def test_solve_inhomogeneous_equation(self):
b = Mat2([[1], [1], [0], [0], [0]])
x = self.m3.solve(b)
self.assertEqual(self.m3 * x, b)
b = Mat2([[1], [0], [1], [1], [0]])
x = self.m4.solve(b)
self.assertEqual(self.m4 * x, b)
def setUp(self):
self.m1 = Mat2([[1, 0], [1, 1]])
self.m2 = Mat2([[1, 1], [1, 1]])
self.m3 = Mat2([[1, 0, 1, 1, 0], [1, 1, 1, 0, 0], [1, 1, 0, 0, 1],
[0, 1, 0, 1, 0], [0, 0, 1, 1, 0]])
self.m4 = Mat2([[1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [1, 1, 0, 0, 1],
[0, 1, 0, 1, 0], [0, 0, 0, 1, 1]])
def update_matrix(self):
self.matrix = Mat2.id(self.n_qubits)
for gate in self.gates:
if hasattr(gate, "name") and gate.name == "CNOT":
self.matrix.row_add(gate.control, gate.target)
else:
print("Warning: CNOT tracker can only be used for circuits with only CNOT gates!")
def fromCircuit(circuit, initial_qubit_placement=None, final_qubit_placement=None):
if isinstance(circuit, TketCircuit):
circuit = tk_to_pyzx(circuit)
zphases = {}
current_parities = mat22partition(Mat2.id(circuit.qubits))
if initial_qubit_placement is not None:
current_parities = ["".join([row[i] for i in initial_qubit_placement]) for row in current_parities]
for gate in circuit.gates:
parity = current_parities[gate.target]
if gate.name in ["CNOT", "CX"]:
# Update current_parities
control = current_parities[gate.control]
current_parities[gate.target] = "".join([str((int(i)+int(j))%2) for i,j in zip(control, parity)])
elif isinstance(gate, ZPhase):
# Add the T rotation to the phases
if parity in zphases:
zphases[parity] += gate.phase
else:
zphases[parity] = gate.phase
else:
print("Gate not supported!", gate.name)
def clamp(phase):
new_phase = phase%2
if new_phase > 1:
return new_phase -2
return new_phase
zphases = {par:clamp(r) for par, r in zphases.items() if clamp(r) != 0}
if final_qubit_placement is not None:
current_parities = [ current_parities[i] for i in final_qubit_placement]
return PhasePoly(zphases, current_parities)
def Ariannes_synth(self, architecture, full=True, depth_aware=False, **kwargs):
kwargs["full_reduce"] = True
#print("------------ START! -----------------------")
if architecture is None:
architecture = create_architecture(FULLY_CONNECTED, n_qubits=len(self.out_par[0]))
n_qubits = architecture.n_qubits
# Obtain the parities
parities_to_reach = self.all_parities
# Make a matrix from the parities
matrix = Mat2([[int(parity[i]) for parity in parities_to_reach] for i in range(architecture.n_qubits)] )
circuit = CNOT_tracker(architecture.n_qubits)
cols_to_reach = self._check_columns(matrix, circuit, [i for i in range(len(parities_to_reach))], parities_to_reach)
self.prev_rows = None
def place_cnot(control, target):
# Place the CNOT on the circuit
circuit.add_gate(CNOT(control, target))
# Adjust the matrix accordingly - reversed elementary row operations
matrix.row_add(target, control)
def base_recurse(cols_to_use, qubits_to_use):
if qubits_to_use != [] and cols_to_use != []:
# Select edge qubits
qubits = architecture.non_cutting_vertices(qubits_to_use)
# Pick the qubit where the recursion split will be most skewed.
chosen_row = max(qubits, key=lambda q: max([len([col for col in cols_to_use if matrix.data[q][col] == i]) for i in [1, 0]], default=-1))
# Split the column into 1s and 0s in that row
cols1 = [col for col in cols_to_use if matrix.data[chosen_row][col] == 1]
cols0 = [col for col in cols_to_use if matrix.data[chosen_row][col] == 0]
base_recurse(cols0, [q for q in qubits_to_use if q != chosen_row])
one_recurse(cols1, qubits_to_use, chosen_row)
def one_recurse(cols_to_use, qubits_to_use, qubit):
if cols_to_use != []:
neighbors = [q for q in architecture.get_neighboring_qubits(qubit) if q in qubits_to_use ]
if neighbors == []:
print(qubits_to_use, qubit)
print(matrix)
exit(42)
chosen_neighbor = max(neighbors, key=lambda q: len([col for col in cols_to_use if matrix.data[q][col] == 1]))
# Place CNOTs if you still need to extract columns
if sum([matrix.data[chosen_neighbor][c] for c in cols_to_use]) != 0: # Check if adding the cnot is useful
place_cnot(qubit, chosen_neighbor)
# Might have changed the matrix.
cols_to_use = self._check_columns(matrix, circuit, cols_to_use, parities_to_reach)
else: # Will never change the matrix
place_cnot(chosen_neighbor, qubit)
place_cnot(qubit, chosen_neighbor)
# Since the neighbor was all zeros, this is effectively a swap and no columns need to be checked.
# Split the column into 1s and 0s in that row
cols0 = [col for col in cols_to_use if matrix.data[qubit][col] == 0]
cols1 = [col for col in cols_to_use if matrix.data[qubit][col] == 1]
base_recurse(cols0, [q for q in qubits_to_use if q != qubit])
one_recurse(cols1, qubits_to_use, qubit)
base_recurse(cols_to_reach, [i for i in range(n_qubits)])
if full:
# Calculate the final parity that needs to be added from the circuit and self.out_par
self._obtain_final_parities(circuit, architecture, **kwargs)
# Return the circuit
circuit.n_gadgets = len(self.zphases.keys())
return circuit, [i for i in range(architecture.n_qubits)], [i for i in range(architecture.n_qubits)]
def gray_synth(self, architecture, full=True, **kwargs):
if architecture is None:
architecture = create_architecture(FULLY_CONNECTED, n_qubits=len(self.out_par[0]))
n_qubits = architecture.n_qubits
# Obtain the parities
parities_to_reach = self.all_parities
# Make a matrix from the parities
matrix = Mat2([[int(parity[i]) for parity in parities_to_reach] for i in range(n_qubits)] )
circuit = CNOT_tracker(n_qubits)
# Make a stack - aka use the python stack >^.^<
def recurse(cols_to_use, qubits_to_use, phase_qubit): # Arguments from the original paper
# Check for finished columns
cols_to_use = self._check_columns(matrix, circuit, cols_to_use, parities_to_reach)
if cols_to_use != [] and qubits_to_use != []:
# Find all qubits (rows) with only 1s on the allowed parities (cols_to_use)
qubits = [i for i in qubits_to_use if sum([matrix.data[i][j] for j in cols_to_use]) == len(cols_to_use)]
if len(qubits) > 1 and phase_qubit is not None:
# Pick the column with the most 1s to extrac the steiner tree with
column = max(cols_to_use, key=lambda c: sum([row[c] for row in matrix.data]))
col = [1 if i in qubits else 0 for i in range(n_qubits)]
cnots = list(steiner_reduce_column(architecture, col, phase_qubit, set(qubits + [phase_qubit]), [i for i in range(n_qubits)], [], upper=True))
# For each returned CNOT:
for target, control in cnots:
# Place the CNOT on the circuit
circuit.add_gate(CNOT(control, target))
# Adjust the matrix accordingly - reversed elementary row operations
matrix.row_add(target, control)
# Keep track of the parities in the circuit - normal elementary row operations
cols_to_use = self._check_columns(matrix, circuit, cols_to_use, parities_to_reach)
# After placing the cnots do recursion
if len(cols_to_use) > 0:
# Choose a row to split on
if len(cols_to_use) == 1:
# Hack because it runs into infinite recursion otherwise, because we do not remove the chosen_row from qubits_to_use
# We do not remove the qubit, because it will skip columns
# It skips columns because it runs out of qubits before all columns are finished for some reason - could not find the bug
qubits = [i for i in qubits_to_use if sum([matrix.data[i][j] for j in cols_to_use]) == 1]
else:
# Ignore rows that are currently all 0s or all 1s
qubits = [i for i in qubits_to_use if sum([matrix.data[i][j] for j in cols_to_use]) not in [0, len(cols_to_use)]]
# Pick the qubit where the recursion split will be most skewed.
chosen_row = max(qubits, key=lambda q: max([len([col for col in cols_to_use if matrix.data[q][col] == i]) for i in [1,0]], default=-1))
# Split the column into 1s and 0s in that row
cols1 = [col for col in cols_to_use if matrix.data[chosen_row][col] == 1]
cols0 = [col for col in cols_to_use if matrix.data[chosen_row][col] == 0]
#qubits_to_use = [i for i in qubits_to_use if i != chosen_row]
recurse(cols0, qubits_to_use, phase_qubit)
recurse(cols1, qubits_to_use, phase_qubit if phase_qubit is not None else chosen_row)
# Put the base case into the python stack
recurse([i for i in range(len(parities_to_reach))], [i for i in range(n_qubits)], None)
if full:
# Calculate the final parity that needs to be added from the circuit and self.out_par
self._obtain_final_parities(circuit, architecture, **kwargs)
# Return the circuit
circuit.n_gadgets = len(self.zphases.keys())
return circuit, [i for i in range(architecture.n_qubits)], [i for i in range(architecture.n_qubits)]
def _obtain_final_parities(self, circuit, architecture, **kwargs):
# Calculate the final parity that needs to be added from the circuit and self.out_par
current_parities = circuit.matrix
output_parities = Mat2([[int(v) for v in row] for row in self.out_par])
last_parities = output_parities*current_parities.inverse()
# Do steiner-gauss to calculate necessary CNOTs and add those to the circuit.
cnots = CNOT_tracker(architecture.n_qubits)
gauss(last_parities, architecture, y=cnots, **kwargs)
for cnot in cnots.gates:
circuit.add_gate(cnot)
def to_tket(self):
if self.out_par != mat22partition(Mat2.id(self.n_qubits)):
print(self.out_par)
raise NotImplementedError("The linear transformation part of the phase polynomial cannot yet be transformed into a tket circuit")
circuit = TketCircuit(self.n_qubits)
for parity, phase in self.zphases.items():
qubits = [i for i,s in enumerate(parity) if s == '1']
circuit.add_pauliexpbox(PauliExpBox([Pauli.Z]*len(qubits), phase), qubits)
# TODO add the linear combination part with CNOTs
Transform.DecomposeBoxes().apply(circuit)
return circuit
def build_random_parity_map(qubits, n_cnots, circuit=None):
"""
Builds a random parity map.
:param qubits: The number of qubits that participate in the parity map
:param n_cnots: The number of CNOTs in the parity map
:param circuit: A (list of) circuit object(s) that implements a row_add() method to add the generated CNOT gates [optional]
:return: a 2D numpy array that represents the parity map.
"""
if circuit is None:
circuit = []
if not isinstance(circuit, list):
circuit = [circuit]
g = generate_cnots(qubits=qubits, depth=n_cnots)
c = Circuit.from_graph(g)
matrix = Mat2.id(qubits)
for gate in c.gates:
matrix.row_add(gate.control, gate.target)
for c in circuit:
c.row_add(gate.control, gate.target)
return matrix.data
def make_random_phase_poly(n_qubits, n_gadgets, return_circuit=False):
parities = set()
if n_gadgets > 2**n_qubits:
n_gadgets=n_qubits^3
if n_qubits < 26:
for integer in np.random.choice(2**n_qubits-1, replace=False, size=n_gadgets):
parities.add(integer+1)
elif n_qubits < 64:
while len(parities) < n_gadgets:
parities.add(np.random.randint(1, 2**n_qubits))
else:
while len(parities) < n_gadgets:
parities.add("".join(np.random.choice(["0", "1"], n_qubits, replace=True)))
if n_qubits < 64:
parities = [("{0:{fill}"+str(n_qubits)+"b}").format(integer, fill='0', align='right') for integer in parities]
zphase_dict = {"".join([str(int(i)) for i in p]):Fraction(1,4) for p in parities}
out_parities = mat22partition(Mat2.id(n_qubits))
phase_poly = PhasePoly(zphase_dict, out_parities)
if return_circuit:
return route_phase_poly(phase_poly, create_architecture(FULLY_CONNECTED, n_qubits=n_qubits), do_matroid="arianne")
return phase_poly
def __init__(self, n_qubits, **kwargs):
super().__init__(n_qubits, **kwargs)
self.matrix = Mat2.id(n_qubits)
self.row_perm = np.arange(n_qubits)
self.col_perm = np.arange(n_qubits)
self.n_qubits = n_qubits
def partition2mat2(partition):
return Mat2([[int(i) for i in parity] for parity in partition])
def test_inverse(self):
inv = self.m4.inverse()
self.assertEqual(inv * self.m4, Mat2.id(5))
self.assertEqual(self.m4 * inv, Mat2.id(5))
def test_matrix_multiplication(self):
result = Mat2([[1, 1], [0, 0]])
self.assertEqual(self.m1 * self.m2, result)
result = Mat2([[0, 1], [0, 1]])
self.assertEqual(self.m2 * self.m1, result)
def rec_steiner_gauss(matrix,
architecture,
full_reduce=False,
x=None,
y=None,
permutation=None,
**kwargs):
"""
Performs recursive Gaussian elimination that is constraint bij the given architecture
:param matrix: PyZX Mat2 matrix to be reduced
:param architecture: The Architecture object to conform to
:param full_reduce: Whether to fully reduce or only create an upper triangular form
:param x:
:param y:
"""
#print(matrix)
if permutation is None:
permutation = [i for i in range(len(matrix.data))]
else:
matrix = Mat2([[row[i] for i in permutation] for row in matrix.data])
#print(matrix)
def row_add(c0, c1):
matrix.row_add(c0, c1)
debug and print("Reducing", c0, c1)
c0 = architecture.qubit_map[c0]
c1 = architecture.qubit_map[c1]
if x != None: x.row_add(c0, c1)
if y != None: y.col_add(c1, c0)
def steiner_reduce(col, root, nodes, usable_nodes, rec_nodes, upper):
generator = steiner_reduce_column(architecture,
[row[col] for row in matrix.data],
root, nodes, usable_nodes, rec_nodes,
upper)
cnot = next(generator, None)
while cnot is not None:
row_add(*cnot)
cnot = next(generator, None)
def rec_step(cols, rows):
size = len(rows)
# Upper triangular form uses the same structure.
p_cols = []
pivot = 0
rows2 = [r for r in range(len(matrix.data[0])) if r in rows]
cols2 = [c for c in range(len(matrix.data)) if c in cols]
for i, c in enumerate(cols2):
if pivot < size:
nodes = [
r for r in rows2[pivot:]
if rows2[pivot] == r or matrix.data[r][c] == 1
]
steiner_reduce(c, rows2[pivot], nodes, cols2[i:], [], True)
if matrix.data[rows2[pivot]][c] == 1:
p_cols.append(c)
pivot += 1
# Full reduce requires the recursion
if full_reduce:
pivot -= 1
for i, c in enumerate(cols):
if c in p_cols:
nodes = [
r for r in rows
if r == rows[pivot] or matrix.data[r][c] == 1
]
usable_nodes = cols[i:]
#rec_nodes = list(set([node for edge in architecture.distances["upper"][c][(max(usable_nodes),c)][1] for node in edge]))
#rec_nodes = [n for n in usable_nodes if n in rec_nodes]
rec_nodes = architecture.shortest_path(
c, max(usable_nodes), usable_nodes)
if len(nodes) > 1:
#print("-", c, nodes, cols, rec_nodes)
steiner_reduce(c, rows[pivot], nodes, cols, rec_nodes,
False)
# Do recursion on the given nodes.
if len(rec_nodes) > 1:
rec_step(list(reversed(rec_nodes)), rec_nodes)
pivot -= 1
#return rank
qubit_order = architecture.reduce_order
rec_step(qubit_order, list(reversed(qubit_order)))
def __init__(self, n_qubits, **kwargs):
super().__init__(n_qubits, **kwargs)
self.matrix = Mat2(np.identity(n_qubits, dtype=np.int32).tolist())
self.row_perm = np.arange(n_qubits)
self.col_perm = np.arange(n_qubits)
self.n_qubits = n_qubits