4_quantum/variational_quantum_circuit.ipynb

{
 "cells": [
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The landscape of a parametrized quantum circuit\n",
    "\n",
    "Here, $U_{1:k}$ and $U_{k+1:N}$ are two random circuits. $U_k(\\eta)$ is a rotation gate defined as $U_k(\\eta) = e^{-i\\Xi \\eta/2}$ with $\\Xi^2 = 1$.\n",
    "\n",
    "> Nakanishi, Ken M., Keisuke Fujii, and Synge Todo. \"Sequential minimal optimization for quantum-classical hybrid algorithms.\" arXiv preprint arXiv:1903.12166 (2019).\n",
    "\n",
    "<img src=\"attachment:_gradient.png\" width=\"400\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the version of Yao is 0.4.1 in this notebook\n",
    "using Yao, Yao.ConstGate\n",
    "using Plots, LaTeXStrings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function scan_params(Uj, observable, nparam::Int)\n",
    "    x = LinRange(0, 2π, nparam)\n",
    "    y = zeros(nparam)\n",
    "    for (i,x) in enumerate(x)\n",
    "        dispatch!(Uj, x)\n",
    "        y[i] = expect(observable, zero_state(N) |> c) |> real\n",
    "    end\n",
    "    x, y\n",
    "end\n",
    "\n",
    "N = 5\n",
    "\n",
    "V1j = rand_unitary(1<<N) |> matblock\n",
    "V2j = rand_unitary(1<<N) |> matblock\n",
    "\n",
    "Uj = put(N, 4=>Rx(0.0))\n",
    "c = chain(N, [V1j, Uj, V2j])\n",
    "\n",
    "observable = put(N, 4=>Z)\n",
    "xs, ys = scan_params(Uj, observable, 100)\n",
    "\n",
    "# see a sine curve\n",
    "pyplot()\n",
    "fnt = Plots.font(\"Helvetica\", 10.0)\n",
    "default(titlefont=fnt, guidefont=fnt, tickfont=fnt, legendfont=fnt)\n",
    "ax = plot(xs, ys, lw=2, xlabel=L\"\\eta\", ylabel=\"Energy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variational Quantum Eigensolver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two site Hubbard Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "hubbard_hamiltonain"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"get the hamiltonian of a Hubbard model\"\"\"\n",
    "function hubbard_hamiltonain(t::Real, U::Real)\n",
    "    0.5t * (kron(X, Z, X, I2) +\n",
    "        kron(Y, Z, Y, I2) + \n",
    "        kron(I2, X, Z, X) +\n",
    "        kron(I2, Y, Z, Y)) +\n",
    "    0.25U * (kron(Z, Z, I2, I2) +\n",
    "        kron(I2, I2, Z, Z))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mnqubits: 4, datatype: Complex{Float64}\u001b[39m\n",
       "\u001b[34m\u001b[1msum\u001b[22m\u001b[39m\n",
       "├─ \u001b[33m\u001b[1m[scale: 0.5] \u001b[22m\u001b[39m\u001b[34m\u001b[1msum\u001b[22m\u001b[39m\n",
       "│     ├─ \u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
       "│     │  ├─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>X gate\n",
       "│     │  ├─ \u001b[37m\u001b[1m2\u001b[22m\u001b[39m=>Z gate\n",
       "│     │  ├─ \u001b[37m\u001b[1m3\u001b[22m\u001b[39m=>X gate\n",
       "│     │  └─ \u001b[37m\u001b[1m4\u001b[22m\u001b[39m=>I2 gate\n",
       "│     ├─ \u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
       "│     │  ├─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>Y gate\n",
       "│     │  ├─ \u001b[37m\u001b[1m2\u001b[22m\u001b[39m=>Z gate\n",
       "│     │  ├─ \u001b[37m\u001b[1m3\u001b[22m\u001b[39m=>Y gate\n",
       "│     │  └─ \u001b[37m\u001b[1m4\u001b[22m\u001b[39m=>I2 gate\n",
       "│     ├─ \u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
       "│     │  ├─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>I2 gate\n",
       "│     │  ├─ \u001b[37m\u001b[1m2\u001b[22m\u001b[39m=>X gate\n",
       "│     │  ├─ \u001b[37m\u001b[1m3\u001b[22m\u001b[39m=>Z gate\n",
       "│     │  └─ \u001b[37m\u001b[1m4\u001b[22m\u001b[39m=>X gate\n",
       "│     └─ \u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
       "│        ├─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>I2 gate\n",
       "│        ├─ \u001b[37m\u001b[1m2\u001b[22m\u001b[39m=>Y gate\n",
       "│        ├─ \u001b[37m\u001b[1m3\u001b[22m\u001b[39m=>Z gate\n",
       "│        └─ \u001b[37m\u001b[1m4\u001b[22m\u001b[39m=>Y gate\n",
       "└─ \u001b[33m\u001b[1m[scale: 0.25] \u001b[22m\u001b[39m\u001b[34m\u001b[1msum\u001b[22m\u001b[39m\n",
       "      ├─ \u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
       "      │  ├─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>Z gate\n",
       "      │  ├─ \u001b[37m\u001b[1m2\u001b[22m\u001b[39m=>Z gate\n",
       "      │  ├─ \u001b[37m\u001b[1m3\u001b[22m\u001b[39m=>I2 gate\n",
       "      │  └─ \u001b[37m\u001b[1m4\u001b[22m\u001b[39m=>I2 gate\n",
       "      └─ \u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
       "         ├─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>I2 gate\n",
       "         ├─ \u001b[37m\u001b[1m2\u001b[22m\u001b[39m=>I2 gate\n",
       "         ├─ \u001b[37m\u001b[1m3\u001b[22m\u001b[39m=>Z gate\n",
       "         └─ \u001b[37m\u001b[1m4\u001b[22m\u001b[39m=>Z gate\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hami = hubbard_hamiltonain(1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ishermitian(hami)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16×16 SparseArrays.SparseMatrixCSC{Complex{Float64},Int64} with 24 stored entries:\n",
       "  [1 ,  1]  =  0.5+0.0im\n",
       "  [5 ,  2]  =  1.0+0.0im\n",
       "  [9 ,  3]  =  1.0+0.0im\n",
       "  [4 ,  4]  =  0.5+0.0im\n",
       "  [7 ,  4]  =  -1.0+0.0im\n",
       "  [10,  4]  =  1.0+0.0im\n",
       "  [2 ,  5]  =  1.0+0.0im\n",
       "  [6 ,  6]  =  -0.5+0.0im\n",
       "  [4 ,  7]  =  -1.0+0.0im\n",
       "  [7 ,  7]  =  -0.5+0.0im\n",
       "  [13,  7]  =  -1.0+0.0im\n",
       "  [14,  8]  =  -1.0+0.0im\n",
       "  [3 ,  9]  =  1.0+0.0im\n",
       "  [4 , 10]  =  1.0+0.0im\n",
       "  [10, 10]  =  -0.5+0.0im\n",
       "  [13, 10]  =  1.0+0.0im\n",
       "  [11, 11]  =  -0.5+0.0im\n",
       "  [15, 12]  =  -1.0+0.0im\n",
       "  [7 , 13]  =  -1.0+0.0im\n",
       "  [10, 13]  =  1.0+0.0im\n",
       "  [13, 13]  =  0.5+0.0im\n",
       "  [8 , 14]  =  -1.0+0.0im\n",
       "  [12, 15]  =  -1.0+0.0im\n",
       "  [16, 16]  =  0.5+0.0im"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hmat = mat(hami)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "using KrylovKit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "search: \u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mi\u001b[22m\u001b[0m\u001b[1mg\u001b[22m\u001b[0m\u001b[1ms\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ml\u001b[22m\u001b[0m\u001b[1mv\u001b[22m\u001b[0m\u001b[1me\u001b[22m g\u001b[0m\u001b[1me\u001b[22mne\u001b[0m\u001b[1mi\u001b[22m\u001b[0m\u001b[1mg\u001b[22m\u001b[0m\u001b[1ms\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ml\u001b[22m\u001b[0m\u001b[1mv\u001b[22m\u001b[0m\u001b[1me\u001b[22m\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "eigsolve(A::AbstractMatrix, [howmany = 1, which = :LM, T = eltype(A)]; kwargs...)\n",
       "eigsolve(f, n::Int, [howmany = 1, which = :LM, T = Float64]; kwargs...)\n",
       "eigsolve(f, x₀, [howmany = 1, which = :LM]; kwargs...)\n",
       "eigsolve(f, x₀, howmany, which, algorithm)\n",
       "\\end{verbatim}\n",
       "Compute at least \\texttt{howmany} eigenvalues from the linear map encoded in the matrix \\texttt{A} or by the function \\texttt{f}. Return eigenvalues, eigenvectors and a \\texttt{ConvergenceInfo} structure.\n",
       "\n",
       "\\subsubsection{Arguments:}\n",
       "The linear map can be an \\texttt{AbstractMatrix} (dense or sparse) or a general function or callable object. If an \\texttt{AbstractMatrix} is used, a starting vector \\texttt{x₀} does not need to be provided, it is then chosen as \\texttt{rand(T, size(A,1))}. If the linear map is encoded more generally as a a callable function or method, the best approach is to provide an explicit starting guess \\texttt{x₀}. Note that \\texttt{x₀} does not need to be of type \\texttt{AbstractVector}, any type that behaves as a vector and supports the required methods (see KrylovKit docs) is accepted. If instead of \\texttt{x₀} an integer \\texttt{n} is specified, it is assumed that \\texttt{x₀} is a regular vector and it is initialized to \\texttt{rand(T,n)}, where the default value of \\texttt{T} is \\texttt{Float64}, unless specified differently.\n",
       "\n",
       "The next arguments are optional, but should typically be specified. \\texttt{howmany} specifies how many eigenvalues should be computed; \\texttt{which} specifies which eigenvalues should be targetted. Valid specifications of \\texttt{which} are given by\n",
       "\n",
       "\\begin{itemize}\n",
       "\\item \\texttt{:LM}: eigenvalues of largest magnitude\n",
       "\n",
       "\n",
       "\\item \\texttt{:LR}: eigenvalues with largest (most positive) real part\n",
       "\n",
       "\n",
       "\\item \\texttt{:SR}: eigenvalues with smallest (most negative) real part\n",
       "\n",
       "\n",
       "\\item \\texttt{:LI}: eigenvalues with largest (most positive) imaginary part, only if \\texttt{T <: Complex}\n",
       "\n",
       "\n",
       "\\item \\texttt{:SI}: eigenvalues with smallest (most negative) imaginary part, only if \\texttt{T <: Complex}\n",
       "\n",
       "\n",
       "\\item \\href{@ref}{\\texttt{EigSorter(f; rev = false)}}: eigenvalues \\texttt{λ} that appear first (or last if   \\texttt{rev == true}) when sorted by \\texttt{f(λ)}\n",
       "\n",
       "\\end{itemize}\n",
       "\\begin{quote}\n",
       "\\textbf{note}\n",
       "\n",
       "Note about selecting `which` eigenvalues\n",
       "\n",
       "Krylov methods work well for extremal eigenvalues, i.e. eigenvalues on the periphery of the spectrum of the linear map. All of they valid \\texttt{Symbol}s for \\texttt{which} have this property, but could also be specified usign \\texttt{EigSorter}, e.g. \\texttt{:LM} is equivalent to \\texttt{Eigsorter(abs; rev = true)}. Note that smallest magnitude sorting is obtained using e.g. \\texttt{EigSorter(abs; rev = false)}, but since no (shift-and)-invert is used, this will only be successfull if you somehow know that eigenvalues close to zero are also close to the periphery of the spectrum.\n",
       "\n",
       "\\end{quote}\n",
       "The argument \\texttt{T} acts as a hint in which \\texttt{Number} type the computation should be performed, but is not restrictive. If the linear map automatically produces complex values, complex arithmetic will be used even though \\texttt{T<:Real} was specified. However, if the linear map and initial guess are real, approximate eigenvalues will be searched for using a partial Schur factorization, which implies that complex conjugate eigenvalues come in pairs and cannot be split. It is then illegal to choose \\texttt{which} in a way that would treat \\texttt{λ} and \\texttt{conj(λ)} differently, i.e. \\texttt{:LI} and \\texttt{:SI} are invalid, as well as any \\texttt{EigSorter} that would lead to \\texttt{by(λ) != by(conj(λ))}.\n",
       "\n",
       "\\subsubsection{Return values:}\n",
       "The return value is always of the form \\texttt{vals, vecs, info = eigsolve(...)} with\n",
       "\n",
       "\\begin{itemize}\n",
       "\\item \\texttt{vals}: a \\texttt{Vector} containing the eigenvalues, of length at least \\texttt{howmany}, but could   be longer if more eigenvalues were converged at the same cost. Eigenvalues will be real   if \\href{@ref}{\\texttt{Lanczos}} was used and complex if \\href{@ref}{\\texttt{Arnoldi}} was used (see below).\n",
       "\n",
       "\n",
       "\\item \\texttt{vecs}: a \\texttt{Vector} of corresponding eigenvectors, of the same length as \\texttt{vals}. Note   that eigenvectors are not returned as a matrix, as the linear map could act on any   custom Julia type with vector like behavior, i.e. the elements of the list \\texttt{vecs} are   objects that are typically similar to the starting guess \\texttt{x₀}, up to a possibly   different \\texttt{eltype}. In particular  for a general matrix (i.e. with \\texttt{Arnoldi}) the   eigenvectors are generally complex and are therefore always returned in a complex   number format. When the linear map is a simple \\texttt{AbstractMatrix}, \\texttt{vecs} will be   \\texttt{Vector\\{Vector\\{<:Number\\}\\}}.\n",
       "\n",
       "\n",
       "\\item \\texttt{info}: an object of type [\\texttt{ConvergenceInfo}], which has the following fields\n",
       "\n",
       "\\begin{itemize}\n",
       "\\item \\texttt{info.converged::Int}: indicates how many eigenvalues and eigenvectors were actually   converged to the specified tolerance \\texttt{tol} (see below under keyword arguments)\n",
       "\n",
       "\n",
       "\\item \\texttt{info.residual::Vector}: a list of the same length as \\texttt{vals} containing the   residuals \\texttt{info.residual[i] = f(vecs[i]) - vals[i] * vecs[i]}\n",
       "\n",
       "\n",
       "\\item \\texttt{info.normres::Vector\\{<:Real\\}}: list of the same length as \\texttt{vals} containing the   norm of the residual \\texttt{info.normres[i] = norm(info.residual[i])}\n",
       "\n",
       "\n",
       "\\item \\texttt{info.numops::Int}: number of times the linear map was applied, i.e. number of times   \\texttt{f} was called, or a vector was multiplied with \\texttt{A}\n",
       "\n",
       "\n",
       "\\item \\texttt{info.numiter::Int}: number of times the Krylov subspace was restarted (see below)\n",
       "\n",
       "\\end{itemize}\n",
       "\\end{itemize}\n",
       "\\begin{quote}\n",
       "\\textbf{warning}\n",
       "\n",
       "Check for convergence\n",
       "\n",
       "No warning is printed if not all requested eigenvalues were converged, so always check if \\texttt{info.converged >= howmany}.\n",
       "\n",
       "\\end{quote}\n",
       "\\subsubsection{Keyword arguments:}\n",
       "Keyword arguments and their default values are given by:\n",
       "\n",
       "\\begin{itemize}\n",
       "\\item \\texttt{verbosity::Int = 0}: verbosity level, i.e. 0 (no messages), 1 (single message   at the end), 2 (information after every iteration), 3 (information per Krylov step)\n",
       "\n",
       "\n",
       "\\item \\texttt{tol::Real}: the requested accuracy (corresponding to the 2-norm of the residual for   Schur vectors, not the eigenvectors). If you work in e.g. single precision (\\texttt{Float32}),   you should definitely change the default value.\n",
       "\n",
       "\n",
       "\\item \\texttt{krylovdim::Integer}: the maximum dimension of the Krylov subspace that will be   constructed. Note that the dimension of the vector space is not known or checked, e.g.   \\texttt{x₀} should not necessarily support the \\texttt{Base.length} function. If you know the actual   problem dimension is smaller than the default value, it is useful to reduce the value of   \\texttt{krylovdim}, though in principle this should be detected.\n",
       "\n",
       "\n",
       "\\item \\texttt{maxiter::Integer}: the number of times the Krylov subspace can be rebuilt; see below   for further details on the algorithms.\n",
       "\n",
       "\n",
       "\\item \\texttt{orth::Orthogonalizer}: the orthogonalization method to be used, see   \\href{@ref}{\\texttt{Orthogonalizer}}\n",
       "\n",
       "\n",
       "\\item \\texttt{issymmetric::Bool}: if the linear map is symmetric, only meaningful if \\texttt{T<:Real}\n",
       "\n",
       "\n",
       "\\item \\texttt{ishermitian::Bool}: if the linear map is hermitian\n",
       "\n",
       "\\end{itemize}\n",
       "The default values are given by \\texttt{tol = KrylovDefaults.tol}, \\texttt{krylovdim = KrylovDefaults.krylovdim}, \\texttt{maxiter = KrylovDefaults.maxiter}, \\texttt{orth = KrylovDefaults.orth}; see \\href{@ref}{\\texttt{KrylovDefaults}} for details.\n",
       "\n",
       "The default value for the last two parameters depends on the method. If an \\texttt{AbstractMatrix} is used, \\texttt{issymmetric} and \\texttt{ishermitian} are checked for that matrix, ortherwise the default values are \\texttt{issymmetric = false} and \\texttt{ishermitian = T <: Real \\&\\& issymmetric}. When values for the keyword arguments are provided, no checks will be performed even in the matrix case.\n",
       "\n",
       "\\subsubsection{Algorithm}\n",
       "The last method, without default values and keyword arguments, is the one that is finally called, and can also be used directly. Here, one specifies the algorithm explicitly as either \\href{@ref}{\\texttt{Lanczos}}, for real symmetric or complex hermitian problems, or \\href{@ref}{\\texttt{Arnoldi}}, for general problems. Note that these names refer to the process for building the Krylov subspace, but the actual algorithm is an implementation of the Krylov-Schur algorithm, which can dynamically shrink and grow the Krylov subspace, i.e. the restarts are so-called thick restarts where a part of the current Krylov subspace is kept.\n",
       "\n",
       "\\begin{quote}\n",
       "\\textbf{note}\n",
       "\n",
       "Note about convergence\n",
       "\n",
       "In case of a general problem, where the \\texttt{Arnoldi} method is used, convergence of an eigenvalue is not based on the norm of the residual \\texttt{norm(f(vecs[i]) - vals[i]*vecs[i])} for the eigenvector but rather on the norm of the residual for the corresponding Schur vectors.\n",
       "\n",
       "See also \\href{@ref}{\\texttt{schursolve}} if you want to use the partial Schur decomposition directly, or if you are not interested in computing the eigenvectors, and want to work in real arithmetic all the way true (if the linear map and starting guess are real).\n",
       "\n",
       "\\end{quote}\n"
      ],
      "text/markdown": [
       "```\n",
       "eigsolve(A::AbstractMatrix, [howmany = 1, which = :LM, T = eltype(A)]; kwargs...)\n",
       "eigsolve(f, n::Int, [howmany = 1, which = :LM, T = Float64]; kwargs...)\n",
       "eigsolve(f, x₀, [howmany = 1, which = :LM]; kwargs...)\n",
       "eigsolve(f, x₀, howmany, which, algorithm)\n",
       "```\n",
       "\n",
       "Compute at least `howmany` eigenvalues from the linear map encoded in the matrix `A` or by the function `f`. Return eigenvalues, eigenvectors and a `ConvergenceInfo` structure.\n",
       "\n",
       "### Arguments:\n",
       "\n",
       "The linear map can be an `AbstractMatrix` (dense or sparse) or a general function or callable object. If an `AbstractMatrix` is used, a starting vector `x₀` does not need to be provided, it is then chosen as `rand(T, size(A,1))`. If the linear map is encoded more generally as a a callable function or method, the best approach is to provide an explicit starting guess `x₀`. Note that `x₀` does not need to be of type `AbstractVector`, any type that behaves as a vector and supports the required methods (see KrylovKit docs) is accepted. If instead of `x₀` an integer `n` is specified, it is assumed that `x₀` is a regular vector and it is initialized to `rand(T,n)`, where the default value of `T` is `Float64`, unless specified differently.\n",
       "\n",
       "The next arguments are optional, but should typically be specified. `howmany` specifies how many eigenvalues should be computed; `which` specifies which eigenvalues should be targetted. Valid specifications of `which` are given by\n",
       "\n",
       "  * `:LM`: eigenvalues of largest magnitude\n",
       "  * `:LR`: eigenvalues with largest (most positive) real part\n",
       "  * `:SR`: eigenvalues with smallest (most negative) real part\n",
       "  * `:LI`: eigenvalues with largest (most positive) imaginary part, only if `T <: Complex`\n",
       "  * `:SI`: eigenvalues with smallest (most negative) imaginary part, only if `T <: Complex`\n",
       "  * [`EigSorter(f; rev = false)`](@ref): eigenvalues `λ` that appear first (or last if   `rev == true`) when sorted by `f(λ)`\n",
       "\n",
       "!!! note \"Note about selecting `which` eigenvalues\"\n",
       "    Krylov methods work well for extremal eigenvalues, i.e. eigenvalues on the periphery of the spectrum of the linear map. All of they valid `Symbol`s for `which` have this property, but could also be specified usign `EigSorter`, e.g. `:LM` is equivalent to `Eigsorter(abs; rev = true)`. Note that smallest magnitude sorting is obtained using e.g. `EigSorter(abs; rev = false)`, but since no (shift-and)-invert is used, this will only be successfull if you somehow know that eigenvalues close to zero are also close to the periphery of the spectrum.\n",
       "\n",
       "\n",
       "The argument `T` acts as a hint in which `Number` type the computation should be performed, but is not restrictive. If the linear map automatically produces complex values, complex arithmetic will be used even though `T<:Real` was specified. However, if the linear map and initial guess are real, approximate eigenvalues will be searched for using a partial Schur factorization, which implies that complex conjugate eigenvalues come in pairs and cannot be split. It is then illegal to choose `which` in a way that would treat `λ` and `conj(λ)` differently, i.e. `:LI` and `:SI` are invalid, as well as any `EigSorter` that would lead to `by(λ) != by(conj(λ))`.\n",
       "\n",
       "### Return values:\n",
       "\n",
       "The return value is always of the form `vals, vecs, info = eigsolve(...)` with\n",
       "\n",
       "  * `vals`: a `Vector` containing the eigenvalues, of length at least `howmany`, but could   be longer if more eigenvalues were converged at the same cost. Eigenvalues will be real   if [`Lanczos`](@ref) was used and complex if [`Arnoldi`](@ref) was used (see below).\n",
       "  * `vecs`: a `Vector` of corresponding eigenvectors, of the same length as `vals`. Note   that eigenvectors are not returned as a matrix, as the linear map could act on any   custom Julia type with vector like behavior, i.e. the elements of the list `vecs` are   objects that are typically similar to the starting guess `x₀`, up to a possibly   different `eltype`. In particular  for a general matrix (i.e. with `Arnoldi`) the   eigenvectors are generally complex and are therefore always returned in a complex   number format. When the linear map is a simple `AbstractMatrix`, `vecs` will be   `Vector{Vector{<:Number}}`.\n",
       "  * `info`: an object of type [`ConvergenceInfo`], which has the following fields\n",
       "\n",
       "      * `info.converged::Int`: indicates how many eigenvalues and eigenvectors were actually   converged to the specified tolerance `tol` (see below under keyword arguments)\n",
       "      * `info.residual::Vector`: a list of the same length as `vals` containing the   residuals `info.residual[i] = f(vecs[i]) - vals[i] * vecs[i]`\n",
       "      * `info.normres::Vector{<:Real}`: list of the same length as `vals` containing the   norm of the residual `info.normres[i] = norm(info.residual[i])`\n",
       "      * `info.numops::Int`: number of times the linear map was applied, i.e. number of times   `f` was called, or a vector was multiplied with `A`\n",
       "      * `info.numiter::Int`: number of times the Krylov subspace was restarted (see below)\n",
       "\n",
       "!!! warning \"Check for convergence\"\n",
       "    No warning is printed if not all requested eigenvalues were converged, so always check if `info.converged >= howmany`.\n",
       "\n",
       "\n",
       "### Keyword arguments:\n",
       "\n",
       "Keyword arguments and their default values are given by:\n",
       "\n",
       "  * `verbosity::Int = 0`: verbosity level, i.e. 0 (no messages), 1 (single message   at the end), 2 (information after every iteration), 3 (information per Krylov step)\n",
       "  * `tol::Real`: the requested accuracy (corresponding to the 2-norm of the residual for   Schur vectors, not the eigenvectors). If you work in e.g. single precision (`Float32`),   you should definitely change the default value.\n",
       "  * `krylovdim::Integer`: the maximum dimension of the Krylov subspace that will be   constructed. Note that the dimension of the vector space is not known or checked, e.g.   `x₀` should not necessarily support the `Base.length` function. If you know the actual   problem dimension is smaller than the default value, it is useful to reduce the value of   `krylovdim`, though in principle this should be detected.\n",
       "  * `maxiter::Integer`: the number of times the Krylov subspace can be rebuilt; see below   for further details on the algorithms.\n",
       "  * `orth::Orthogonalizer`: the orthogonalization method to be used, see   [`Orthogonalizer`](@ref)\n",
       "  * `issymmetric::Bool`: if the linear map is symmetric, only meaningful if `T<:Real`\n",
       "  * `ishermitian::Bool`: if the linear map is hermitian\n",
       "\n",
       "The default values are given by `tol = KrylovDefaults.tol`, `krylovdim = KrylovDefaults.krylovdim`, `maxiter = KrylovDefaults.maxiter`, `orth = KrylovDefaults.orth`; see [`KrylovDefaults`](@ref) for details.\n",
       "\n",
       "The default value for the last two parameters depends on the method. If an `AbstractMatrix` is used, `issymmetric` and `ishermitian` are checked for that matrix, ortherwise the default values are `issymmetric = false` and `ishermitian = T <: Real && issymmetric`. When values for the keyword arguments are provided, no checks will be performed even in the matrix case.\n",
       "\n",
       "### Algorithm\n",
       "\n",
       "The last method, without default values and keyword arguments, is the one that is finally called, and can also be used directly. Here, one specifies the algorithm explicitly as either [`Lanczos`](@ref), for real symmetric or complex hermitian problems, or [`Arnoldi`](@ref), for general problems. Note that these names refer to the process for building the Krylov subspace, but the actual algorithm is an implementation of the Krylov-Schur algorithm, which can dynamically shrink and grow the Krylov subspace, i.e. the restarts are so-called thick restarts where a part of the current Krylov subspace is kept.\n",
       "\n",
       "!!! note \"Note about convergence\"\n",
       "    In case of a general problem, where the `Arnoldi` method is used, convergence of an eigenvalue is not based on the norm of the residual `norm(f(vecs[i]) - vals[i]*vecs[i])` for the eigenvector but rather on the norm of the residual for the corresponding Schur vectors.\n",
       "\n",
       "    See also [`schursolve`](@ref) if you want to use the partial Schur decomposition directly, or if you are not interested in computing the eigenvectors, and want to work in real arithmetic all the way true (if the linear map and starting guess are real).\n",
       "\n"
      ],
      "text/plain": [
       "\u001b[36m  eigsolve(A::AbstractMatrix, [howmany = 1, which = :LM, T = eltype(A)]; kwargs...)\u001b[39m\n",
       "\u001b[36m  eigsolve(f, n::Int, [howmany = 1, which = :LM, T = Float64]; kwargs...)\u001b[39m\n",
       "\u001b[36m  eigsolve(f, x₀, [howmany = 1, which = :LM]; kwargs...)\u001b[39m\n",
       "\u001b[36m  eigsolve(f, x₀, howmany, which, algorithm)\u001b[39m\n",
       "\n",
       "  Compute at least \u001b[36mhowmany\u001b[39m eigenvalues from the linear map encoded in the\n",
       "  matrix \u001b[36mA\u001b[39m or by the function \u001b[36mf\u001b[39m. Return eigenvalues, eigenvectors and a\n",
       "  \u001b[36mConvergenceInfo\u001b[39m structure.\n",
       "\n",
       "\u001b[1m  Arguments:\u001b[22m\n",
       "\u001b[1m  ––––––––––––\u001b[22m\n",
       "\n",
       "  The linear map can be an \u001b[36mAbstractMatrix\u001b[39m (dense or sparse) or a general\n",
       "  function or callable object. If an \u001b[36mAbstractMatrix\u001b[39m is used, a starting vector\n",
       "  \u001b[36mx₀\u001b[39m does not need to be provided, it is then chosen as \u001b[36mrand(T, size(A,1))\u001b[39m. If\n",
       "  the linear map is encoded more generally as a a callable function or method,\n",
       "  the best approach is to provide an explicit starting guess \u001b[36mx₀\u001b[39m. Note that \u001b[36mx₀\u001b[39m\n",
       "  does not need to be of type \u001b[36mAbstractVector\u001b[39m, any type that behaves as a\n",
       "  vector and supports the required methods (see KrylovKit docs) is accepted.\n",
       "  If instead of \u001b[36mx₀\u001b[39m an integer \u001b[36mn\u001b[39m is specified, it is assumed that \u001b[36mx₀\u001b[39m is a\n",
       "  regular vector and it is initialized to \u001b[36mrand(T,n)\u001b[39m, where the default value\n",
       "  of \u001b[36mT\u001b[39m is \u001b[36mFloat64\u001b[39m, unless specified differently.\n",
       "\n",
       "  The next arguments are optional, but should typically be specified. \u001b[36mhowmany\u001b[39m\n",
       "  specifies how many eigenvalues should be computed; \u001b[36mwhich\u001b[39m specifies which\n",
       "  eigenvalues should be targetted. Valid specifications of \u001b[36mwhich\u001b[39m are given by\n",
       "\n",
       "    •    \u001b[36m:LM\u001b[39m: eigenvalues of largest magnitude\n",
       "\n",
       "    •    \u001b[36m:LR\u001b[39m: eigenvalues with largest (most positive) real part\n",
       "\n",
       "    •    \u001b[36m:SR\u001b[39m: eigenvalues with smallest (most negative) real part\n",
       "\n",
       "    •    \u001b[36m:LI\u001b[39m: eigenvalues with largest (most positive) imaginary part, only\n",
       "        if \u001b[36mT <: Complex\u001b[39m\n",
       "\n",
       "    •    \u001b[36m:SI\u001b[39m: eigenvalues with smallest (most negative) imaginary part,\n",
       "        only if \u001b[36mT <: Complex\u001b[39m\n",
       "\n",
       "    •    \u001b[36mEigSorter(f; rev = false)\u001b[39m: eigenvalues \u001b[36mλ\u001b[39m that appear first (or\n",
       "        last if \u001b[36mrev == true\u001b[39m) when sorted by \u001b[36mf(λ)\u001b[39m\n",
       "\n",
       "\u001b[39m\u001b[1m  │ \u001b[22m\u001b[39m\u001b[1mNote about selecting `which` eigenvalues\u001b[22m\n",
       "\u001b[39m\u001b[1m  │\u001b[22m\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  Krylov methods work well for extremal eigenvalues, i.e.\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  eigenvalues on the periphery of the spectrum of the linear map.\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  All of they valid \u001b[36mSymbol\u001b[39ms for \u001b[36mwhich\u001b[39m have this property, but could\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  also be specified usign \u001b[36mEigSorter\u001b[39m, e.g. \u001b[36m:LM\u001b[39m is equivalent to\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  \u001b[36mEigsorter(abs; rev = true)\u001b[39m. Note that smallest magnitude sorting\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  is obtained using e.g. \u001b[36mEigSorter(abs; rev = false)\u001b[39m, but since no\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  (shift-and)-invert is used, this will only be successfull if you\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  somehow know that eigenvalues close to zero are also close to the\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  periphery of the spectrum.\n",
       "\n",
       "  The argument \u001b[36mT\u001b[39m acts as a hint in which \u001b[36mNumber\u001b[39m type the computation should be\n",
       "  performed, but is not restrictive. If the linear map automatically produces\n",
       "  complex values, complex arithmetic will be used even though \u001b[36mT<:Real\u001b[39m was\n",
       "  specified. However, if the linear map and initial guess are real,\n",
       "  approximate eigenvalues will be searched for using a partial Schur\n",
       "  factorization, which implies that complex conjugate eigenvalues come in\n",
       "  pairs and cannot be split. It is then illegal to choose \u001b[36mwhich\u001b[39m in a way that\n",
       "  would treat \u001b[36mλ\u001b[39m and \u001b[36mconj(λ)\u001b[39m differently, i.e. \u001b[36m:LI\u001b[39m and \u001b[36m:SI\u001b[39m are invalid, as well\n",
       "  as any \u001b[36mEigSorter\u001b[39m that would lead to \u001b[36mby(λ) != by(conj(λ))\u001b[39m.\n",
       "\n",
       "\u001b[1m  Return values:\u001b[22m\n",
       "\u001b[1m  ––––––––––––––––\u001b[22m\n",
       "\n",
       "  The return value is always of the form \u001b[36mvals, vecs, info = eigsolve(...)\u001b[39m with\n",
       "\n",
       "    •    \u001b[36mvals\u001b[39m: a \u001b[36mVector\u001b[39m containing the eigenvalues, of length at least\n",
       "        \u001b[36mhowmany\u001b[39m, but could be longer if more eigenvalues were converged at\n",
       "        the same cost. Eigenvalues will be real if \u001b[36mLanczos\u001b[39m was used and\n",
       "        complex if \u001b[36mArnoldi\u001b[39m was used (see below).\n",
       "\n",
       "    •    \u001b[36mvecs\u001b[39m: a \u001b[36mVector\u001b[39m of corresponding eigenvectors, of the same length\n",
       "        as \u001b[36mvals\u001b[39m. Note that eigenvectors are not returned as a matrix, as\n",
       "        the linear map could act on any custom Julia type with vector like\n",
       "        behavior, i.e. the elements of the list \u001b[36mvecs\u001b[39m are objects that are\n",
       "        typically similar to the starting guess \u001b[36mx₀\u001b[39m, up to a possibly\n",
       "        different \u001b[36meltype\u001b[39m. In particular for a general matrix (i.e. with\n",
       "        \u001b[36mArnoldi\u001b[39m) the eigenvectors are generally complex and are therefore\n",
       "        always returned in a complex number format. When the linear map is\n",
       "        a simple \u001b[36mAbstractMatrix\u001b[39m, \u001b[36mvecs\u001b[39m will be \u001b[36mVector{Vector{<:Number}}\u001b[39m.\n",
       "\n",
       "    •    \u001b[36minfo\u001b[39m: an object of type [\u001b[36mConvergenceInfo\u001b[39m], which has the following\n",
       "        fields\n",
       "      \n",
       "          •    \u001b[36minfo.converged::Int\u001b[39m: indicates how many eigenvalues and\n",
       "              eigenvectors were actually converged to the specified\n",
       "              tolerance \u001b[36mtol\u001b[39m (see below under keyword arguments)\n",
       "      \n",
       "          •    \u001b[36minfo.residual::Vector\u001b[39m: a list of the same length as \u001b[36mvals\u001b[39m\n",
       "              containing the residuals \u001b[36minfo.residual[i] = f(vecs[i]) -\n",
       "              vals[i] * vecs[i]\u001b[39m\n",
       "      \n",
       "          •    \u001b[36minfo.normres::Vector{<:Real}\u001b[39m: list of the same length as\n",
       "              \u001b[36mvals\u001b[39m containing the norm of the residual \u001b[36minfo.normres[i]\n",
       "              = norm(info.residual[i])\u001b[39m\n",
       "      \n",
       "          •    \u001b[36minfo.numops::Int\u001b[39m: number of times the linear map was\n",
       "              applied, i.e. number of times \u001b[36mf\u001b[39m was called, or a vector\n",
       "              was multiplied with \u001b[36mA\u001b[39m\n",
       "      \n",
       "          •    \u001b[36minfo.numiter::Int\u001b[39m: number of times the Krylov subspace\n",
       "              was restarted (see below)\n",
       "\n",
       "\u001b[39m\u001b[1m  │ \u001b[22m\u001b[39m\u001b[1mCheck for convergence\u001b[22m\n",
       "\u001b[39m\u001b[1m  │\u001b[22m\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  No warning is printed if not all requested eigenvalues were\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  converged, so always check if \u001b[36minfo.converged >= howmany\u001b[39m.\n",
       "\n",
       "\u001b[1m  Keyword arguments:\u001b[22m\n",
       "\u001b[1m  ––––––––––––––––––––\u001b[22m\n",
       "\n",
       "  Keyword arguments and their default values are given by:\n",
       "\n",
       "    •    \u001b[36mverbosity::Int = 0\u001b[39m: verbosity level, i.e. 0 (no messages), 1\n",
       "        (single message at the end), 2 (information after every\n",
       "        iteration), 3 (information per Krylov step)\n",
       "\n",
       "    •    \u001b[36mtol::Real\u001b[39m: the requested accuracy (corresponding to the 2-norm of\n",
       "        the residual for Schur vectors, not the eigenvectors). If you work\n",
       "        in e.g. single precision (\u001b[36mFloat32\u001b[39m), you should definitely change\n",
       "        the default value.\n",
       "\n",
       "    •    \u001b[36mkrylovdim::Integer\u001b[39m: the maximum dimension of the Krylov subspace\n",
       "        that will be constructed. Note that the dimension of the vector\n",
       "        space is not known or checked, e.g. \u001b[36mx₀\u001b[39m should not necessarily\n",
       "        support the \u001b[36mBase.length\u001b[39m function. If you know the actual problem\n",
       "        dimension is smaller than the default value, it is useful to\n",
       "        reduce the value of \u001b[36mkrylovdim\u001b[39m, though in principle this should be\n",
       "        detected.\n",
       "\n",
       "    •    \u001b[36mmaxiter::Integer\u001b[39m: the number of times the Krylov subspace can be\n",
       "        rebuilt; see below for further details on the algorithms.\n",
       "\n",
       "    •    \u001b[36morth::Orthogonalizer\u001b[39m: the orthogonalization method to be used, see\n",
       "        \u001b[36mOrthogonalizer\u001b[39m\n",
       "\n",
       "    •    \u001b[36missymmetric::Bool\u001b[39m: if the linear map is symmetric, only meaningful\n",
       "        if \u001b[36mT<:Real\u001b[39m\n",
       "\n",
       "    •    \u001b[36mishermitian::Bool\u001b[39m: if the linear map is hermitian\n",
       "\n",
       "  The default values are given by \u001b[36mtol = KrylovDefaults.tol\u001b[39m, \u001b[36mkrylovdim =\n",
       "  KrylovDefaults.krylovdim\u001b[39m, \u001b[36mmaxiter = KrylovDefaults.maxiter\u001b[39m, \u001b[36morth =\n",
       "  KrylovDefaults.orth\u001b[39m; see \u001b[36mKrylovDefaults\u001b[39m for details.\n",
       "\n",
       "  The default value for the last two parameters depends on the method. If an\n",
       "  \u001b[36mAbstractMatrix\u001b[39m is used, \u001b[36missymmetric\u001b[39m and \u001b[36mishermitian\u001b[39m are checked for that\n",
       "  matrix, ortherwise the default values are \u001b[36missymmetric = false\u001b[39m and\n",
       "  \u001b[36mishermitian = T <: Real && issymmetric\u001b[39m. When values for the keyword\n",
       "  arguments are provided, no checks will be performed even in the matrix case.\n",
       "\n",
       "\u001b[1m  Algorithm\u001b[22m\n",
       "\u001b[1m  –––––––––––\u001b[22m\n",
       "\n",
       "  The last method, without default values and keyword arguments, is the one\n",
       "  that is finally called, and can also be used directly. Here, one specifies\n",
       "  the algorithm explicitly as either \u001b[36mLanczos\u001b[39m, for real symmetric or complex\n",
       "  hermitian problems, or \u001b[36mArnoldi\u001b[39m, for general problems. Note that these names\n",
       "  refer to the process for building the Krylov subspace, but the actual\n",
       "  algorithm is an implementation of the Krylov-Schur algorithm, which can\n",
       "  dynamically shrink and grow the Krylov subspace, i.e. the restarts are\n",
       "  so-called thick restarts where a part of the current Krylov subspace is\n",
       "  kept.\n",
       "\n",
       "\u001b[39m\u001b[1m  │ \u001b[22m\u001b[39m\u001b[1mNote about convergence\u001b[22m\n",
       "\u001b[39m\u001b[1m  │\u001b[22m\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  In case of a general problem, where the \u001b[36mArnoldi\u001b[39m method is used,\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  convergence of an eigenvalue is not based on the norm of the\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  residual \u001b[36mnorm(f(vecs[i]) - vals[i]*vecs[i])\u001b[39m for the eigenvector\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  but rather on the norm of the residual for the corresponding Schur\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  vectors.\n",
       "\u001b[39m\u001b[1m  │\u001b[22m\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  See also \u001b[36mschursolve\u001b[39m if you want to use the partial Schur\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  decomposition directly, or if you are not interested in computing\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  the eigenvectors, and want to work in real arithmetic all the way\n",
       "\u001b[39m\u001b[1m  │\u001b[22m  true (if the linear map and starting guess are real)."
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?eigsolve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.0615528128088276"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = randn(ComplexF64, size(Hmat, 2)) |> normalize!\n",
    "E, V = eigsolve(Hmat, x0, 1, :SR)\n",
    "EG = E[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Differential programming to obtain the ground state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Zygote: gradient\n",
    "using Zygote"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E[1] = -2.0615528128088267\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-2.0615528128088267"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "\n",
    "E, V = eigen(Hmat |> Matrix)\n",
    "@show E[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy is 0.22666801364824013\n",
      "Energy is 0.11131886054443056\n",
      "Energy is 0.002457927656256108\n",
      "Energy is -0.09946397880125618\n",
      "Energy is -0.19440169258022058\n",
      "Energy is -0.28263939070603716\n",
      "Energy is -0.36470215668593525\n",
      "Energy is -0.44126943258983126\n",
      "Energy is -0.5130992743100669\n",
      "Energy is -0.5809674557950162\n",
      "Energy is -0.6456218463454786\n",
      "Energy is -0.7077503450601299\n",
      "Energy is -0.7679597693646811\n",
      "Energy is -0.826763059346681\n",
      "Energy is -0.8845725891969145\n",
      "Energy is -0.9416979776559967\n",
      "Energy is -0.9983473716885012\n",
      "Energy is -1.05463163752743\n",
      "Energy is -1.1105711865511603\n",
      "Energy is -1.1661052857019898\n",
      "Energy is -1.2211036754536415\n",
      "Energy is -1.2753801831262588\n",
      "Energy is -1.3287078277199973\n",
      "Energy is -1.3808347206899039\n",
      "Energy is -1.4314999269100988\n",
      "Energy is -1.4804483995626974\n",
      "Energy is -1.5274441593978876\n",
      "Energy is -1.5722810471601572\n",
      "Energy is -1.61479061195212\n",
      "Energy is -1.6548469688406073\n",
      "Energy is -1.6923687237376712\n",
      "Energy is -1.7273182861734429\n",
      "Energy is -1.759699047153199\n",
      "Energy is -1.789550980876552\n",
      "Energy is -1.8169452401989985\n",
      "Energy is -1.841978270379385\n",
      "Energy is -1.8647658825824822\n",
      "Energy is -1.8854376267377393\n",
      "Energy is -1.9041316987650005\n",
      "Energy is -1.9209905214836986\n",
      "Energy is -1.9361570586247239\n",
      "Energy is -1.949771860072432\n",
      "Energy is -1.9619707935483792\n",
      "Energy is -1.9728833912675914\n",
      "Energy is -1.9826317265729902\n",
      "Energy is -1.9913297318883707\n",
      "Energy is -1.9990828724743506\n",
      "Energy is -2.0059880978608353\n",
      "Energy is -2.0121340024675294\n",
      "Energy is -2.0176011373618574\n",
      "Energy is -2.0224624253649863\n",
      "Energy is -2.0267836412015185\n",
      "Energy is -2.030623926778266\n",
      "Energy is -2.03403631885122\n",
      "Energy is -2.037068272305041\n",
      "Energy is -2.0397621671120345\n",
      "Energy is -2.042155790883487\n",
      "Energy is -2.044282791917091\n",
      "Energy is -2.0461730999207615\n",
      "Energy is -2.0478533132863217\n",
      "Energy is -2.0493470530123754\n",
      "Energy is -2.0506752842338685\n",
      "Energy is -2.0518566068894777\n",
      "Energy is -2.05290751741559\n",
      "Energy is -2.053842643551707\n",
      "Energy is -2.054674954420404\n",
      "Energy is -2.0554159480392666\n",
      "Energy is -2.056075818358536\n",
      "Energy is -2.0566636038165105\n",
      "Energy is -2.057187319279688\n",
      "Energy is -2.0576540730971216\n",
      "Energy is -2.0580701708564657\n",
      "Energy is -2.0584412072878653\n",
      "Energy is -2.0587721476254215\n",
      "Energy is -2.0590673996063127\n",
      "Energy is -2.0593308771666794\n",
      "Energy is -2.059566056781505\n",
      "Energy is -2.0597760272933336\n",
      "Energy is -2.0599635339815707\n",
      "Energy is -2.0601310175400314\n",
      "Energy is -2.060280648554696\n",
      "Energy is -2.0604143580059664\n",
      "Energy is -2.0605338642591424\n",
      "Energy is -2.0606406969530484\n",
      "Energy is -2.060736218148844\n",
      "Energy is -2.0608216410586717\n",
      "Energy is -2.0608980466362303\n",
      "Energy is -2.0609663982781368\n",
      "Energy is -2.0610275548556287\n",
      "Energy is -2.061082282270281\n",
      "Energy is -2.0611312637045422\n",
      "Energy is -2.0611751087178205\n",
      "Energy is -2.0612143613210523\n",
      "Energy is -2.0612495071471217\n",
      "Energy is -2.061280979820672\n",
      "Energy is -2.0613091666187713\n",
      "Energy is -2.0613344135031793\n",
      "Energy is -2.061357029595565\n",
      "Energy is -2.0613772911587414\n",
      "Energy is -2.0613954451396466\n"
     ]
    }
   ],
   "source": [
    "f(x) = real(x'*Hmat*x/(x'*x))[]\n",
    "\n",
    "x = randn(ComplexF64, size(Hmat, 2))\n",
    "α = 0.5\n",
    "\n",
    "for i = 1:100\n",
    "    g = f'(x)\n",
    "    x -= α .* g\n",
    "    println(\"Energy is $(f(x))\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random\n",
    "using QuAlgorithmZoo: random_diff_circuit\n",
    "using Plots\n",
    "Random.seed!(2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "train! (generic function with 1 method)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function train!(circuit, hami; maxiter=200, α=0.3)\n",
    "    nbit = nqubits(circuit)\n",
    "    rots = collect_blocks(RotationGate, circuit)\n",
    "    loss_history = Float64[]\n",
    "    for i in 0:maxiter\n",
    "        for (j,r) in enumerate(rots)\n",
    "            dispatch!(+, r, π/2)\n",
    "            E₊ = expect(hami, zero_state(nbit) |> circuit) |> real\n",
    "            dispatch!(-, r, π)\n",
    "            E₋ = expect(hami, zero_state(nbit) |> circuit) |> real\n",
    "            dispatch!(+, r, π/2)\n",
    "            g = 0.5(E₊ - E₋)\n",
    "            dispatch!(-, r, α*g)\n",
    "        end\n",
    "        push!(loss_history, expect(hami, zero_state(nbit) |> circuit) |> real)\n",
    "        \n",
    "        if i%10 == 0\n",
    "            println(\"Iter $i, E = $(loss_history[end])\")\n",
    "        end\n",
    "    end\n",
    "    loss_history, circuit\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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[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",
       "│  │  │  └─ rot(X gate, 0.0)\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",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│  │  │  └─ 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",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│  │  │  └─ 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",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│     │  └─ 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",
       "│        └─ rot(Z gate, 0.0)\n",
       "├─ \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[31m\u001b[1mcontrol(\u001b[22m\u001b[39m\u001b[31m\u001b[1m4\u001b[22m\u001b[39m\u001b[31m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│     └─ \u001b[37m\u001b[1m(1,)\u001b[22m\u001b[39m X gate\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",
       "│  │  │  └─ rot(Z gate, 0.0)\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",
       "│  │  │  └─ rot(X gate, 0.0)\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",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│  │  │  └─ 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",
       "│  │  │  └─ 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",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│  │  │  └─ 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",
       "│  │  │  └─ 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",
       "│  │     └─ rot(Z gate, 0.0)\n",
       "│  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│     │  └─ 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",
       "│     │  └─ 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",
       "│        └─ rot(Z gate, 0.0)\n",
       "├─ \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[31m\u001b[1mcontrol(\u001b[22m\u001b[39m\u001b[31m\u001b[1m4\u001b[22m\u001b[39m\u001b[31m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│     └─ \u001b[37m\u001b[1m(1,)\u001b[22m\u001b[39m X gate\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",
       "   │  │  └─ rot(Z gate, 0.0)\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",
       "   │     └─ rot(X gate, 0.0)\n",
       "   ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "   │  │  └─ 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",
       "   │     └─ rot(X gate, 0.0)\n",
       "   ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "   │  │  └─ 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",
       "   │     └─ rot(X gate, 0.0)\n",
       "   └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "      │  └─ 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",
       "         └─ rot(X gate, 0.0)\n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = random_diff_circuit(4, 2, [1=>2, 2=>3, 3=>4, 4=>1])"
   ]
  },
  {
   "attachments": {
    "_differentiable.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![_differentiable.png](attachment:_differentiable.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.35253669297396184 - 1.734723475976807e-18im"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expect(hami, rand_state(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter 0, E = 0.1331457495868531\n",
      "Iter 10, E = -0.9855303775878353\n",
      "Iter 20, E = -1.2297955326313268\n",
      "Iter 30, E = -1.9142937704748313\n",
      "Iter 40, E = -2.049605803218168\n",
      "Iter 50, E = -2.060489756340246\n",
      "Iter 60, E = -2.0614341280106534\n",
      "Iter 70, E = -2.0615385176045344\n",
      "Iter 80, E = -2.0615510453788284\n",
      "Iter 90, E = -2.0615525917224944\n",
      "Iter 100, E = -2.0615527849758575\n",
      "Iter 110, E = -2.0615528092908484\n",
      "Iter 120, E = -2.0615528123629607\n",
      "Iter 130, E = -2.061552812752211\n",
      "Iter 140, E = -2.061552812801631\n",
      "Iter 150, E = -2.0615528128079132\n",
      "Iter 160, E = -2.0615528128087144\n",
      "Iter 170, E = -2.061552812808816\n",
      "Iter 180, E = -2.061552812808828\n",
      "Iter 190, E = -2.0615528128088307\n",
      "Iter 200, E = -2.06155281280883\n",
      "Iter 210, E = -2.0615528128088303\n",
      "Iter 220, E = -2.061552812808829\n",
      "Iter 230, E = -2.0615528128088307\n",
      "Iter 240, E = -2.06155281280883\n",
      "Iter 250, E = -2.0615528128088307\n",
      "Iter 260, E = -2.061552812808831\n",
      "Iter 270, E = -2.0615528128088307\n",
      "Iter 280, E = -2.0615528128088303\n",
      "Iter 290, E = -2.06155281280883\n",
      "Iter 300, E = -2.0615528128088307\n",
      "Iter 310, E = -2.0615528128088307\n",
      "Iter 320, E = -2.0615528128088303\n",
      "Iter 330, E = -2.0615528128088294\n",
      "Iter 340, E = -2.0615528128088303\n",
      "Iter 350, E = -2.06155281280883\n",
      "Iter 360, E = -2.061552812808831\n",
      "Iter 370, E = -2.06155281280883\n",
      "Iter 380, E = -2.0615528128088307\n",
      "Iter 390, E = -2.0615528128088307\n",
      "Iter 400, E = -2.0615528128088307\n",
      "Iter 410, E = -2.06155281280883\n",
      "Iter 420, E = -2.0615528128088294\n",
      "Iter 430, E = -2.0615528128088303\n",
      "Iter 440, E = -2.0615528128088294\n",
      "Iter 450, E = -2.06155281280883\n",
      "Iter 460, E = -2.0615528128088294\n",
      "Iter 470, E = -2.0615528128088303\n",
      "Iter 480, E = -2.0615528128088303\n",
      "Iter 490, E = -2.0615528128088294\n",
      "Iter 500, E = -2.06155281280883\n",
      "Iter 510, E = -2.06155281280883\n",
      "Iter 520, E = -2.0615528128088307\n",
      "Iter 530, E = -2.061552812808831\n",
      "Iter 540, E = -2.0615528128088307\n",
      "Iter 550, E = -2.06155281280883\n",
      "Iter 560, E = -2.06155281280883\n",
      "Iter 570, E = -2.0615528128088307\n",
      "Iter 580, E = -2.0615528128088303\n",
      "Iter 590, E = -2.0615528128088307\n",
      "Iter 600, E = -2.0615528128088294\n",
      "Iter 610, E = -2.061552812808829\n",
      "Iter 620, E = -2.06155281280883\n",
      "Iter 630, E = -2.0615528128088307\n",
      "Iter 640, E = -2.0615528128088303\n",
      "Iter 650, E = -2.0615528128088303\n",
      "Iter 660, E = -2.06155281280883\n",
      "Iter 670, E = -2.0615528128088307\n",
      "Iter 680, E = -2.06155281280883\n",
      "Iter 690, E = -2.0615528128088316\n",
      "Iter 700, E = -2.0615528128088303\n",
      "Iter 710, E = -2.06155281280883\n",
      "Iter 720, E = -2.061552812808831\n",
      "Iter 730, E = -2.061552812808831\n",
      "Iter 740, E = -2.06155281280883\n",
      "Iter 750, E = -2.06155281280883\n",
      "Iter 760, E = -2.06155281280883\n",
      "Iter 770, E = -2.0615528128088294\n",
      "Iter 780, E = -2.06155281280883\n",
      "Iter 790, E = -2.0615528128088303\n",
      "Iter 800, E = -2.06155281280883\n",
      "Iter 810, E = -2.0615528128088303\n",
      "Iter 820, E = -2.0615528128088303\n",
      "Iter 830, E = -2.0615528128088303\n",
      "Iter 840, E = -2.0615528128088303\n",
      "Iter 850, E = -2.0615528128088303\n",
      "Iter 860, E = -2.0615528128088307\n",
      "Iter 870, E = -2.0615528128088307\n",
      "Iter 880, E = -2.06155281280883\n",
      "Iter 890, E = -2.0615528128088316\n",
      "Iter 900, E = -2.0615528128088303\n",
      "Iter 910, E = -2.0615528128088303\n",
      "Iter 920, E = -2.06155281280883\n",
      "Iter 930, E = -2.0615528128088307\n",
      "Iter 940, E = -2.0615528128088294\n",
      "Iter 950, E = -2.0615528128088303\n",
      "Iter 960, E = -2.0615528128088307\n",
      "Iter 970, E = -2.061552812808831\n",
      "Iter 980, E = -2.061552812808831\n",
      "Iter 990, E = -2.0615528128088294\n",
      "Iter 1000, E = -2.06155281280883\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([0.133146, -0.0189387, -0.19048, -0.378445, -0.565894, -0.72406, -0.835082, -0.903543, -0.943936, -0.968687  …  -2.06155, -2.06155, -2.06155, -2.06155, -2.06155, -2.06155, -2.06155, -2.06155, -2.06155, -2.06155], \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[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",
       "│  │  │  └─ rot(X gate, 1.138621687317084)\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",
       "│  │     └─ rot(Z gate, 0.8585240974715916)\n",
       "│  ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│  │  │  └─ rot(X gate, 6.328271240363392e-16)\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",
       "│  │     └─ rot(Z gate, 0.11994832844542769)\n",
       "│  ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│  │  │  └─ rot(X gate, 0.9532258307583561)\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",
       "│  │     └─ rot(Z gate, 0.050430442156283714)\n",
       "│  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│     │  └─ rot(X gate, -4.440892098500626e-16)\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",
       "│        └─ rot(Z gate, 0.7085839331430747)\n",
       "├─ \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[31m\u001b[1mcontrol(\u001b[22m\u001b[39m\u001b[31m\u001b[1m4\u001b[22m\u001b[39m\u001b[31m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│     └─ \u001b[37m\u001b[1m(1,)\u001b[22m\u001b[39m X gate\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",
       "│  │  │  └─ rot(Z gate, -0.05043044215628426)\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",
       "│  │  │  └─ rot(X gate, 1.570796326794896)\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",
       "│  │     └─ rot(Z gate, -6.827871601444713e-16)\n",
       "│  ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│  │  │  └─ rot(Z gate, 0.7122722293233048)\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",
       "│  │  │  └─ rot(X gate, 1.570796326794896)\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",
       "│  │     └─ rot(Z gate, 1.554312234475219e-16)\n",
       "│  ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│  │  │  └─ rot(Z gate, 0.5085087268743465)\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",
       "│  │  │  └─ rot(X gate, -3.3306690738754695e-17)\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",
       "│  │     └─ rot(Z gate, 0.7709318859944477)\n",
       "│  └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "│     │  └─ rot(Z gate, 0.2913557139261026)\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",
       "│     │  └─ rot(X gate, 1.4446654228988633)\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",
       "│        └─ rot(Z gate, 1.5707963267948966)\n",
       "├─ \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[31m\u001b[1mcontrol(\u001b[22m\u001b[39m\u001b[31m\u001b[1m4\u001b[22m\u001b[39m\u001b[31m\u001b[1m)\u001b[22m\u001b[39m\n",
       "│     └─ \u001b[37m\u001b[1m(1,)\u001b[22m\u001b[39m X gate\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",
       "   │  │  └─ rot(Z gate, 1.570796326794896)\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",
       "   │     └─ rot(X gate, 1.5707963267948974)\n",
       "   ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "   │  │  └─ rot(Z gate, 1.2111000956824478)\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",
       "   │     └─ rot(X gate, 0.0)\n",
       "   ├─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "   │  │  └─ rot(Z gate, 0.9979826705084403)\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",
       "   │     └─ rot(X gate, 2.220446049250313e-16)\n",
       "   └─ \u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\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",
       "      │  └─ rot(Z gate, 1.570796326794896)\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",
       "         └─ rot(X gate, 1.696927230690929)\n",
       ")"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train!(dispatch!(circuit, :random), hami; maxiter=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## If we have time, I will show the analytical approach for two-site Hubbard model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Float64,2}:\n",
       "  0.5   1.0  -1.0   0.0\n",
       "  1.0  -0.5   0.0   1.0\n",
       " -1.0   0.0  -0.5  -1.0\n",
       "  0.0   1.0  -1.0   0.5"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = [0.5 1 -1 0; 1 -0.5 0 1; -1 0 -0.5 -1; 0 1 -1 0.5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Complex{Float64},2}:\n",
       "  0.5+0.0im   1.0+0.0im  -1.0+0.0im   0.0+0.0im\n",
       "  1.0+0.0im  -0.5+0.0im   0.0+0.0im   1.0+0.0im\n",
       " -1.0+0.0im   0.0+0.0im  -0.5+0.0im  -1.0+0.0im\n",
       "  0.0+0.0im   1.0+0.0im  -1.0+0.0im   0.5+0.0im"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat(0.5kron(Z,Z)- kron(Z,X)+kron(X,Z)) |> Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Eigen{Float64,Float64,Array{Float64,2},Array{Float64,1}}\n",
       "eigenvalues:\n",
       "4-element Array{Float64,1}:\n",
       " -2.0615528128088267\n",
       " -0.5               \n",
       "  0.5000000000000018\n",
       "  2.0615528128088303\n",
       "eigenvectors:\n",
       "4×4 Array{Float64,2}:\n",
       " -0.435162  0.0       -0.707107      0.557345\n",
       "  0.557345  0.707107  -4.71028e-16   0.435162\n",
       " -0.557345  0.707107   4.71028e-16  -0.435162\n",
       " -0.435162  0.0        0.707107      0.557345"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigen(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0615528128088303"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_exact = sqrt(4.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Vanishing Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9-element Array{Float64,1}:\n",
       " 0.4059330395956129  \n",
       " 0.25136200168409156 \n",
       " 0.1970885973573447  \n",
       " 0.12772870055240237 \n",
       " 0.109690519544569   \n",
       " 0.07760827186061026 \n",
       " 0.05082867358284546 \n",
       " 0.03170525147755411 \n",
       " 0.021470617399368067"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Statistics\n",
    "\n",
    "function rand_gradient(hami::AbstractBlock)\n",
    "    N = nqubits(hami)\n",
    "    V1j = rand_unitary(1<<N) |> matblock\n",
    "    V2j = rand_unitary(1<<N) |> matblock\n",
    "\n",
    "    Uj = put(N, 1=>Rx(0.0))\n",
    "    c = chain(N, [V1j, Uj, V2j])\n",
    "    \n",
    "    η = rand()*2π\n",
    "    dispatch!(Uj, η+π/2)\n",
    "    y₊ = expect(hami, zero_state(N) |> c) |> real\n",
    "\n",
    "    dispatch!(Uj, η-π/2)\n",
    "    y₋ = expect(hami, zero_state(N) |> c) |> real\n",
    "    (y₊ - y₋)/2\n",
    "end\n",
    "\n",
    "maxN = 9\n",
    "grad_vars = [mean([abs(rand_gradient(put(N, 1=>Z))) for i=1:100]) for N=1:maxN]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see a exponential decreasing curve\n",
    "ax = plot(1:maxN, grad_vars, yscale=:log2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "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
}