feat(block-encoding): added paper implementation as per Issue 1267

Author: virajd98

applications/Block_encoding-ND_Laplacian/1D_Lap_BE.png

@@ -0,0 +1,25 @@
+qfunc subtractor_mod(a: qnum) {
+  a += -1;
+}
+
+qfunc adder_mod(a: qnum) {
+  a += 1;
+}
+
+qfunc main(output j: qnum, output l: qnum) {
+  allocate(5, j);
+  allocate(2, l);
+  apply_to_all(H, l);
+  apply_to_all(Z, l);
+  l_arr: qbit[];
+  l -> l_arr;
+  control (l_arr[0] == 0) {
+    subtractor_mod(j);
+  }
+  control (l_arr[1] == 1) {
+    adder_mod(j);
+  }
+  l_arr -> l;
+  apply_to_all(H, l);
+  apply_to_all(Z, l);
+}

applications/Block_encoding-ND_Laplacian/1D_Periodic_Laplacian_BE.qmod

@@ -0,0 +1,45 @@
+{
+  "constraints": {
+    "max_gate_count": {},
+    "max_width": 18,
+    "optimization_parameter": "depth"
+  },
+  "preferences": {
+    "custom_hardware_settings": {
+      "basis_gates": [
+        "tdg",
+        "z",
+        "sx",
+        "u1",
+        "cx",
+        "h",
+        "p",
+        "x",
+        "ry",
+        "s",
+        "cy",
+        "t",
+        "r",
+        "cz",
+        "u",
+        "rx",
+        "y",
+        "id",
+        "sdg",
+        "u2",
+        "rz",
+        "sxdg"
+      ],
+      "is_symmetric_connectivity": true
+    },
+    "debug_mode": true,
+    "machine_precision": 8,
+    "optimization_level": 1,
+    "output_format": ["qasm"],
+    "pretty_qasm": true,
+    "random_seed": 185454979,
+    "synthesize_all_separately": false,
+    "timeout_seconds": 300,
+    "transpilation_option": "auto optimize"
+  }
+}