From 1440172d815c7355ebc75663ae497802003b28ab Mon Sep 17 00:00:00 2001
From: davidedellagiustina <davide@dellagiustina.com>
Date: Thu, 8 Feb 2024 18:17:50 +0000
Subject: [PATCH] Added Example 5.1.1 plus minor fixes

---
 src/examples/quantum_counting.py           |  4 +-
 src/examples/quantum_counting_advanced.py  |  4 +-
 src/examples/quantum_faceted_navigation.py | 92 ++++++++++++++++++++++
 3 files changed, 96 insertions(+), 4 deletions(-)
 create mode 100644 src/examples/quantum_faceted_navigation.py

diff --git a/src/examples/quantum_counting.py b/src/examples/quantum_counting.py
index 6b49798..2dbc99a 100644
--- a/src/examples/quantum_counting.py
+++ b/src/examples/quantum_counting.py
@@ -18,8 +18,8 @@
 
 # Hardcoded list of stable models
 STABLE_MODELS = [
-    [('p', True), ('q', False), ('r', True)],  # {p, r}
-    [('p', False), ('q', True), ('r', True)],  # {q, r}
+    {('p', True), ('q', False), ('r', True)},  # {p, r}
+    {('p', False), ('q', True), ('r', True)},  # {q, r}
 ]
 
 
diff --git a/src/examples/quantum_counting_advanced.py b/src/examples/quantum_counting_advanced.py
index 72351bd..193b793 100644
--- a/src/examples/quantum_counting_advanced.py
+++ b/src/examples/quantum_counting_advanced.py
@@ -17,8 +17,8 @@
 
 # Hardcoded list of stable models
 STABLE_MODELS = [
-    [('p', True), ('q', False), ('r', True)],  # {p, r}
-    [('p', False), ('q', True), ('r', True)],  # {q, r}
+    {('p', True), ('q', False), ('r', True)},  # {p, r}
+    {('p', False), ('q', True), ('r', True)},  # {q, r}
 ]
 
 
diff --git a/src/examples/quantum_faceted_navigation.py b/src/examples/quantum_faceted_navigation.py
new file mode 100644
index 0000000..ca4c92e
--- /dev/null
+++ b/src/examples/quantum_faceted_navigation.py
@@ -0,0 +1,92 @@
+'''Count the number of stable models of an ASP program after some navigation steps, using the QWMC \
+circuit.
+
+This example implements Example 5.1.1 in the thesis document, where we use the Quanutm WMC circuit \
+to estimate the number of solutions to a program after navigating its solution space using a route \
+delta.
+'''
+
+import math
+from src import qasp
+from src.examples.util import tab, pause
+
+# ASP program
+PRGM = '''
+    p :- not q.
+    q :- not p.
+    r :- p.
+    r :- q.
+'''
+
+# Hardcoded list of stable models
+STABLE_MODELS = [
+    {('p', True), ('q', False), ('r', True)},  # {p, r}
+    {('p', False), ('q', True), ('r', True)},  # {q, r}
+]
+
+# Hardcoded navigation route and relative weight function
+DELTA = [('p', True)]
+WEIGHTS = [1, 1/2, 1/2]  # Order: p < q < r
+
+
+def count_fn(phase: float) -> float:
+    '''Estimate the number of solutions to PRGM from the value of the estimated phase.
+
+    #### Arguments
+        phase (float): Estimated phase.
+
+    #### Return
+        float: Estimated number of solutions.
+    '''
+    n = len(STABLE_MODELS[0])
+    k = len(DELTA)
+    coeff = 2**(n-k)
+    return coeff * 2 * math.sin(phase/2)**2
+
+
+def main():
+    '''Entrypoint.
+    '''
+    print(f'ASP program:\n{tab(PRGM.strip(), striplines=True)}\n')
+    pause()
+
+    # Program parameters
+    n = len(STABLE_MODELS[0])
+    print(f'Number of variables: {n}.')
+    print()
+    pause()
+
+    # Route
+    route = ', '.join(
+        [('' if value else 'not ') + f'{atom}' for (atom, value) in DELTA]
+    )
+    print(f'Route delta: <{route}>')
+    print()
+    pause()
+
+    # Initialization algorithm
+    algorithm = qasp.init_algorithm.alg_from_weights(WEIGHTS)  # Rot gate
+    print(f'Initialization algorithm:\n{tab(str(algorithm.draw()))}\n')
+    pause()
+
+    # Oracle
+    oracle = qasp.oracle.from_asp_stable_models(
+        STABLE_MODELS, var_order=['p', 'q', 'r'])
+    print(f'Quantum oracle:\n{tab(str(oracle[1].draw()))}\n')
+    pause()
+
+    # Simulation
+    m = 5  # NOTE: This is the only change from `quantum_counting' example
+    eps = 1/6
+    # pylint: disable=invalid-name
+    (circuit, _, M) = qasp.problems.estimation.exec_count(
+        algorithm, oracle, m, eps, count_fn=count_fn)
+    print(f'Used circuit:\n{tab(str(circuit.draw()))}\n')
+    pause()
+    print(
+        f'Estimated number of solutions: {M.lower:.2f} <= M <= {M.upper:.2f}.')
+    print()
+
+
+if __name__ == '__main__':
+    main()