diff --git a/community/QInnovision_2025/advection_equation/advection.ipynb b/community/QInnovision_2025/advection_equation/advection.ipynb new file mode 100644 index 000000000..f61f66fb7 --- /dev/null +++ b/community/QInnovision_2025/advection_equation/advection.ipynb @@ -0,0 +1,892 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solving the Advection Equation\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Author\n", + "\n", + "The work is submitted by Yevgeny Menaker (registered as @yev as part of team @quantotto on Aqora platform) for QInnovision World Challenge 2025.\n", + "\n", + "LinkedIn: https://www.linkedin.com/in/yevgeny-menaker-5a2b841/\n", + "\n", + "Email: yev@quantotto.io" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from classiq import *\n", + "from classiq.execution import (\n", + " ClassiqBackendPreferences,\n", + " ExecutionPreferences,\n", + " ClassiqSimulatorBackendNames,\n", + ")\n", + "from classiq.synthesis import set_execution_preferences\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we define hyper-parameters for the quantum program." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "n_qbits = 7 # number of qubit to use\n", + "t = 1.0 # evolution time\n", + "tau = 1.0/32 # time step for trotterization\n", + "shots = 4096 # Number of shots to sample\n", + "\n", + "def get_steps(t: float, tau: float) -> int:\n", + " return int(np.floor(t/tau))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "In this work, we will be solving Partial Differential Equation governing the fluid dynamics (advection) on a quantum computer. The algorithm will leverage the Hamiltonian simulation after transforming the given advection equation into the Shrödinger one. The work is based on a scientific paper by Yuki Sato et. al \"Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits\".\n", + "\n", + "The advection equation is of the following form:\n", + "\n", + "$\\frac{\\partial{\\phi}}{\\partial{t}}+\\frac{\\partial{\\phi}}{\\partial{x}}=0$\n", + "\n", + "with the Dirichlet boundary conditions:\n", + "\n", + "$\\phi(0, x)=\n", + "\\begin{cases}\n", + "1, & \\text{if } 1 < x < 2\\\\\n", + "0, & \\text{otherwise}\n", + "\\end{cases}\n", + "$\n", + "\n", + "Note that the more general form of the advection equation is:\n", + "\n", + "$\\frac{\\partial{\\phi}}{\\partial{t}}+U\\frac{\\partial{\\phi}}{\\partial{x}}=0$\n", + "\n", + "where $U$ is the fluid speed. In our case, we assume $U=1$. Hence, it is omitted.\n", + "\n", + "\n", + "The solution is organized in five parts. Part I presents a numeric solution using the classical algorithm to serve as a reference for evaluating the accuracy of quantum results. Part II describes the transformation of advection equation into a Shrödinger form and builds a relevant Hamiltonian. Part III constructs the Classiq based program, executes the simulation, provides graphical visualization and analyzes the results. Part IV discusses the effciency of the circuit with respect to the CX gates count. Part V summarizes the findings." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part I - Classical Solution\n", + "\n", + "Here we present the classical way to solving the advection equation at $t=1.0$. We will disretise the space variable $x$ and the values at each point will be computed iteratively. The approach was inspired by the Julia code in Reference #2." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def phi_0_x(x):\n", + " if 1 < x < 2:\n", + " return 1\n", + " else:\n", + " return 0\n", + "\n", + "n = 2 ** n_qbits\n", + "x_axis = np.linspace(0, 4, n)\n", + "boundary = [phi_0_x(x) for x in x_axis]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(x_axis, boundary, label=\"φ(x, t=0.0)\")\n", + "\n", + "ax.set_xlabel(\"X\")\n", + "ax.set_ylabel(\"phi\")\n", + "ax.legend()\n", + "\n", + "ax.set_title(f\"Dirichlet Boundary\")\n", + "plt.show(block=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We need to evolve the initial (boundary) vector representing phi at $t=0$ for a few computational steps till $t=1$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def step(phi: list[float], dt: float, dx: float) -> list[float]:\n", + " new_phi = np.zeros(len(phi))\n", + " for i in range(1, len(phi)-1):\n", + " new_phi[i] = phi[i] - dt * (phi[i+1] - phi[i-1]) / (2*dx)\n", + " return new_phi\n", + "\n", + "def evolve(initial, t, dt, dx):\n", + " phi = initial\n", + " cur_t = dt\n", + " while cur_t <= t:\n", + " phi = step(phi, dt, dx)\n", + " cur_t += dt\n", + " return phi" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "dx = x_axis[1]-x_axis[0]\n", + "dt = 0.001\n", + "solution = evolve(boundary, t, dt, dx)\n", + "fig, ax = plt.subplots()\n", + "ax.plot(x_axis, boundary, label=\"φ(x, t=0.0)\")\n", + "ax.plot(x_axis, solution, label=f\"φ(x, t={t})\")\n", + "\n", + "ax.set_xlabel(\"X\")\n", + "ax.set_ylabel(\"φ\")\n", + "ax.legend()\n", + "\n", + "ax.set_title(f\"Classical Numeric Solution at t={t}\")\n", + "plt.show(block=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see in the plot, the particles moved to the right the distance of 1.0 at the time 1.0. This makes sense, because our advection equation assumes $U=1$ (the speed of the fluid; as mentioned in the Introduction section)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have the reference solution, we will move on to building the quantum algorithm for solving the partial differential equation by means of Hamiltonian simulation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part II - Building Hamiltonian\n", + "\n", + "Our goal is to transform the Advection equation into the Shrödinger form and build the respective Hamiltonian that can be simulated on a quantum computer. The following mathematical steps show the transformation. Note that, like in the scientific paper, we switch to the $\\nabla$ operator for the spatial derivative:\n", + "\n", + "$\\nabla=\\frac{\\partial{\\phi}}{x}$\n", + "\n", + "Another \"trick\" that is used is multiplying one side of equation by $-i\\cdot-i$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the steps:\n", + "\n", + "$\\frac{\\partial{\\phi}}{\\partial{t}}+\\frac{\\partial{\\phi}}{\\partial{x}}=0$\n", + "\n", + "$\\frac{\\partial{\\phi}}{\\partial{t}}+\\nabla\\phi(t, x)=0$\n", + "\n", + "$\\frac{\\partial{\\phi}}{\\partial{t}}=-\\nabla\\phi(t, x)$\n", + "\n", + "$\\frac{\\partial{\\phi}}{\\partial{t}}=-i\\cdot(-i)\\cdot\\nabla\\phi(t, x)$\n", + "\n", + "And from this, our Hamiltonian is:\n", + "\n", + "$H=(-i)\\cdot\\nabla$\n", + "\n", + "The $\\nabla$ operator can be represented by the central difference discretization $(D^\\pm)$:\n", + "\n", + "$H=-i(D^\\pm)$\n", + "\n", + "$(D^\\pm)_j=\\frac{u_{j+1}-u_{j-1}}{2l} for j=0, 1, ..., N-1$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the next section, we will build a circuit that will evolve the Hamiltonian from time $t=0$ till $t=1$. The initial state is defined by the Dirichlet boundary conditions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part III - Constructing and Executing the Quantum Circuit\n", + "\n", + "Our quantum program will consist of the following high level steps:\n", + "\n", + "- Encoding initial scalar field (as defined by Dirichlet boundary conditions for $\\phi(0,x)$ in the Introduction section)\n", + "- Evolving the quantum state using the Hamiltonian simulation\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While we leverage the technique from the scientific paper, we do introduce a few modifications in terms of choice of gates and also Hamiltonian simulation approximation.\n", + "\n", + "### Initial State\n", + "\n", + "The given advection equation will be solved by the approximated evolution of the Hamiltonian applied to the initial state.\n", + "\n", + "- We divide the $x$ axis $[0, 4]$ into $2^n$ ($n$ is number of qubits) discrete segments of length $l=\\frac{1}{2^n}$\n", + "- We prepare the initial state having equal amplitudes in $[1, 2]$ and 0 everywhere else\n", + "\n", + "As an example, in case of 7 qubits, we will have 128 segments. Amplitudes 0-31 refer to $\\phi(0, x)$ values at $[0, 1)$, 32-63 at $[1, 2)$ etc. So, the Dirichlet boundary for our concrete case of the Advection equation will be expressed by setting the 32-63 amplitudes to be equal $\\sqrt{\\frac{1}{32}}$ (which means they all have the same probability of $\\frac{1}{32}$).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Time Evolution Operator\n", + "\n", + "The time evolution operator is denoted as $V(\\gamma\\tau, \\lambda)$.\n", + "- $\\gamma$ is the scaling parameter and it is equal to $\\frac{1}{2l}$ for the centrall difference operator, where $l$ is length of a segment\n", + "- $\\tau$ is the time length of the evolution step and this is our hyper-parameter. After verious tests it was chosen to be $\\frac{1}{32}$\n", + "- $\\lambda$ is the phase parameter. This comes from the fact that the Hamiltonian is based on the Central Difference operator, which is expressed as sum of sums of two shift operators. \n", + "\n", + "$H = -i(D^\\pm) = \\sum_{j=1}^{n}(-i)(s^-)_j-(-i)(s^+)_j = \\sum_{j=1}^{n}(-i)(s^-)_j+i(s^+)_j$\n", + "\n", + "In the more generic terms used for the derivation of the approximate time evolution operator, each j-th term is expressed as $e^{i\\lambda}(s^-)_j+e^{-i\\lambda}(s^+)_j$. Hence, we set $e^{i\\lambda}=-i$ and $e^{-i\\lambda}=i$ for advection equation and we obtain $\\lambda=-\\frac{\\pi}{2}$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### RY substitution\n", + "\n", + "The scientific paper shows that the forementioned operator $V$ can be expressed as product of $W_j$ operators:\n", + "\n", + "$V=\\prod_{j=1}^{n}W_j(\\gamma\\tau, \\lambda)=\\prod_{j=1}^{n}W_j(\\frac{1}{2l}\\cdot\\tau, \\frac{-\\pi}{2})$\n", + "\n", + "The paper shows that each $W_j$ is implemented using the Phase shift, Hadamard and CRZ gates (between a ladder of CNOT gates). We note that in case of Advection equation, we can substitute the hadamard, phase shift and CRZ gates with a single gate CRY. This comes from the fact that the phase $\\lambda=-\\frac{\\pi}{2}$. It doesn't necessarily produce more efficient circuit, but it makes the code more concise. We modified the circuit depicted on FIG. 1 in the paper as shown below." + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2nd Order Approximation\n", + "\n", + "Based on multiple runs and hyper-parameters tuning, we notice that the best results are obtained with the 2nd order approximation described by the equation (44) in the scientific paper.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$W_1$ operator doesn't introduce extra CNOT gates because it acts on a single qubit." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Circuit Code\n", + "\n", + "With the above details in place, we can now implement the circuit using the Classiq platform. We haven't used the specialized `suzuki_trotter` function offered by Classiq, becuase it requires the Hamiltonian argument to be defined in terms of Pauli operators. In case of Advection equation, this would result in the exponential number of terms (more precisely $2^n-1$ Pauli terms). Due to this reason, the \"trotterization\" was implemented manually." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "@qfunc\n", + "def u(qbits: QArray[QBit], j: CInt):\n", + " # CNOT ladder\n", + " repeat(count=j, iteration=lambda i: CX(qbits[j], qbits[i]))\n", + "\n", + "@qfunc\n", + "def controlled_rotate(control_qbits: QArray[QBit], target: QBit, dt: CReal):\n", + " control(ctrl=control_qbits, stmt_block=lambda: RY(2*dt, target))\n", + "\n", + "@qfunc\n", + "def step(qbits: QArray[QBit], j: CInt, dt: CReal):\n", + " within_apply(\n", + " within=lambda: u(qbits, j),\n", + " apply=lambda: controlled_rotate(qbits[0:j], qbits[j], dt)\n", + " )\n", + "\n", + "@qfunc\n", + "def ladder(qbits: QArray[QBit], dt: CReal):\n", + " \"\"\"Use second order approximation\n", + " \"\"\"\n", + " # W1(-$\\tau$/2)\n", + " RY(-dt, qbits[0])\n", + "\n", + " # V\n", + " RY(2*dt, qbits[0])\n", + " repeat(count=qbits.len-1, iteration=lambda i: step(qbits[0:i+2], i+1, dt))\n", + " \n", + " # W1($\\tau$/2)\n", + " RY(dt, qbits[0])\n", + "\n", + "def model_factory(n_qbits: int, t: CReal, tau: CReal) -> QCallable:\n", + " steps = get_steps(t, tau)\n", + " initial = np.zeros(2**n_qbits)\n", + " domain_length = 4\n", + " segment_one = 2**n_qbits // domain_length\n", + " l = 1 / segment_one\n", + " initial[segment_one:2*segment_one] = np.sqrt(1/segment_one)\n", + "\n", + " @qfunc\n", + " def main(qbits: Output[QArray[n_qbits]]):\n", + " prepare_amplitudes(amplitudes=initial.tolist(), bound=0.01, out=qbits)\n", + " repeat(count=steps, iteration=lambda i: ladder(qbits, t/(2*l)/steps))\n", + "\n", + " return main" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`create_program` function synthesizes the quantum program for a given set of hyper-parameters and evolution time $t$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "async def create_program(n_qbits: int, t: float, tau: float, factory: callable=model_factory):\n", + " backend_preferences = ClassiqBackendPreferences(backend_name=ClassiqSimulatorBackendNames.SIMULATOR_STATEVECTOR)\n", + " model = create_model(factory(n_qbits, t, tau))\n", + " model = set_execution_preferences(\n", + " model,\n", + " execution_preferences=ExecutionPreferences(\n", + " num_shots=shots, backend_preferences=backend_preferences\n", + " ),\n", + " )\n", + " qprog = await synthesize_async(model)\n", + " return qprog" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`solve` function puts it all together and executes the Quantum Program returning both the result and the synthesized program (to allow circuit analysis)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "async def solve(n_qbits: int, t: float, tau: float, factory: callable=model_factory):\n", + " qprog = await create_program(n_qbits, t, tau, factory)\n", + " result = await execute_async(qprog)\n", + " return (await result.result_async())[0].value.model_dump(), qprog" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we obtain the solution for time $t$ and also display basic information about the circuit (width, depth and CX gates count).\n", + "\n", + "The solution is extracted from counts of each state dividing by number of shots and multiplying by the appropriate scaling factor.\n", + "\n", + "We use 7 qubits, $\\tau=\\frac{1}{32}$ and 4096 shots (configured in the beginning of the Notebook)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "width=9\n", + "depth=15789\n", + "cx count=10750\n" + ] + } + ], + "source": [ + "r, qprog_t_1 = await solve(n_qbits, t, tau)\n", + "circuit = QuantumProgram.from_qprog(qprog_t_1)\n", + "width = circuit.data.width\n", + "depth = circuit.transpiled_circuit.depth\n", + "cx_count = circuit.transpiled_circuit.count_ops[\"cx\"]\n", + "print(f\"width={width}\\ndepth={depth}\\ncx count={cx_count}\")\n", + "\n", + "position = np.linspace(0.0, 4.0, 2 ** n_qbits)\n", + "states = [f\"{i:0{n_qbits}b}\" for i in range(2 ** n_qbits)]\n", + "scale = ((2 ** n_qbits) // 4)\n", + "quantum_solution = [scale*(r[\"counts\"].get(state, 0)/shots) for state in states]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are now ready to plot the solution. The resulting function $\\phi(x, t=1.0)$ is shown below." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(position, quantum_solution, label=f\"quantum φ(x, t={t})\")\n", + "\n", + "ax.set_xlabel(\"X\")\n", + "ax.set_ylabel(\"φ\")\n", + "ax.legend()\n", + "\n", + "ax.set_title(f\"Quantum Solution at t={t} (with {n_qbits} qubits)\")\n", + "plt.show(block=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we plot the initial state and two solutions (classical and quantum) side by side to show a significant overlap. Quantum solution doesn't suffer from the oscillations outside of the [2.0, 3.0] segment like the classical numeric one." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(position, boundary, label=\"φ(x, t=0.0)\")\n", + "ax.plot(position, solution, label=f\"classical φ(x, t={t})\")\n", + "ax.plot(position, quantum_solution, label=f\"quantum φ(x, t={t})\")\n", + "\n", + "ax.set_xlabel(\"X\")\n", + "ax.set_ylabel(\"φ\")\n", + "ax.legend()\n", + "\n", + "ax.set_title(f\"Classical and Quantum Solutions at t={t}\")\n", + "plt.show(block=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part IV - CX Gates Count Analysis\n", + "\n", + "Let us now look at the CX gates count for various values of evolution time $t$.\n", + "\n", + "Here we create a few functions to facilitate the CX count calculation (either extracting from Quantum Program or calculating based on the scientific paper formula)." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "def count_cx_ops_in_qprog(qprog) -> int:\n", + " circuit = QuantumProgram.from_qprog(qprog)\n", + " return circuit.transpiled_circuit.count_ops[\"cx\"]\n", + "\n", + "async def count_cx_ops(n_qbits: int, t: float, tau: float) -> int:\n", + " qprog = await create_program(n_qbits, t, tau)\n", + " return count_cx_ops_in_qprog(qprog)\n", + "\n", + "def count_cx_theory(n_qbits: int, t: float, tau: float) -> int:\n", + " steps = get_steps(t, tau)\n", + " return steps*((9*(n_qbits**2)) - (33*n_qbits) + 34)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we extract the CX gates count from the quantum program we executed above for $t=1$ and compare it with paper prediction." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Classiq CX count: 10750; Paper CX estimation: 7808\n" + ] + } + ], + "source": [ + "classiq_cx_count = count_cx_ops_in_qprog(qprog_t_1)\n", + "paper_cx_estimation = count_cx_theory(n_qbits, t, tau)\n", + "print(f\"Classiq CX count: {classiq_cx_count}; Paper CX estimation: {paper_cx_estimation}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we can calculate the CX counts for different values of evolution time $t$. Below we do that for $t=0.5, 1.0, 1.5, 2.0$ and plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "times = np.linspace(0.5, 2.0, 4)\n", + "cx_counts = [await count_cx_ops(n_qbits, t_, tau) for t_ in times]\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(times, cx_counts, label=\"CX counts\")\n", + "\n", + "ax.set_xlabel(\"t\")\n", + "ax.set_ylabel(\"CX count\")\n", + "ax.legend()\n", + "\n", + "ax.set_title(f\"CX Gates Count per t\")\n", + "plt.show(block=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is also beneficial to plot it against the values predicted in the paper. Additionally, we calculate the ratio of Classiq CX gates and paper predicted counts." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "paper_cx_counts = [count_cx_theory(n_qbits, t_, tau) for t_ in times]\n", + "ratio = [cx_counts[i]/paper_cx_counts[i] for i in range(len(times))]" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(times, cx_counts, label=\"Classiq CX counts\")\n", + "ax.plot(times, paper_cx_counts, label=\"Paper CX counts\")\n", + "\n", + "ax.set_xlabel(\"t\")\n", + "ax.set_ylabel(\"CX count\")\n", + "ax.legend()\n", + "\n", + "ax.set_title(f\"CX Gates Count per t (Comparison)\")\n", + "plt.show(block=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(times, ratio, label=\"CX ratio\")\n", + "\n", + "ax.set_ylim(1, 2)\n", + "ax.set_xlabel(\"t\")\n", + "ax.set_ylabel(\"ratio\")\n", + "ax.legend()\n", + "\n", + "ax.set_title(f\"CX Gates Ratio (Classiq/Paper) per t\")\n", + "plt.show(block=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The number of CX in the Classiq's generated circuit is slightly more than projected by the scientific paper. As we can see from the plot above the ratio `classiq_cx/paper_cx` is close to $1.4$.\n", + "\n", + "Below we explain the discrepancy.\n", + "\n", + "The paper predicts $16*n-40$ CX gates for CRZ decomposition, but Classiq's one is sometimes bigger as calculated below. Also, note that synthesizing the same circuit may produce different results in terms of CX gates count from run to run." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CX count for CRY:\n", + "[2 qubits] classiq's count: 2; paper prediction: 2\n", + "[3 qubits] classiq's count: 12; paper prediction: 8\n", + "[4 qubits] classiq's count: 18; paper prediction: 24\n", + "[5 qubits] classiq's count: 24; paper prediction: 40\n", + "[6 qubits] classiq's count: 106; paper prediction: 56\n", + "[7 qubits] classiq's count: 168; paper prediction: 72\n" + ] + } + ], + "source": [ + "qbits_range = list(range(2, n_qbits+1))\n", + "async def count_cx_for_cry(n: CInt) -> int:\n", + " @qfunc\n", + " def main(control_qbits: Output[QArray], target: Output[QBit]):\n", + " allocate(n-1, control_qbits)\n", + " allocate(1, target)\n", + " hadamard_transform(control_qbits)\n", + " X(target)\n", + " control(ctrl=control_qbits, stmt_block=lambda: RY(np.pi/4, target))\n", + "\n", + " my_model = create_model(main)\n", + " my_qprog = await synthesize_async(my_model)\n", + " circuit = QuantumProgram.from_qprog(my_qprog)\n", + " return circuit.transpiled_circuit.count_ops[\"cx\"]\n", + "\n", + "cx_counts_for_cry = { qbits: (await count_cx_for_cry(qbits), 16*qbits - 40 if qbits > 2 else 2) for qbits in qbits_range }\n", + "print(f\"CX count for CRY:\")\n", + "for qbits, counts in cx_counts_for_cry.items():\n", + " print(f\"[{qbits} qubits] classiq's count: {counts[0]}; paper prediction: {counts[1]}\")\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Graphically, the comparison will look as below." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(qbits_range, cx_counts_for_cry.values(), label=(\"Classiq\", \"Paper\"))\n", + "\n", + "ax.set_xlabel(\"number of qubits\")\n", + "ax.set_ylabel(\"CX count\")\n", + "ax.set_xticks(qbits_range)\n", + "ax.legend()\n", + "\n", + "ax.set_title(f\"CX Gates Count per CRY\")\n", + "plt.show(block=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Based on this, it makes sense that we are getting higher counts of CX gates from the Classiq platform." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part V - Summary\n", + "\n", + "In this work, we focused on implementing the algorithm solving the Advection Equation by means of Hamiltonian simulation relying on the technique from the scientific paper (Reference 1). We have designated several hyper-parameters to tune the model and also analyzed the resulting CX gates count for different inputs. We ended up using the 2nd order Trotter Approximation. It results in a more accurate differential equation solution without higher CX gates count.\n", + "\n", + "We found the ration of ~1.4 for $\\frac{CX(Classiq)}{CX(Paper)}$.\n", + "\n", + "We opted for making the following choice of hyper-parameters:\n", + "- 7 qubits\n", + "- 4096 shots\n", + "- $\\frac{1}{32}$ as the time step for approximate evolution of Hamiltonian\n", + "\n", + "One of the future directions to explore would be looking at 1-sparse Hamiltonian simulation as well as more tuning of hyper-parameters and analyzing the resulting circuits' depth and CX gates count." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "\n", + "1. [\"Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits\"](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.6.033246) Physical Review Research 6.3 (2024): 033246 by Sato, Yuki, et al. \n", + "2. [\"Evolution in time and space: Advection and diffusion in 1D\"](https://computationalthinking.mit.edu/Fall24/climate_science/advection_and_diffusion/), Introduction to Computational Thinking course at MIT by by Alan Edelman, David P. Sanders & Charles E. Leiserson " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "clqenv", + "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": "3.10.11" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tests/resources/timeouts.yaml b/tests/resources/timeouts.yaml index 7798b4ca3..e2114c0a6 100644 --- a/tests/resources/timeouts.yaml +++ b/tests/resources/timeouts.yaml @@ -315,6 +315,7 @@ pennylane_cat_qsvt_example.ipynb: 300 qiskit_qsvt.ipynb: 300 time_marching.ipynb: 500 time_marching.qmod: 400 +advection.ipynb: 500 solving_qlsp_with_aqc.ipynb: 800 solving_qlsp_with_aqc.qmod: 800 combinatorial_qmod_workshop_for_maxcut.ipynb: 250