Refactor block encoding bloqs to use abstract base class.

qualtran/bloqs/block_encoding.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "774a1b4a",
+   "id": "f74727f8",
    "metadata": {
     "cq.autogen": "title_cell"
    },
@@ -11,28 +11,38 @@
     "\n",
     "High level bloqs for defining bloq encodings and operations on block encodings.\n",
     "\n",
-    "Given an operator $V$ which can be expressed as a linear combination of unitaries\n",
+    "In general, given an $s$-qubit operator $H$ then the $(s+a)$-qubit unitary $U$ is\n",
+    "a $(\\alpha, a, \\epsilon)$-block encoding of $H$ if it satisfies:\n",
     "\n",
     "$$\n",
-    "    V = \\sum_l^L w_l U_l,\n",
+    "    \\lVert H - \\alpha (\\langle G|_a\\otimes I_s U |G\\rangle_a \\otimes I_s) \\rVert\n",
+    "    \\le \\epsilon,\n",
     "$$\n",
-    "where $w_l \\ge 0$, $w_l \\in \\mathbb{R}$, and $U_l$ is a unitary, then the block\n",
-    "encoding $\\mathcal{B}\\left[\\frac{V}{\\lambda}\\right]$ satisifies\n",
+    "\n",
+    "where $a$ is an ancilla register and $s$ is the system register, $U$ is a unitary sometimes\n",
+    "called a signal oracle and encodes $H$ in its top right corner, $\\alpha \\ge\n",
+    "\\lVert H\\rVert$ (where $\\lVert \\cdot \\rVert$ denotes the spectral norm), and\n",
+    "$\\epsilon$ is the precision to which the block encoding is prepared. The state\n",
+    "$|G\\rangle_a$ is sometimes called the signal state, and its form depends on the\n",
+    "details of the block encoding. \n",
+    "\n",
+    "For LCU based block encodings \n",
+    "we have\n",
     "$$\n",
-    "    _a\\langle 0| \\mathcal{B}\\left[\\frac{V}{\\lambda}\\right] |0\\rangle_a\n",
-    "    |\\psi\\rangle_s = \\frac{V}{\\lambda}|\\psi\\rangle_s\n",
+    "U = \\sum_l |l\\rangle\\langle l| \\otimes U_l\n",
     "$$\n",
-    "where the subscripts $a$ and $s$ signify ancilla and system registers\n",
-    "respectively, and $\\lambda = \\sum_l w_l$. The ancilla register is at least of size $\\log L$. In our\n",
-    "implementations we typically split the ancilla registers into selection registers (i.e.\n",
-    "the $l$ registers above) and junk registers which are extra qubits needed by\n",
-    "state preparation but not controlled upon during SELECT."
+    "and $|G\\rangle = \\sum_l \\sqrt{\\frac{\\alpha_l}{\\alpha}}|0\\rangle_a$, which define the\n",
+    "usual SELECT and PREPARE oracles.\n",
+    "\n",
+    "Other ways of building block encodings exist so we define the abstract base\n",
+    "class `BlockEncoding` bloq, which expects values for $\\alpha$, $\\epsilon$,\n",
+    "system and ancilla registers and a bloq which prepares the state $|G\\rangle$. "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b4bc97c7",
+   "id": "032a712d",
    "metadata": {
     "cq.autogen": "top_imports"
    },
@@ -49,17 +59,17 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b5bfa35",
+   "id": "d16f721f",
    "metadata": {
-    "cq.autogen": "BlackBoxBlockEncoding.bloq_doc.md"
+    "cq.autogen": "LCUBlockEncoding.bloq_doc.md"
    },
    "source": [
-    "## `BlackBoxBlockEncoding`\n",
-    "Black box implementation of a block encoding using SELECT and PREPARE.\n",
+    "## `LCUBlockEncoding`\n",
+    "LCU based block encoding using SELECT and PREPARE oracles.\n",
     "\n",
     "Builds the block encoding via\n",
     "$$\n",
-    "    \\mathcal{B}[V] = \\mathrm{PREPARE}^\\dagger \\cdot \\mathrm{SELECT} \\cdot \\mathrm{PREPARE},\n",
+    "    U[H] = \\mathrm{PREPARE}^\\dagger \\cdot \\mathrm{SELECT} \\cdot \\mathrm{PREPARE},\n",
     "$$\n",
     "where\n",
     "$$\n",
@@ -70,33 +80,46 @@
     "    \\mathrm{SELECT} |l\\rangle_a|\\psi\\rangle_s = |l\\rangle_a U_l |\\psi\\rangle_s.\n",
     "$$\n",
     "\n",
+    "The ancilla register is at least of size $\\log L$.\n",
+    "\n",
+    "In our implementations we typically split the ancilla registers into\n",
+    "selection registers (i.e.  the $l$ registers above) and junk registers which\n",
+    "are extra qubits needed by state preparation but not controlled upon during\n",
+    "SELECT.\n",
+    "\n",
+    "Here $|G\\rangle = \\mathrm{PREPARE}|0\\rangle$.\n",
+    "\n",
     "#### Parameters\n",
     " - `select`: The bloq implementing the `SelectOracle` interface.\n",
-    " - `prepare`: The bloq implementing the `SelectOracle` interface. \n",
+    " - `prepare`: The bloq implementing the `PrepareOracle` interface. \n",
     "\n",
     "#### Registers\n",
     " - `selection`: The combined selection register.\n",
     " - `junk`: Additional junk registers not prepared upon.\n",
-    " - `system`: The combined system register.\n"
+    " - `system`: The combined system register. \n",
+    "\n",
+    "#### References\n",
+    " - [Hamiltonian Simulation by Qubitization](https://quantum-journal.org/papers/q-2019-07-12-163/).     Sec 3.1, page 7 and 8 for high level overview and definitions. A     block encoding is called a standard form encoding there.\n",
+    " - [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://arxiv.org/abs/1804.01973).     Definition 3 page 8.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0d0e1f95",
+   "id": "0dc5476c",
    "metadata": {
-    "cq.autogen": "BlackBoxBlockEncoding.bloq_doc.py"
+    "cq.autogen": "LCUBlockEncoding.bloq_doc.py"
    },
    "outputs": [],
    "source": [
-    "from qualtran.bloqs.block_encoding import BlackBoxBlockEncoding"
+    "from qualtran.bloqs.block_encoding import LCUBlockEncoding"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "ba37811d",
+   "id": "5ab0f455",
    "metadata": {
-    "cq.autogen": "BlackBoxBlockEncoding.example_instances.md"
+    "cq.autogen": "LCUBlockEncoding.example_instances.md"
    },
    "source": [
     "### Example Instances"
@@ -105,26 +128,32 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "38a4e1fc",
+   "id": "349a4f99",
    "metadata": {
-    "cq.autogen": "BlackBoxBlockEncoding.black_box_block_bloq"
+    "cq.autogen": "LCUBlockEncoding.black_box_block_bloq"
    },
    "outputs": [],
    "source": [
-    "from qualtran.bloqs.block_encoding import BlackBoxBlockEncoding, BlackBoxPrepare, BlackBoxSelect\n",
     "from qualtran.bloqs.hubbard_model import PrepareHubbard, SelectHubbard\n",
     "\n",
+    "# 3x3 hubbard model U/t = 4\n",
     "dim = 3\n",
-    "select = BlackBoxSelect(SelectHubbard(x_dim=dim, y_dim=dim))\n",
-    "prepare = BlackBoxPrepare(PrepareHubbard(x_dim=dim, y_dim=dim, t=1, mu=4))\n",
-    "black_box_block_bloq = BlackBoxBlockEncoding(select=select, prepare=prepare)"
+    "select = SelectHubbard(x_dim=dim, y_dim=dim)\n",
+    "U = 4\n",
+    "t = 1\n",
+    "prepare = PrepareHubbard(x_dim=dim, y_dim=dim, t=t, mu=U)\n",
+    "N = dim * dim * 2\n",
+    "qlambda = 2 * N * t + (N * U) // 2\n",
+    "black_box_block_bloq = LCUBlockEncoding(\n",
+    "    select=select, prepare=prepare, alpha=qlambda, epsilon=0.0\n",
+    ")"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "fafa7659",
+   "id": "cb3538d3",
    "metadata": {
-    "cq.autogen": "BlackBoxBlockEncoding.graphical_signature.md"
+    "cq.autogen": "LCUBlockEncoding.graphical_signature.md"
    },
    "source": [
     "#### Graphical Signature"
@@ -133,9 +162,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4e0223af",
+   "id": "b6354639",
    "metadata": {
-    "cq.autogen": "BlackBoxBlockEncoding.graphical_signature.py"
+    "cq.autogen": "LCUBlockEncoding.graphical_signature.py"
    },
    "outputs": [],
    "source": [
@@ -146,9 +175,9 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8664826d",
+   "id": "09bb24fc",
    "metadata": {
-    "cq.autogen": "BlackBoxBlockEncoding.call_graph.md"
+    "cq.autogen": "LCUBlockEncoding.call_graph.md"
    },
    "source": [
     "### Call Graph"
@@ -157,9 +186,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fdb0d03b",
+   "id": "fc3c71be",
    "metadata": {
-    "cq.autogen": "BlackBoxBlockEncoding.call_graph.py"
+    "cq.autogen": "LCUBlockEncoding.call_graph.py"
    },
    "outputs": [],
    "source": [
@@ -171,7 +200,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "995d6d20",
+   "id": "2ed5cb18",
    "metadata": {
     "cq.autogen": "ChebyshevPolynomial.bloq_doc.md"
    },
@@ -198,13 +227,13 @@
     " - `order`: order of Chebychev polynomial. \n",
     "\n",
     "#### References\n",
-    " - [Quantum computing enhanced computational catalysis](     https://arxiv.org/abs/2007.14460). Page 45; Theorem 1.\n"
+    " - [Quantum computing enhanced computational catalysis](https://arxiv.org/abs/2007.14460).     Page 45; Theorem 1.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1b553eeb",
+   "id": "721cad00",
    "metadata": {
     "cq.autogen": "ChebyshevPolynomial.bloq_doc.py"
    },
@@ -215,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8f02214",
+   "id": "5bc78942",
    "metadata": {
     "cq.autogen": "ChebyshevPolynomial.example_instances.md"
    },
@@ -226,25 +255,31 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "df1de952",
+   "id": "8af92b76",
    "metadata": {
     "cq.autogen": "ChebyshevPolynomial.chebyshev_poly"
    },
    "outputs": [],
    "source": [
-    "from qualtran.bloqs.block_encoding import BlackBoxBlockEncoding, BlackBoxPrepare, BlackBoxSelect\n",
+    "from qualtran.bloqs.block_encoding import LCUBlockEncoding\n",
     "from qualtran.bloqs.hubbard_model import PrepareHubbard, SelectHubbard\n",
     "\n",
     "dim = 3\n",
-    "select = BlackBoxSelect(SelectHubbard(x_dim=dim, y_dim=dim))\n",
-    "prepare = BlackBoxPrepare(PrepareHubbard(x_dim=dim, y_dim=dim, t=1, mu=4))\n",
-    "black_box_block_bloq = BlackBoxBlockEncoding(select=select, prepare=prepare)\n",
+    "select = SelectHubbard(x_dim=dim, y_dim=dim)\n",
+    "U = 4\n",
+    "t = 1\n",
+    "prepare = PrepareHubbard(x_dim=dim, y_dim=dim, t=t, mu=U)\n",
+    "N = dim * dim * 2\n",
+    "qlambda = 2 * N * t + (N * U) // 2\n",
+    "black_box_block_bloq = LCUBlockEncoding(\n",
+    "    select=select, prepare=prepare, alpha=qlambda, epsilon=0.0\n",
+    ")\n",
     "chebyshev_poly = ChebyshevPolynomial(black_box_block_bloq, order=3)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "135e9723",
+   "id": "c8dc645a",
    "metadata": {
     "cq.autogen": "ChebyshevPolynomial.graphical_signature.md"
    },
@@ -255,7 +290,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "34b86d0b",
+   "id": "50b2e9c7",
    "metadata": {
     "cq.autogen": "ChebyshevPolynomial.graphical_signature.py"
    },
@@ -268,7 +303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7ffbd99",
+   "id": "8abadaed",
    "metadata": {
     "cq.autogen": "ChebyshevPolynomial.call_graph.md"
    },
@@ -279,7 +314,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "62c9b270",
+   "id": "8209eb98",
    "metadata": {
     "cq.autogen": "ChebyshevPolynomial.call_graph.py"
    },
@@ -299,16 +334,8 @@
    "name": "python3"
   },
   "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
    "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.11.5"
+   "version": "3.11.8"
   }
  },
  "nbformat": 4,