Brownian

applications/finance/brownian_chebyshev_polynomials/brownian_chebyshev_polynomials.metadata.json

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+{
+  "friendly_name": "Stochastic Modeling of Brownian Motion",
+  "description": "Building a Geometric Brownian Motion (GBM) Price Model — from Analytic Formula to Quantum Circuit",
+  "vertical_tags": ["finance"],
+  "problem_domain_tags": ["risk analysis"],
+  "qmod_type": ["application"],
+  "level": ["demos"]
+}

applications/finance/brownian_chebyshev_polynomials/brownian_chebyshev_polynomials.qmod

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+qperm two_cos_pi_x(const x: qnum, output out: qnum) {
+  out = (-6.283185307179586) * (x - 0.5);
+}
+
+qperm uk(const two_x: qnum, const uk_1: qnum, const uk_2: qnum, output uk: qnum) {
+  uk = (two_x * uk_1) - uk_2;
+}
+
+qperm sin_pi_x(const x: qnum, output out: qnum) {
+  out = ((-5) * ((x - 0.5) ** 2)) + 1;
+}
+
+qfunc truncated_wiener_series(t: qnum, output out: qnum) {
+  a0: qnum;
+  a1: qnum;
+  a2: qnum;
+  a3: qnum;
+  prepare_state([0.5, 0.5], 0, a0);
+  prepare_state([0.5, 0.5], 0, a1);
+  prepare_state([0.5, 0.5], 0, a2);
+  prepare_state([0.5, 0.5], 0, a3);
+  two_cos_pi_t: qnum;
+  sin_pi_t: qnum;
+  U0: qnum;
+  U1: qnum;
+  U2: qnum;
+  U3: qnum;
+  two_cos_pi_x(t, two_cos_pi_t);
+  U0 = 1;
+  U1 = two_cos_pi_t;
+  uk(two_cos_pi_t, U1, U0, U2);
+  uk(two_cos_pi_t, U2, U1, U3);
+  sin_pi_x(t, sin_pi_t);
+  out = (a0 * t) + ((0.450158158078553 * sin_pi_t) * (((0 + (a1 * U1)) + (a2 * U2)) + (a3 * U3)));
+  drop(a0);
+  drop(a1);
+  drop(a2);
+  drop(a3);
+  drop(U0);
+  drop(U1);
+  drop(U2);
+  drop(U3);
+}
+
+qperm return_to_price_space(const returns: qnum, const t: qnum, output price: qnum) {
+  price = ((2 * returns) + ((-1.0) * t)) + 1;
+}
+
+qfunc main(output t: qnum, output G: qnum) {
+  B: qnum;
+  allocate(1, t);
+  hadamard_transform(t);
+  truncated_wiener_series(t, B);
+  return_to_price_space(B, t, G);
+  drop(B);
+}

applications/finance/brownian_chebyshev_polynomials/brownian_chebyshev_polynomials.synthesis_options.json

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+{
+  "constraints": {
+    "max_gate_count": {},
+    "max_width": 139,
+    "optimization_parameter": "width"
+  },
+  "preferences": {
+    "custom_hardware_settings": {
+      "basis_gates": [
+        "t",
+        "u2",
+        "tdg",
+        "u1",
+        "h",
+        "sdg",
+        "x",
+        "cx",
+        "u",
+        "y",
+        "rz",
+        "sxdg",
+        "z",
+        "sx",
+        "id",
+        "ry",
+        "s",
+        "cy",
+        "rx",
+        "p",
+        "r",
+        "cz"
+      ],
+      "is_symmetric_connectivity": true
+    },
+    "debug_mode": true,
+    "machine_precision": 8,
+    "optimization_level": 1,
+    "output_format": ["qasm"],
+    "pretty_qasm": true,
+    "random_seed": 4280272080,
+    "synthesize_all_separately": false,
+    "timeout_seconds": 300,
+    "transpilation_option": "none"
+  }
+}

tests/notebooks/test_brownian_chebyshev_polynomials.py

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+from tests.utils_for_testbook import (
+    validate_quantum_program_size,
+    validate_quantum_model,
+    wrap_testbook,
+)
+from testbook.client import TestbookNotebookClient
+
+
+@wrap_testbook("brownian_chebyshev_polynomials", timeout_seconds=1000)
+def test_notebook(tb: TestbookNotebookClient) -> None:
+    # test models
+    validate_quantum_model(tb.ref("qmod"))
+    # test quantum programs
+    validate_quantum_program_size(
+        tb.ref_pydantic("qprog"),
+        expected_width=135,
+        expected_depth=None,
+        expected_cx_count=None,
+    )