4_quantum/qcbm_gaussian.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum Circuit Born Machine\n",
    "\n",
    "Yao is designed with variational quantum circuits in mind, and this tutorial\n",
    "will introduce how to use Yao for this kind of task by implementing a quantum\n",
    "circuit born machine described in [Jin-Guo Liu, Lei Wang (2018)](https://arxiv.org/abs/1804.04168)\n",
    "\n",
    "let's use the package first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Plots.PyPlotBackend()"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Yao, LinearAlgebra\n",
    "using Plots\n",
    "pyplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training Target\n",
    "\n",
    "In this tutorial, we will ask the variational circuit to learn the most basic\n",
    "distribution: a guassian distribution. It is defined as follows:\n",
    "\n",
    "$$\n",
    "f(x \\left| \\mu, \\sigma^2\\right) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}\n",
    "$$\n",
    "\n",
    "We implement it as `gaussian_pdf`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "function gaussian_pdf(x, μ::Real, σ::Real)\n",
    "    pl = @. 1 / sqrt(2pi * σ^2) * exp(-(x - μ)^2 / (2 * σ^2))\n",
    "    pl / sum(pl)\n",
    "end\n",
    "pg = gaussian_pdf(1:1<<6, 1<<5-0.5, 1<<4);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(1:1<<6, pg, ylabel=\"prob\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the Circuit\n",
    "\n",
    "A quantum circuit born machine looks like the following:\n",
    "\n",
    "![differentiable ciruit](images/differentiable.png)\n",
    "\n",
    "It is composited by two different layers: **rotation layer** and **entangler layer**.\n",
    "\n",
    "## Rotation Layer\n",
    "\n",
    "Arbitrary rotation is built with **Rotation Gate** on **Z, X, Z** axis\n",
    "with parameters.\n",
    "\n",
    "$$\n",
    "Rz(\\theta) \\cdot Rx(\\theta) \\cdot Rz(\\theta)\n",
    "$$\n",
    "\n",
    "Since our input will be a $|0\\dots 0\\rangle$ state.\n",
    "The first layer of arbitrary rotation can just\n",
    "use $Rx(\\theta) \\cdot Rz(\\theta)$ and the last\n",
    "layer of arbitrary rotation could just\n",
    "use $Rz(\\theta)\\cdot Rx(\\theta)$\n",
    "\n",
    "In **幺**, every Hilbert operator is a **block** type, this\n",
    "ncludes all **quantum gates** and **quantum oracles**.\n",
    "In general, operators appears in a quantum circuit\n",
    "can be divided into **Composite Blocks** and **Primitive Blocks**.\n",
    "\n",
    "We follow the low abstraction principle and\n",
    "thus each block represents a certain approach\n",
    "of calculation. The simplest **Composite Block**\n",
    "is a **Chain Block**, which chains other blocks\n",
    "(oracles) with the same number of qubits together.\n",
    "It is just a simple mathematical composition of\n",
    "operators with same size. e.g.\n",
    "\n",
    "\n",
    "$$\n",
    "\\text{chain(X, Y, Z)} \\iff X \\cdot Y \\cdot Z\n",
    "$$\n",
    "\n",
    "We can construct an arbitrary rotation block by chain ``Rz``, ``Rx``, ``Rz`` together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mnqubits: 1, datatype: Complex{Float64}\u001b[39m\n",
       "\u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "├─ rot(Z gate, 0.0)\n",
       "├─ rot(X gate, 0.0)\n",
       "└─ rot(Z gate, 0.0)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chain(Rz(0.0), Rx(0.0), Rz(0.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[`Rx`](@ref), [`Rz`](@ref) will construct new rotation gate,\n",
    "which are just shorthands for `rot(X, 0.0)`, etc.\n",
    "\n",
    "Then let's chain them up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "layer(nbit::Int, x::Symbol) = layer(nbit, Val(x))\n",
    "layer(nbit::Int, ::Val{:first}) = chain(nbit, put(i=>chain(Rx(0), Rz(0))) for i = 1:nbit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do not need to feed the first `n` parameter into `put` here.\n",
    "All factory methods can be **lazy** evaluate **the first arguements**, which is the number of qubits.\n",
    "It will return a lambda function that requires a single interger input.\n",
    "The instance of desired block will only be constructed until all the information is filled.\n",
    "When you filled all the information in somewhere of the declaration, 幺 will be able to infer the others.\n",
    "We will now define the rest of rotation layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "layer(nbit::Int, ::Val{:last}) = chain(nbit, put(i=>chain(Rz(0), Rx(0))) for i = 1:nbit)\n",
    "layer(nbit::Int, ::Val{:mid}) = chain(nbit, put(i=>chain(Rz(0), Rx(0), Rz(0))) for i = 1:nbit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entangler\n",
    "\n",
    "Another component of quantum circuit born machine are\n",
    "several **CNOT** operators applied on different qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "entangler(pairs) = chain(control(ctrl, target=>X) for (ctrl, target) in pairs);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then define such a born machine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "build_circuit (generic function with 1 method)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function build_circuit(n, nlayers, pairs)\n",
    "    circuit = chain(n)\n",
    "    push!(circuit, layer(n, :first))\n",
    "    for i in 2:nlayers\n",
    "        push!(circuit, cache(entangler(pairs)))\n",
    "        push!(circuit, layer(n, :mid))\n",
    "    end\n",
    "    push!(circuit, cache(entangler(pairs)))\n",
    "    push!(circuit, layer(n, :last))\n",
    "    return circuit\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the method `cache` here to tag the entangler block that it\n",
    "should be cached after its first run, because it is actually a\n",
    "constant oracle. Let's see what will be constructed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mnqubits: 4, datatype: Complex{Float64}\u001b[39m\n",
       "\u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "│  ├─ \u001b[36m\u001b[1mput on (\u001b[22m\u001b[39m\u001b[36m\u001b[1m1\u001b[22m\u001b[39m\u001b[36m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│  │  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "│  │     ├─ rot(X gate, 0.0)\n",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  ├─ \u001b[36m\u001b[1mput on (\u001b[22m\u001b[39m\u001b[36m\u001b[1m2\u001b[22m\u001b[39m\u001b[36m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│  │  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "│  │     ├─ rot(X gate, 0.0)\n",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  ├─ \u001b[36m\u001b[1mput on (\u001b[22m\u001b[39m\u001b[36m\u001b[1m3\u001b[22m\u001b[39m\u001b[36m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│  │  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "│  │     ├─ rot(X gate, 0.0)\n",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  └─ \u001b[36m\u001b[1mput on (\u001b[22m\u001b[39m\u001b[36m\u001b[1m4\u001b[22m\u001b[39m\u001b[36m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│     └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "│        ├─ rot(X gate, 0.0)\n",
       "│        └─ rot(Z gate, 0.0)\n",
       "├─ \u001b[33m\u001b[1m[cached] \u001b[22m\u001b[39m\u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "│     ├─ \u001b[31m\u001b[1mcontrol(\u001b[22m\u001b[39m\u001b[31m\u001b[1m1\u001b[22m\u001b[39m\u001b[31m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│     │  └─ \u001b[37m\u001b[1m(2,)\u001b[22m\u001b[39m X gate\n",
       "│     ├─ \u001b[31m\u001b[1mcontrol(\u001b[22m\u001b[39m\u001b[31m\u001b[1m2\u001b[22m\u001b[39m\u001b[31m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│     │  └─ \u001b[37m\u001b[1m(3,)\u001b[22m\u001b[39m X gate\n",
       "│     └─ \u001b[31m\u001b[1mcontrol(\u001b[22m\u001b[39m\u001b[31m\u001b[1m3\u001b[22m\u001b[39m\u001b[31m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│        └─ \u001b[37m\u001b[1m(4,)\u001b[22m\u001b[39m X gate\n",
       "└─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "   ├─ \u001b[36m\u001b[1mput on (\u001b[22m\u001b[39m\u001b[36m\u001b[1m1\u001b[22m\u001b[39m\u001b[36m\u001b[1m)\u001b[22m\u001b[39m\n",
       "   │  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "   │     ├─ rot(Z gate, 0.0)\n",
       "   │     └─ rot(X gate, 0.0)\n",
       "   ├─ \u001b[36m\u001b[1mput on (\u001b[22m\u001b[39m\u001b[36m\u001b[1m2\u001b[22m\u001b[39m\u001b[36m\u001b[1m)\u001b[22m\u001b[39m\n",
       "   │  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "   │     ├─ rot(Z gate, 0.0)\n",
       "   │     └─ rot(X gate, 0.0)\n",
       "   ├─ \u001b[36m\u001b[1mput on (\u001b[22m\u001b[39m\u001b[36m\u001b[1m3\u001b[22m\u001b[39m\u001b[36m\u001b[1m)\u001b[22m\u001b[39m\n",
       "   │  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "   │     ├─ rot(Z gate, 0.0)\n",
       "   │     └─ rot(X gate, 0.0)\n",
       "   └─ \u001b[36m\u001b[1mput on (\u001b[22m\u001b[39m\u001b[36m\u001b[1m4\u001b[22m\u001b[39m\u001b[36m\u001b[1m)\u001b[22m\u001b[39m\n",
       "      └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
       "         ├─ rot(Z gate, 0.0)\n",
       "         └─ rot(X gate, 0.0)\n"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "build_circuit(4, 1, [1=>2, 2=>3, 3=>4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MMD Loss & Gradients\n",
    "\n",
    "The MMD loss is describe below:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathcal{L} &= \\left| \\sum_{x} p \\theta(x) \\phi(x) - \\sum_{x} \\pi(x) \\phi(x) \\right|^2\\\\\n",
    "            &= \\langle K(x, y) \\rangle_{x \\sim p_{\\theta}, y\\sim p_{\\theta}} - 2 \\langle K(x, y) \\rangle_{x\\sim p_{\\theta}, y\\sim \\pi} + \\langle K(x, y) \\rangle_{x\\sim\\pi, y\\sim\\pi}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "\n",
    "We will use a squared exponential kernel here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "kexpect (generic function with 1 method)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "struct RBFKernel\n",
    "    σ::Float64\n",
    "    m::Matrix{Float64}\n",
    "end\n",
    "\n",
    "function RBFKernel(σ::Float64, space)\n",
    "    dx2 = (space .- space').^2\n",
    "    return RBFKernel(σ, exp.(-1/2σ * dx2))\n",
    "end\n",
    "\n",
    "kexpect(κ::RBFKernel, x, y) = x' * κ.m * y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two different way to define the loss:\n",
    "\n",
    "In simulation we can use the probability distribution of the state directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "loss (generic function with 1 method)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_prob(qcbm) = probs(zero_state(nqubits(qcbm)) |> qcbm)\n",
    "\n",
    "function loss(κ, c, target)\n",
    "    p = get_prob(c) - target\n",
    "    return kexpect(κ, p, p)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or if you want to simulate the whole process with measurement (which is entirely\n",
    "physical), you should define the loss with measurement results, for convenience\n",
    "we directly use the simulated results as our loss\n",
    "\n",
    "### Gradients\n",
    "the gradient of MMD loss is\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\theta^i_l} &= \\langle K(x, y) \\rangle_{x\\sim p_{\\theta^+}, y\\sim p_{\\theta}} - \\langle K(x, y) \\rangle_{x\\sim p_{\\theta}^-, y\\sim p_{\\theta}}\\\\\n",
    "&- \\langle K(x, y) \\rangle _{x\\sim p_{\\theta^+}, y\\sim\\pi} + \\langle K(x, y) \\rangle_{x\\sim p_{\\theta^-}, y\\sim\\pi}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "which can be implemented as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gradient (generic function with 1 method)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gradient(qcbm, κ, ptrain)\n",
    "    n = nqubits(qcbm)\n",
    "    prob = get_prob(qcbm)\n",
    "    grad = zeros(Float64, nparameters(qcbm))\n",
    "\n",
    "    count = 1\n",
    "    for k in 1:2:length(qcbm), each_line in qcbm[k], gate in content(each_line)\n",
    "        dispatch!(+, gate, π/2)\n",
    "        prob_pos = probs(zero_state(n) |> qcbm)\n",
    "\n",
    "        dispatch!(-, gate, π)\n",
    "        prob_neg = probs(zero_state(n) |> qcbm)\n",
    "\n",
    "        dispatch!(+, gate, π/2) # set back\n",
    "\n",
    "        grad_pos = kexpect(κ, prob, prob_pos) - kexpect(κ, prob, prob_neg)\n",
    "        grad_neg = kexpect(κ, ptrain, prob_pos) - kexpect(κ, ptrain, prob_neg)\n",
    "        grad[count] = grad_pos - grad_neg\n",
    "        count += 1\n",
    "    end\n",
    "    return grad\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's setup the training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64-element Array{Float64,1}:\n",
       " 0.004949796033194015 \n",
       " 0.008610452538485582 \n",
       " 0.004306470020658978 \n",
       " 0.007612462243589652 \n",
       " 0.00703871374806971  \n",
       " 0.01022684746639653  \n",
       " 0.005020982471676006 \n",
       " 0.008275845132628135 \n",
       " 0.011551680615306367 \n",
       " 0.009241203376824835 \n",
       " 0.007271743580633538 \n",
       " 0.014097516828957437 \n",
       " 0.016060555095142693 \n",
       " ⋮                    \n",
       " 0.012189392112723994 \n",
       " 0.011788883954540651 \n",
       " 0.005573432794460104 \n",
       " 0.01400420812013604  \n",
       " 0.0034933802748169504\n",
       " 0.008303658194569132 \n",
       " 0.00651435766826844  \n",
       " 0.0061301956626380666\n",
       " 0.006836520752272872 \n",
       " 0.009192425196840234 \n",
       " 0.0016167091926223784\n",
       " 0.008330754662834103 "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Flux.Optimise\n",
    "qcbm = build_circuit(6, 10, [1=>2, 3=>4, 5=>6, 2=>3, 4=>5, 6=>1])\n",
    "dispatch!(qcbm, :random) # initialize the parameters\n",
    "\n",
    "κ = RBFKernel(0.25, 0:2^6-1)\n",
    "pg = gaussian_pdf(1:1<<6, 1<<5-0.5, 1<<4);\n",
    "opt = ADAM()\n",
    "\n",
    "function train(qcbm, κ, opt, target)\n",
    "    history = Float64[]\n",
    "    for _ in 1:100\n",
    "        push!(history, loss(κ, qcbm, target))\n",
    "        ps = parameters(qcbm)\n",
    "        Optimise.update!(opt, ps, gradient(qcbm, κ, target))\n",
    "        popdispatch!(qcbm, ps)\n",
    "    end\n",
    "    return history\n",
    "end\n",
    "\n",
    "history = train(qcbm, κ, opt, pg)\n",
    "trained_pg = probs(zero_state(nqubits(qcbm)) |> qcbm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we have the history of training which is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig1 = plot(history; legend=nothing)\n",
    "title!(\"training history\")\n",
    "xlabel!(\"steps\"); ylabel!(\"loss\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](../assets/figures/history.png)\n",
    "\n",
    "And let's check what we got"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig2 = plot(1:1<<6, trained_pg; label=\"trained\")\n",
    "plot!(fig2, 1:1<<6, pg; label=\"target\")\n",
    "title!(\"distribution\")\n",
    "xlabel!(\"x\"); ylabel!(\"p\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](../assets/figures/distribution.png)\n",
    "\n",
    "So within 50 steps, we got a pretty close estimation of our\n",
    "target distribution!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.1.0",
   "language": "julia",
   "name": "julia-1.1"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.1.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}