomial_file_id': '6672ed6798263204a365ddc1'}},\n", " 'device_config': {'dirac-3': {'num_samples': 15,\n", " 'relaxation_schedule': 1,\n", " 'solution_precision': 1,\n", " 'sum_constraint': 10}}}}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "job_body = client.build_job_body(job_type=\"sample-hamiltonian\", polynomial_file_id=file_id, job_params={\"device_type\": \"dirac-3\", \"sum_constraint\": 10, \"solution_precision\": 1, \"relaxation_schedule\": 1, \"num_samples\": 15})\n", "job_body" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2024-06-19 08:38:31 - Dirac allocation balance = 0 s (unmetered)\n", "2024-06-19 08:38:31 - Job submitted: job_id='6672ed67a3e6a645a5c4e7c5'\n", "2024-06-19 08:38:31 - QUEUED\n", "2024-06-19 08:38:34 - RUNNING\n", "2024-06-19 08:38:55 - COMPLETED\n", "2024-06-19 08:38:57 - Dirac allocation balance = 0 s (unmetered)\n" ] } ], "source": [ "response = client.process_job(job_body=job_body)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'job_info': {'job_id': '6672ed67a3e6a645a5c4e7c5',\n", " 'job_submission': {'problem_config': {'normalized_qudit_hamiltonian_optimization': {'polynomial_file_id': '6672ed6798263204a365ddc1'}},\n", " 'device_config': {'dirac-3': {'num_samples': 15,\n", " 'relaxation_schedule': 1,\n", " 'solution_precision': 1,\n", " 'sum_constraint': 10}}},\n", " 'job_status': {'submitted_at_rfc3339nano': '2024-06-19T14:38:31.913Z',\n", " 'queued_at_rfc3339nano': '2024-06-19T14:38:31.913Z',\n", " 'running_at_rfc3339nano': '2024-06-19T14:38:32.764Z',\n", " 'completed_at_rfc3339nano': '2024-06-19T14:38:54.734Z'},\n", " 'job_result': {'file_id': '6672ed7e98263204a365ddc3', 'device_usage_s': 20}},\n", " 'status': 'COMPLETED',\n", " 'results': {'counts': [4, 4, 2, 2, 2, 1],\n", " 'energies': [-77.1194382,\n", " -84.6596832,\n", " -74.1873169,\n", " -83.8009644,\n", " -83.8447723,\n", " -86.1170654],\n", " 'solutions': [[7.1276598, 2.8723404],\n", " [8.182374, 1.817626],\n", " [7.0072289, 2.9927711],\n", " [7.504097, 2.4959033],\n", " [7.5076513, 2.4923487],\n", " [7.8074245, 2.1925759]],\n", " 'distilled_energies': [-86, -86, -86, -86, -86, -86],\n", " 'distilled_solutions': [[8, 2], [8, 2], [8, 2], [8, 2], [8, 2], [8, 2]]}}" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "response" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dirac-3 has identified multiple solutions near the integer optimal solution `[8, 2]` with a value of -86 with some less than -86.\n", "\n", "### Next Steps\n", "\n", "Beyond two variables, visualization becomes tricky, but the value of the solver becomes higher. The current version of Dirac-3 supports 135 variables with rank 3 polynomials. \n", "\n", "Try experimenting with different polynomials using the format described." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this tutorial, we have shown how to perform polynomial optimization using multi-body terms on our Dirac-3 device. While polynomial optimization is less explored than conventional combinatorial optimization, it is still a powerful paradigm. The importance of multibody capabilities (beyond quadratic) terms is highlighted by the fact that while continuum quadratic optimization (at least in the case of unbounded variables and no constraints) is known to be solvable using well established techniques, the addition of fourth order terms renders these problems NP-hard. This tutorial gives an example of how our hardware can be used to explore new frontiers in optimization using cutting edge optical hardware." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.4" } }, "nbformat": 4, "nbformat_minor": 4 }