From 8808d2d668a2815571470d75c5378d60341ecf96 Mon Sep 17 00:00:00 2001 From: ASRouillard Date: Mon, 14 Aug 2023 11:45:07 +0200 Subject: [PATCH 1/3] grover - final draft --- examples/grover_algorithm_tutorial.ipynb | 101 +++++++++++++---------- 1 file changed, 57 insertions(+), 44 deletions(-) diff --git a/examples/grover_algorithm_tutorial.ipynb b/examples/grover_algorithm_tutorial.ipynb index f422cef..ef44df2 100644 --- a/examples/grover_algorithm_tutorial.ipynb +++ b/examples/grover_algorithm_tutorial.ipynb @@ -10,7 +10,7 @@ }, { "cell_type": "code", - "execution_count": 149, + "execution_count": 1, "id": "297e1588-6df5-4246-91ad-fe1da9da921c", "metadata": {}, "outputs": [], @@ -20,7 +20,7 @@ }, { "cell_type": "code", - "execution_count": 150, + "execution_count": 2, "id": "e1a2dbcc", "metadata": {}, "outputs": [], @@ -154,7 +154,7 @@ }, { "cell_type": "code", - "execution_count": 151, + "execution_count": 3, "id": "be283fed", "metadata": {}, "outputs": [], @@ -174,7 +174,7 @@ }, { "cell_type": "code", - "execution_count": 152, + "execution_count": 4, "id": "5f7c68ef", "metadata": {}, "outputs": [], @@ -195,7 +195,7 @@ }, { "cell_type": "code", - "execution_count": 153, + "execution_count": 5, "id": "79f81eb9", "metadata": {}, "outputs": [], @@ -220,7 +220,7 @@ }, { "cell_type": "code", - "execution_count": 154, + "execution_count": 6, "id": "8123710a", "metadata": {}, "outputs": [], @@ -243,7 +243,7 @@ }, { "cell_type": "code", - "execution_count": 155, + "execution_count": 7, "id": "98da2199", "metadata": {}, "outputs": [], @@ -260,18 +260,18 @@ }, { "cell_type": "code", - "execution_count": 156, + "execution_count": 8, "id": "b94c3c42", "metadata": {}, "outputs": [ { "data": { - "image/png": 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" ] }, - "execution_count": 156, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -291,7 +291,7 @@ }, { "cell_type": "code", - "execution_count": 157, + "execution_count": 9, "id": "3eee5cca", "metadata": {}, "outputs": [], @@ -303,7 +303,7 @@ }, { "cell_type": "code", - "execution_count": 158, + "execution_count": 10, "id": "74870d58", "metadata": {}, "outputs": [], @@ -336,18 +336,18 @@ }, { "cell_type": "code", - "execution_count": 159, + "execution_count": 11, "id": "3fe4233d", "metadata": {}, "outputs": [ { "data": { - "image/png": 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u91BMJyJcGtX/2myfjRlm3LkBAAD6i9wQgGAIC5dSsr1vlzpNFL14INXg16XkhjzjS24oOUOKjPZ7KKYzPE6KMnB6h1C/BxgPwox9gOHDaVdffbUkaeXKlV0KUXbs2KH58+ersrJSUvdik46ZVZ5//nlVVVVJkpxOp9atW6clS5Zo0KBBknovfImMjNTdd9+t2tov16Jbv369li5dKkl66aWXui2F1NH27GN2LHtkt9s7Z7DxlMPh0K233qr33ntPqampev/99zV69GivjoHQEBkZqcTEREVGGviOKQBLGJEuDR3p+f4RUVLaJYGLx0zCbMa+uOJNf88MTZZGePG6wRYmTZgTuHjMxsh+GOrJDQAAYG3khgAES+p0yZsVgKOHSqN9KJaxovjB7ocRwmzS6POMOXeoGZEuxXmZHx13ceDiMZMwm5RqZH40xHNDjAdhxj5A4ctpy5cv17Bhw3TkyBFlZmYqKytL6enpmjVrliZMmKArr7xSUvdik2XLlikiIkI7d+5UamqqMjIylJSUpJtuukn33XefUlNTJXUvmOmYteWZZ57Rpk2blJqaqlmzZmnMmDFasmSJampq9Mc//lHXXXddt1h7m/ElMzNTY8eO1bFjxzR27Fhddtllmjt3buesM+fy6quvau3atZKkQYMG6Vvf+pbmzp3b46OioqLvXygGrLKyMt19990qKyszOhQAJhcWLk37uhTrweRh4YOkaTdIsSH+giGYpo015rzJ8dLIocacOxRlLpASx/W9ny3s9L4GXddQZNQ9EB0pTfZ9qVkAAADDkRsCECyDYqQZ/yQNiu1736g4acaNzATsDaNeF1+QKkWGG3PuUBMWIU3/uhTrwYd3yI96b7pB98CoeGlEiOdHGQ/CjH2AwpfTUlNT9cknn2jRokWKjo5WSUmJEhMT9dxzz2nDhg2ds8CcXfiSnZ2tDRs2aNasWQoPD1d1dbWuuuoqbd68WQ888ICKi4sVERHRZW2siooKHT9+XImJibrzzju1fv16ZWRkaO/evWpubtbXv/51bdu2TT/60Y+6xWm321VVVaWkpCSlpKR02RYdHa23335bS5YsUWRkpLZv364tW7ZoyJAhff78LS0tnf8+dOiQtmzZ0uujubnZq98tBpZTp05p06ZNOnXqlNGhALCAqFjp4m9KY2a6P7FwNpvN/cmHi78pnTcm+PGFsovGGzOd55x093WDZ8Ij3QmOCXN6T/QljpMu/IZ7Klt4bnKylOTFJwf95ZKJ0iADp9IFAADoL3JDAIJpSJI06zZp1AXuD0mdLSxCGp0lXXwrb/h7a066tc4bqqJipYv6yo9Odt8D5Ee9c9F4Y3I0cyaHfn6U8SDM2AdI2Z4hIyNDb775Zrfn6+vrVVJSorCwMF1wwQXdtl9zzTW65pprejymw+Ho9lxycrJcLlfn94sWLdKiRYs8ijE1NbVL27NNnTpVb7zxhkfHOtOyZcu0bNkyr9sBANCXiChpynxp0lzpeJFU8PaX2+b8QIo24I1rM4iOlC4eL20+ELxzRkVIF08I3vnMIixcmnCZlDZLOnlQ2rP+y22XfY/Enq/CbNLcdOmNnOCd0yZpNgk+AAAAAPBK9FAp81op/QrpxH6p8P0vt33lh1JktHGxhbKR8e4PhRQFcZL+4XFSOrOgei0y+nR+dM7p/Og7X26b+89SVN+fX0cPBg9yF798GsT8aHSk+5wABh5mfPFAfn6+XC6X0tPTFRMTY3Q4AACEpPBIaXSm3O8cy/2Vopf+uTZbGtLDJ0UCZfEM94s7+CYsXBo5WV3uAYpe+mfuZPfyW8Fyxfks9QUAAAAAvho0WEqdri6viyl66Z+lM6XwIL7Td+PF7g+iwDfhg6TRF6jLPUDRS/8syJZiyY8CEIUvHtmzZ4+k7sscAQAAGGlItHTjrOCcK30kM11g4IkIl269LDhJt+Fx0kJeDgAAAAAABpBRCdLXsoJzrtmTpCmjgnMuwFNx0e6CrGCYnOy+DwAMTBS+eIDCF5jJyJEj9eCDD2rkyJFGhwIA8IPpY6VLJ3rXpq5Jqml0f/VEXLR0y6V8ogcD09hh3hekeHsPRIZL35ptzLrRAAAA/kZuCADM5aqp0iQv/6R7+7o4OV66/kLvYwOCYcY4aZaXy7N7ew8MjZZuuUSymSQ/yngQZuwDpG49QOELzCQpKUnLli0zOgwAgB/dNEtqapXyjni2/2/f6XufDrFR0g+vlIYx7SoGsKumSg0t0qZ9nu3vzT0QESZ973JpXJJvsQEAAAw05IYAwFzCw6Q7r5Ce+UAqq/KsjTevi5PipLuuZHkXDGw3XyI1t0m7A5gfTTRRfpTxIMzYB5jxxQMbN26Uy+XSokWLjA4F6Lfa2lq98847qq2tNToUAICfhIdJt8+VLvPzVJuJsdI9X5VSzvPvcQF/s9mk62dIC7O/XCbbH2IGSf98pZQx2o8HBQAAMBi5IQAwn+hI6e6rpPP9vBTRmETpJ1+V4mP8e1zA38LDpO/M9X5m7L4MG+LOj442WX6U8SDM2AcofAEsxm636/7775fdbjc6FACAH4WHuT/ZcMfl7qWJ+mtuuvTgIvdUtkAosNmka7Kke6+Rhsf1/3jZY6SfXyelm2e2TwAAAEnkhgDArKIjpX+eL910sRTVz/UewsPcHy6572tS3GD/xAcEWniYe7n27/krPzpZWr7QnPlRxoMwYx9gqSMAAAATyRojTRghvZ8vbT8oNbZ6137KKOnqTN7sR+gaP1z62ULpw0JpS5FU6+FazR3GDZPmT5WmjTHPus0AAAAAAGuw2aQ5k6XzR0v/2CvtLJHaHJ63D7O5PwhyzQXmm+EC1pE9Rpo4wn0PbD/kXiLeG+efzo9OIj8KhBQKXwAAAEwmNkpacqG0IFvaVepe29Ze3XMBQGS4O5Excbh7qaThQ4MfL+BvgyLcSbqrpkr5R6WcEulItVRV333fMJs0OkFKS5IumSiNGRbsaAEAAAAA8K9hQ9wzX1w/Q/rskLSv3J0bamjpvm90pJSaKE0eKV0ySYpnhheYQGyUdMNMaeE0KadU2tNHfjTlPPeHCS+b5J+ZhAEEH4UvAAAAJjUowv1G/iWn17ata3K/8d/mcE/9GTNIGjHU/W/AjMLD3J/yyR7j/r6xRTpxSmprdxe8REW6p6uNCDc2TgAAAAAAAiEmSpqX4X64XNIXDVJNo9TulCLC3MvBDItzv0YGzGhQhHTpRPdD6p4fjY1yF7qQHwVCH4UvgMVER0crIyND0dF+WOAQABBShg52PwCriomS0qKMjgIAAMBY5IYAwJpsNilxiPsBWBX5UTfGgzBjH6DwBbCYiRMnat26dUaHAQAAAAAAAAOQGwIAALA2xoMwYx9g4iYAAAAAAAAAAAAAAACEJApfAIspKChQdna2CgoKjA4FAAAAAAAAQUZuCAAAwNoYD8KMfYDCF8BiXC6X2tra5HK5jA4FAAAAAAAAQUZuCAAAwNoYD8KMfYDCFwAAAAAAAAAAAAAAAIQkCl8AAAAAAAAAAAAAAAAQkih8AQAAAAAAAAAAAAAAQEii8AWwmIkTJ2r9+vWaOHGi0aEAHklLS9OUKVM0ffp0TZ06VU8//XSv+950003aunWr38792muv6bvf/a5uuOEGTZ48WdOmTdNXv/pVFRcXd9nvK1/5ig4fPuy38+JLXH9YXaDuAU/6N30bAADAnMgNIZSQFwB9AFZHbgiBwHgQZuwDFL4AFhMdHa309HRFR0cbHQrgsTVr1ig3N1dvv/22fvGLX2j37t3d9vnss89UXV2tyy67zG/nff3113XDDTfoBz/4gfbv36+8vDwtWbJEd955Z5f9HnjgAT300EN+Oy+64vrD6gJxD3jSv+nbAAAA5kRuCKGGvADoA7A6ckPwN8aDMGMfoPAFsJijR4/qV7/6lY4ePWp0KIDXxo0bpylTpqioqKjbtueee0633nqrx8eqqalRamqqhg0bpunTpysjI0NRUVGdA/u2tjZt2bJFCxcu1MKFC2Wz2SRJl156qUpKSroca9GiRXr77bdVW1vr+w+HPnH9YXWe3gP+6t/0bQAAAHMiN4RQRV4A9AFYHbkh+AvjQZixD1D4AlhMTU2N1q5dq5qaGqNDAby2Z88eFRYWatq0ad22ffjhh7rkkks8PlZCQoJuvfVW3XfffcrNzdXvf/97XXrppVq1apUkadOmTZo9e7YiIyO7tHvyySe1ZMmSLs9FRkYqKytLn3zyiQ8/FTzF9YfVeXoP+Kt/07cBAADMidwQQhV5AdAHYHXkhuAvjAdhxj4QYXQAAAD05eabb9bgwYMVExOjF198Uenp6d32sdvtGjlyZOf3l112mQ4cONDj8Xbt2qUxY8YoNzdX9957ryRp586dmjFjRuc+b7zxhpYuXdql3SOPPKLi4mJ98MEH3Y6ZnJwsu93u08+Hc+P6w+p8uQf81b/p2wAAAACMRl4A9AFYHbkhAOgbhS8AgAFvzZo1mj59+jn3iYmJUXNzc+f3W7du7fO4ubm5nQP+nTt36vrrr5ckuVwuvfvuu3rsscc6933iiSe0bt06vf/++4qJiel2rObmZg0ePNiTHwde4vrD6ny5B/zVv+nbAAAAAIxGXgD0AVgduSEA6BtLHQEATCE7O1v79+/3eP+jR4/KZrMpJSVFkrR7925lZWVJkj777DNlZGRoyJAhkqTf/va3euWVV/SPf/xDCQkJPR5v3759PU4xieDg+sPqzrwH/Nm/6dsAAAAAQgF5AdAHYHXkhgBYHYUvgMWEhYXp4osvVlgYtz/M5cYbb9S7777r8f67du3qMr1jQkKCnnnmGUnS66+/rhtuuEGSe4rIBx54QDU1NZo/f76mT5/ebb3gkpISORwOXgAYiOsPqzvzHvBX/6ZvAwAAmBO5IZgReQHQB2B15IbgDcaDMGMfsLlcLpfRQQDon8LCQo/3zc/P14033qjXXntNmZmZHrc7//zzfQkN6Ob9/5LkkmSTrn7Af8e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" ] }, - "execution_count": 159, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -360,7 +360,7 @@ }, { "cell_type": "code", - "execution_count": 160, + "execution_count": 12, "id": "8b17b9e4", "metadata": {}, "outputs": [], @@ -393,22 +393,19 @@ }, { "cell_type": "code", - "execution_count": 161, + "execution_count": 31, "id": "1e5c2dd4", "metadata": {}, "outputs": [], "source": [ "# Unitary to prepare the initial state |phi>\n", - "# Option 1:\n", - "# phi = psi (optimal)\n", - "# U_phi = Qcycle(mapping=H)\n", - "# Option 2:\n", - "# possibly with some small orthogonal component to the plane spanned by T and psi\n", - "U_phi = Qpivot(\n", - " mapping=H, global_pattern=bin(np.random.randint(0, 2 ** int(n / 4)))[2:].zfill(n)\n", - ") + Qcycle(mapping=H)\n", - "# Option 3:\n", - "# The zero state (suboptimal - large orthogonal component to the plane spanned by T and psi)\n", + "# Option 1: phi == psi (optimal)\n", + "U_phi = Qcycle(mapping=H)\n", + "# Option 2: possibly with some small orthogonal component to the plane spanned by T and psi\n", + "# U_phi = Qpivot(\n", + "# mapping=H, global_pattern=bin(np.random.randint(0, 2 ** int(n / 4)))[2:].zfill(n)\n", + "# ) + Qcycle(mapping=H)\n", + "# Option 3: The zero state (suboptimal - large orthogonal component to the plane spanned by T and psi)\n", "# U_phi = Qcycle(mapping=H) + Qcycle(mapping=H)\n" ] }, @@ -422,7 +419,7 @@ }, { "cell_type": "code", - "execution_count": 162, + "execution_count": 32, "id": "6fd607b2", "metadata": {}, "outputs": [], @@ -434,7 +431,7 @@ }, { "cell_type": "code", - "execution_count": 163, + "execution_count": 33, "id": "ac94cfed", "metadata": {}, "outputs": [ @@ -446,7 +443,7 @@ "Number of ancillas: 4\n", "Total number of qubits: 11\n", "Search space size: 128\n", - "Target state: 0010100 = 20\n", + "Target state: 1100111 = 103\n", "\n", "Interactions of Grover to perform 8\n", "Optimal number of iterations 8\n" @@ -469,7 +466,7 @@ }, { "cell_type": "code", - "execution_count": 164, + "execution_count": 34, "id": "59774eea", "metadata": {}, "outputs": [], @@ -487,7 +484,7 @@ }, { "cell_type": "code", - "execution_count": 165, + "execution_count": 35, "id": "011d26ab", "metadata": {}, "outputs": [], @@ -507,7 +504,7 @@ }, { "cell_type": "code", - "execution_count": 166, + "execution_count": 36, "id": "e8e4930f", "metadata": {}, "outputs": [], @@ -530,7 +527,7 @@ }, { "cell_type": "code", - "execution_count": 167, + "execution_count": 37, "id": "5b61d34d", "metadata": {}, "outputs": [], @@ -547,7 +544,7 @@ }, { "cell_type": "code", - "execution_count": 168, + "execution_count": 38, "id": "b769cc17", "metadata": {}, "outputs": [], @@ -581,7 +578,7 @@ }, { "cell_type": "code", - "execution_count": 169, + "execution_count": 39, "id": "fb8162c5", "metadata": { "tags": [] @@ -591,25 +588,25 @@ "name": "stdout", "output_type": "stream", "text": [ - "Target state: 0010100 = 20\n", + "Target state: 1100111 = 103\n", "\n", "Interactions of Grover performed: 8\n", "Optimal number of iterations: 8\n", "\n", "State associate with the 5 largest number of count\n", - "['0010100', '1101110', '1101010', '1001101', '1001001']\n", + "['1100111', '1111010', '1101001', '0111110', '0110000']\n", "Number of counts\n", - "[1019, 1, 1, 1, 1]\n" + "[1018, 1, 1, 1, 1]\n" ] }, { "data": { - "image/png": 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", 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" ] }, - "execution_count": 169, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" } @@ -634,13 +631,29 @@ "\n", "plot_histogram(counts_q, figsize=(int(len(x)/4) if len(x)>100 else 15,5))\n" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f01896cc", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "573f31b8", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "unitary_hack", + "display_name": ".venv", "language": "python", - "name": "unitary_hack" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -652,7 +665,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.9" + "version": "3.11.2" } }, "nbformat": 4, From e27461f058910479823a3f783861252588bcfa06 Mon Sep 17 00:00:00 2001 From: ASRouillard Date: Wed, 16 Aug 2023 12:12:32 +0200 Subject: [PATCH 2/3] Grover - typos, minor edits --- examples/grover_algorithm_tutorial.ipynb | 36 +++++++++++++++--------- 1 file changed, 23 insertions(+), 13 deletions(-) diff --git a/examples/grover_algorithm_tutorial.ipynb b/examples/grover_algorithm_tutorial.ipynb index ef44df2..bfadfe6 100644 --- a/examples/grover_algorithm_tutorial.ipynb +++ b/examples/grover_algorithm_tutorial.ipynb @@ -41,9 +41,10 @@ "source": [ "## Background\n", "\n", - "Imagine someone hands you a definition of a word. They then ask you to use a dictionary to find the word that has a definition that exactly matches the given definition. If your dictionary contains $N$ words, on average you will need to check (query) $N/2$ times whether a word's definition exactly matches the given definition before you can expect to find an exact match. This is intuitively correct since sometimes you will be lucky and find the word immediately, while other times you will need to search through the entire dictionary before you find the word you seek. \n", + "Imagine someone hands you a definition of a word. They then ask you to use a dictionary to find the word that has a definition that exactly matches the given definition. If your dictionary contains $N$ words, you will need to check (query) $N/2$ times on average whether a word's definition exactly matches the given definition before you can expect to find the match. Intuitively this makes sense, because sometimes you will be lucky and find the word immediately, while other times you will need to search through the entire dictionary before you find the word you seek.\n", + "\n", + "This is a typical example of a search of an unstructured database. In our example a dictionary, while clearly structured alphabetically, is not structured with respect to the definitions it contains. Grover's algorithm is a quantum algorithm that provides a speed-up with respect to the number of steps required, allowing one to find the sought entry on the order of $\\sqrt{N}$ queries.\n", "\n", - "This is a typical example of a search of an unstructured database. In our example a dictionary, while clearly structured alphabetically, is not structured with respect to the definitions it contains. Grover's algorithm is a quantum algorithm that provides a speed-up with respect to the number of steps needed, allowing one to find the sought entry in order $\\sqrt{N}$ queries.\n", "\n", "### The algorithm\n", "\n", @@ -51,9 +52,9 @@ "\n", "Grover's algorithm works in two steps:\n", "\n", - "Step 1: Apply the oracle. \n", + "**Step 1:** Apply the oracle. \n", "\n", - "Step 2: Reflect in a hyperplane orthogonal to some state $\\psi$. \n", + "**Step 2:** Reflect in a hyperplane orthogonal to some state $\\psi$. \n", "\n", "It turns out that step 1 and 2 are in fact the same type of operation, namely a reflection. Reflecting a vector is nothing other than changing the sign of the component of the vector that is parallel to the normal to the (hyper)plane of reflection, while doing nothing to all other components of the vector. Step 1 is therefore nothing other than a reflection in the hyperplane orthogonal to the target state $T$. \n", "\n", @@ -64,13 +65,13 @@ "We shall see that the algorithm performs optimally if $\\psi$, $T$ and the initial state of the system all lie in the same plane.\n", "\n", "### *Side note on reflections* \n", - "In descriptions of Grover's algorithm the second step is commonly characterized as a reflection *across a state* in the plane, with this state taken to be the equal superposition of all computational basis states. A reflection across a state can be written as\n", - "$$V = - \\mathbb{I} + 2|\\hat{r} \\rangle\\langle \\hat{r} |$$\n", - "where $\\hat{r}$ is the state across which we reflect. It is straightforward to check that $V$ can also be written as\n", - "$$V = - \\big(\\mathbb{I} - 2|\\hat{r}_\\perp \\rangle\\langle \\hat{r}_\\perp | \\big)$$\n", - "where $\\hat{r}_\\perp$ is a vector perpendicular to $\\hat{r}$. The above equality shows that any reflection *across a state $\\hat{r}$ in a hyperplane* can be reformulated at a reflection *in the hyperplane orthogonal to a state* $\\hat{r}_\\perp$.\n", - " \n", - "Since $\\psi$ is some arbitrary state, $V$ and $U_{\\text{reflect}}$ differ only by a global phase factor.\n", + "In descriptions of Grover's algorithm the second step is commonly characterized as a reflection *across a state* in the plane, with this state taken to be the equal superposition of all computational basis states. In such a description it is also implicit that the plane we are referring to is the plane spanned by $\\psi$ and the target state $T$. A reflection across a state in a plane can be written as\n", + "$$V = - \\mathbb{I}_p + 2|\\hat{r} \\rangle\\langle \\hat{r} |$$\n", + "where $\\hat{r}$ is the state across which we reflect and $\\mathbb{I}_p$ represents the identity operator in the plane of reflection. Reformulating $V$ in terms of $\\hat{r}_\\perp$, the vector perpendicular to $\\hat{r}$ in the plane of reflection, gives\n", + "$$V = \\mathbb{I}_p - 2|\\hat{r}_\\perp \\rangle\\langle \\hat{r}_\\perp | \\,,$$\n", + "where we use that $\\mathbb{I}_p = |\\hat{r}\\rangle\\langle\\hat{r}| + |\\hat{r}_\\perp\\rangle\\langle\\hat{r}_\\perp|$. Furthermore, $\\mathbb{I}_p$ can be expanded, without changing the action of $V$, to $\\mathbb{I}$ that it the identity operator in the full space,\n", + "$$V = \\mathbb{I} - 2|\\hat{r}_\\perp \\rangle\\langle \\hat{r}_\\perp | \\,.$$\n", + "The above equality shows that any reflection *across a state $\\hat{r}$ in a plane* can be reformulated as a reflection *in the hyperplane orthogonal to a state* $\\hat{r}_\\perp$.\n", "\n", "\n", "### Evolution according to Grover\n", @@ -227,7 +228,8 @@ "source": [ "# Unitary to prepare the state |psi>\n", "U_psi = Qcycle(mapping=H)\n", - "# Unitary to prepare the target state |T>\n", + "# Unitary to prepare the target state |T> \n", + "# (the target string is reversed here to account for the reversed ordering for the output when using Qiskit)\n", "U_T = Qpivot(mapping=X, global_pattern=target_string[::-1])\n" ] }, @@ -258,6 +260,14 @@ "U_toffoli += Qpivot(mapping=H, global_pattern=\"*1\")\n" ] }, + { + "cell_type": "markdown", + "id": "5bfb1f23", + "metadata": {}, + "source": [ + "To verify that this is the circuit that implements the Toffoli gate, note that the controlled phase gate $P_{-\\pi/2}$ is in fact $\\sqrt{\\sigma_z}$, and that $H \\sigma_z H = \\sigma_x$." + ] + }, { "cell_type": "code", "execution_count": 8, @@ -315,7 +325,7 @@ "multiCZ += Qpivot(mapping=H, global_pattern=\"*1\")\n", "# Apply the Toffoli gate sequentially to each pair of qubits with intermediate steps stored on the ancillary qubits\n", "multiCZ += Qcycle(mapping=U_toffoli, step=2, boundary=\"open\")\n", - "# The final qubit is not an ancillary qubit, so we need to unmask it\n", + "# The final qubit is not an ancillary qubit, so we need to mask it before unitarily resetting all ancillary qubits to 0\n", "multiCZ += Qmask(\"*1\")\n", "# Apply the same sequence of Toffoli gates in reverse order in order to reset the ancillary qubits to 0\n", "multiCZ += Qcycle(mapping=U_toffoli, step=2, boundary=\"open\", edge_order=[-1])\n", From e6809a2703e1afd974e0fd60edb3a53e05d6e1cc Mon Sep 17 00:00:00 2001 From: ASRouillard Date: Wed, 16 Aug 2023 21:17:44 +0200 Subject: [PATCH 3/3] check post processing: --- examples/grover_algorithm_tutorial.ipynb | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/examples/grover_algorithm_tutorial.ipynb b/examples/grover_algorithm_tutorial.ipynb index bfadfe6..3f3dc08 100644 --- a/examples/grover_algorithm_tutorial.ipynb +++ b/examples/grover_algorithm_tutorial.ipynb @@ -559,7 +559,10 @@ "metadata": {}, "outputs": [], "source": [ - "# Post preprocess the results of the Grover algorithm by tracing over ancillary qubits\n", + "# Post preprocess the results\n", + "# The ancillary qubits always end in the zero state and are therefore separable from the final state. \n", + "# TODO sanity check this reasoning\n", + "# We can disregard the ancillary states by summing over all possible ancillary qubit states. \n", "Q = []\n", "mask = [\"q\" if n.split(\"_\")[0] == \"q\" else \"a\" for n in q_names]\n", "for k in counts.keys():\n",