Added Simon's Algorithm Example

examples/simon.py

@@ -0,0 +1,339 @@
+'''
+---------------------------------
+SIMONS'S ALGORITHM - OVERVIEW
+---------------------------------
+Simon's Algorithm solves the problem of finding a particular value of s when some function f:{0, 1}^n --> {0, 1}^n
+is inputted into the program that follows this rule: "f(x) = f(y) if and only if x (+) y is in the set {0^n, s}"
+---------------------------------
+STEPS OF THE ALGORITHM
+---------------------------------
+1. Begin with two n-qubit registers, each in the |0> state
+2. Apply a Hadamard transform to the first n-qubit register, therefore creating an even superposition of states
+3. The oracle (which encodes values of the function) is queried B_f |x>|y> = |x>|y (+) f(x)>, therefore mapping |0^n> --> |f(x)>
+4. Apply a Hadamard transform to the first n-qubit register
+---------------------------------
+MEASUREMENT
+---------------------------------
+It can be found that for an output string y, then y (dot mod 2) s is always equal to 0, as we can calculate y (dot mod 2) s = 1 occuring with probability = 0
+We get a system of eqautions, which we can use to solve for s (provided y_1, ..., y_(n-1) are linearlly independent)! We measure the string y to be the first n-qubit register
+'''
+
+import cirq
+import random
+import numpy as np
+import copy
+import sympy
+import itertools
+
+# Qubit preparation
+
+number_qubits = #Number of qubits
+
+def main(number_qubits):
+
+    circuit_sampling = number_qubits-1
+
+    #Create the qubits which are used within the circuit
+
+    first_qubits = [cirq.GridQubit(i, 0) for i in range(number_qubits)]
+    second_qubits = [cirq.GridQubit(i, 0) for i in range(number_qubits, 2*number_qubits)]
+
+    the_activator = cirq.GridQubit(2*number_qubits, 0)
+
+    #Create the qubits that can be used for large-input Toffoli gates
+    ancilla = []
+    for v in range(2*number_qubits+1, 3*number_qubits):
+        ancilla.append(cirq.GridQubit(v, 0))
+
+    #Create the function that is inputted into the algorithm (secret!)
+
+    domain = []
+    selector = []
+    co_domain = []
+    fixed = []
+
+    for k in range(0, 2**number_qubits):
+        domain.append(k)
+        selector.append(k)
+        co_domain.append(False)
+        fixed.append(k)
+
+    #Create the "secret string"
+    s = domain[random.randint(0, len(domain)-1)]
+
+    #Create the "secret function"
+    for g in range(0, int((2**number_qubits)/2)):
+        v = random.choice(selector)
+        x = random.choice(domain)
+        co_domain[x] = v
+        co_domain[x^s] = v
+        del selector[selector.index(v)]
+        del domain[domain.index(x)]
+        if (s != 0):
+            del domain[domain.index(x^s)]
+
+    secret_function = [fixed, co_domain]
+
+    oracle = make_oracle(ancilla, secret_function, first_qubits, second_qubits, s, the_activator)
+
+    c = make_simon_circuit(first_qubits, second_qubits, oracle)
+
+    #Sampling the circuit
+
+    simulator = cirq.Simulator()
+    result = simulator.run(c, repetitions=number_qubits-1)
+    final = result.histogram(key='y')
+    print("Secret String: "+str(s))
+    print("Secret Function (Domain and Co-Domain): "+str(secret_function))
+    final = str(result)[str(result).index("y")+2:len(str(result))].split(", ")
+    last = []
+    for i in range(0, number_qubits-1):
+        holder = []
+        for j in final:
+            holder.append(int(j[i]))
+        holder.append(0)
+        last.append(holder)
+
+    print("Results: "+str(last))
+    return [last, secret_function, s, last]
+
+
+
+
+def make_oracle(ancilla, secret_function, first_qubits, second_qubits, s, the_activator):
+
+    #Hard-code oracle on a case-by-case basis
+
+
+    for o in range(0, len(secret_function[0])):
+        counter = 0
+        for j in list(str(format(secret_function[0][o], "0"+str(number_qubits)+"b"))):
+            if (int(j) == 0):
+                yield cirq.X.on(first_qubits[counter])
+            counter = counter+1
+        yield apply_n_qubit_tof(ancilla, first_qubits+[the_activator])
+        counter = 0
+        for j in list(str(format(secret_function[0][o], "0"+str(number_qubits)+"b"))):
+            if (int(j) == 0):
+                yield cirq.X.on(first_qubits[counter])
+            counter = counter+1
+
+        counter = 0
+        for j in list(str(format(secret_function[1][o], "0"+str(number_qubits)+"b"))):
+            if (int(j) == 1):
+                yield cirq.CNOT.on(the_activator, second_qubits[counter])
+            counter = counter+1
+
+        counter = 0
+        for j in list(str(format(secret_function[0][o], "0"+str(number_qubits)+"b"))):
+            if (int(j) == 0):
+                yield cirq.X.on(first_qubits[counter])
+            counter = counter+1
+        yield apply_n_qubit_tof(ancilla, first_qubits+[the_activator])
+        counter = 0
+        for j in list(str(format(secret_function[0][o], "0"+str(number_qubits)+"b"))):
+            if (int(j) == 0):
+                yield cirq.X.on(first_qubits[counter])
+            counter = counter+1
+
+def apply_n_qubit_tof(ancilla, args):
+
+    if (len(args) == 3):
+        yield cirq.CCX.on(args[0], args[1], args[2])
+
+    else:
+
+        yield cirq.CCX.on(args[0], args[1], ancilla[0])
+        for k in range(2, len(args)-1):
+            yield cirq.CCX(args[k], ancilla[k-2], ancilla[k-1])
+
+        yield cirq.CNOT.on(ancilla[len(args)-3], args[len(args)-1])
+
+        for k in range(len(args)-2, 1, -1):
+            yield cirq.CCX(args[k], ancilla[k-2], ancilla[k-1])
+        yield cirq.CCX.on(args[0], args[1], ancilla[0])
+
+
+def make_simon_circuit(first_qubits, second_qubits, oracle):
+
+    circuit = cirq.Circuit()
+
+    #Apply the first set of Hadamard gates
+
+    for i in range(0, number_qubits):
+        circuit.append(cirq.H.on(first_qubits[i]))
+
+    #Apply the oracle
+
+    circuit.append(oracle)
+
+    #Apply the second set of Hadamard gates
+
+    for i in range(0, number_qubits):
+        circuit.append(cirq.H.on(first_qubits[i]))
+
+    #Perform measurements upon the qubits
+
+    circuit.append(cirq.measure(*second_qubits, key='x'))
+    circuit.append(cirq.measure(*first_qubits, key='y'))
+
+    return circuit
+
+run = main(number_qubits)
+matrix_input = run[0]
+secret_function = run[1]
+string_secret = run[2]
+r = run[3]
+
+def shuffle_op(matrix, point):
+
+
+    for i in range(0, len(matrix)):
+        if (matrix[i] == [0 for l in range(0, len(matrix[0]))]):
+            raise ValueError("System of equations not linearly independent, try again")
+        for j in range(0, len(matrix)):
+            if (matrix[i] == matrix[j] and i != j):
+                raise ValueError("System of equations not linearly independent, try again")
+
+
+    for i in range(1, len(matrix)+1):
+      for c in list(itertools.combinations([y[0:len(matrix)+1] for y in matrix], i)):
+        hol = []
+        for b in c:
+          hol.append(b)
+        calc = [sum(x)%2 for x in zip(*hol)]
+        ha = True
+        for ij in range (0, len(hol)):
+            for ik in range (0, len(hol)):
+                if (hol[ik] == hol[ij] and ik != ij):
+                    ha = False
+        if (ha == True and calc == [0 for p in range(0, len(calc))]):
+          raise ValueError("System of equations not linearly independent, try again")
+
+    flip = False
+    passage = False
+
+    for i in range(0, len(matrix)):
+        for j in range(i+1, len(matrix)):
+            if (matrix[i][i] != 0):
+                x = -1*matrix[j][i]/matrix[i][i]
+                iterator = map(lambda y: y*int(x), matrix[i])
+                new = [sum(z)%2 for z in zip(matrix[j], iterator)]
+                matrix[j] = new
+
+
+    for a in range(0, len(matrix)+1):
+
+        fml = []
+        flip = a
+
+        work = copy.deepcopy(matrix)
+
+        h = [0 for i in range(0, len(matrix[0])-2)]+[point]
+        h.insert(flip, 1)
+        work.append(h)
+
+        for j in range(0, len(work[0])-1):
+            temporary = []
+            for g in range(0, len(work)):
+                if (work[g][j] == 1):
+                    temporary.append(work[g])
+            fml.append(temporary)
+
+        cv = False
+
+        if ([] not in fml):
+            for element in itertools.product(*fml):
+
+                if (sorted(work) == sorted(element)):
+
+                    cv = True
+
+                    last_work = copy.deepcopy(list(element))
+
+                    #Check for linear independence
+
+                    for i in range(0, len(last_work)):
+                        if (last_work[i] == [0 for l in range(0, len(last_work[0]))]):
+                            cv = False
+                        for j in range(0, len(last_work)):
+                            if (last_work[i] == last_work[j] and i != j):
+                                cv = False
+
+
+                    for i in range(1, len(last_work)+1):
+                      for c in list(itertools.combinations([y[0:len(last_work)] for y in last_work], i)):
+                        hol = []
+                        for b in c:
+                          hol.append(b)
+                        calc = [sum(x)%2 for x in zip(*hol)]
+                        ha = True
+                        for ij in range (0, len(hol)):
+                            for ik in range (0, len(hol)):
+                                if (hol[ik] == hol[ij] and ik != ij):
+                                    ha = False
+                        if (ha == True and calc == [0 for p in range(0, len(calc))]):
+                          cv = False
+
+                    #Check if the matrix can be reduced
+
+                    for i in range(0, len(last_work)):
+                        for j in range(i+1, len(last_work)):
+                            if (last_work[i][i] == 0):
+                                cv = False
+                            else:
+                                x = -1*last_work[j][i]/last_work[i][i]
+                                iterator = map(lambda y: y*int(x), last_work[i])
+                                new = [sum(z)%2 for z in zip(last_work[j], iterator)]
+                                last_work[j] = new
+
+                    if (cv == True):
+                        break;
+
+
+        if (cv == True):
+            break;
+
+    matrix = last_work
+
+    return last_work
+
+def construct_solve(matrix_out):
+
+    final_matrix = matrix_out
+
+    solution = []
+
+    for i in range(len(final_matrix)-1, 0, -1):
+      solution.append(final_matrix[i][len(final_matrix[i])-1])
+      for j in range(0, i):
+        if (final_matrix[j][i] == 1):
+          final_matrix[j][len(final_matrix[i])-1] = (final_matrix[j][len(final_matrix[i])-1]-final_matrix[i][len(final_matrix[i])-1])%2
+    solution.append(final_matrix[0][len(final_matrix[i])-1])
+
+    solution.reverse()
+
+    return solution
+
+
+other_matrix_input = copy.deepcopy(matrix_input)
+
+first_shot = shuffle_op(matrix_input, 0)
+try_1 = construct_solve(first_shot)
+second_shot = shuffle_op(other_matrix_input, 1)
+try_2 = construct_solve(second_shot)
+
+processing1 = ''.join(str(x) for x in try_1)
+processing2 = ''.join(str(x) for x in try_2)
+
+the_last = 0
+if (secret_function[1][secret_function[0].index(0)] == secret_function[1][secret_function[0].index(int(processing1, 2))] and secret_function[1][secret_function[0].index(0)] == secret_function[1][secret_function[0].index(int(processing2, 2))]):
+    final = int(processing1, 2)
+    if (int(processing1, 2) == 0):
+        final = int(processing2, 2)
+    print("The secret string is: "+str(final))
+    the_last = final
+
+else:
+    print("The secret string is 0")
+    the_last = 0