def _represent_ZGate(self, basis, **options):
"""
Represents the (I)QFT In the Z Basis
"""
nqubits = options.get('nqubits',0)
if nqubits == 0:
raise QuantumError('The number of qubits must be given as nqubits.')
if nqubits < self.min_qubits:
raise QuantumError(
'The number of qubits %r is too small for the gate.' % nqubits
)
size = self.size
omega = self.omega
#Make a matrix that has the basic Fourier Transform Matrix
arrayFT = [[omega**(i*j%size)/sqrt(size) for i in range(size)] for j in range(size)]
matrixFT = Matrix(arrayFT)
#Embed the FT Matrix in a higher space, if necessary
if self.label[0] != 0:
matrixFT = matrix_tensor_product(eye(2**self.label[0]), matrixFT)
if self.min_qubits < nqubits:
matrixFT = matrix_tensor_product(matrixFT, eye(2**(nqubits-self.min_qubits)))
return matrixFT
def _eval_args(self, args):
if len(args) != 2:
raise QuantumError('QFT/IQFT only takes two arguments, got: %r' %
args)
if args[0] >= args[1]:
raise QuantumError("Start must be smaller than finish")
return Gate._eval_args(args)
def random_oracle(nqubits, min_img=1, max_img=1, q_type='bin'):
"""Create a random OracleGate under the given parameter
Parameters
==========
nqubits : int
The number of qubits for OracleGate
min_pic : int
Minimum number of inverse images that are mapped to 1
max_pic : int
Maximum number of inverse images that are mapped to 1
q_type : OracleGate
Type of the Qubits that the oracle should be applied on.
Can be 'bin' for binary (Qubit()) or 'int' for integer (IntQubit()).
Returns
=======
OracleGate : random OracleGate under the given parameter
Examples
========
Generate random OracleGate that outputs 1 for 2-4 inputs::
>>> from sympy.physics.quantum.grover import random_oracle
>>> oracle = random_oracle(4, min_img=2, max_img=4, q_type="bin")
"""
if q_type != 'bin' and q_type != 'int':
raise QuantumError("q_type must be 'int' or 'bin'")
if min_img < 1 or max_img < 1:
raise QuantumError("min_pic, max_pic must be > 0")
if min_img > max_img:
raise QuantumError("max_pic must be >= min_pic")
if min_img >= 2 ** nqubits or max_img > 2 ** nqubits:
raise QuantumError("min_pic must be < 2**nqubits and max_pic must be <= 2**nqubits")
import random
pics = random.randint(min_img, max_img)
integers = random.sample(range(2 ** nqubits), pics)
if q_type == "int":
items = [IntQubit(i) for i in integers]
else:
items = [Qubit(IntQubit(i)) for i in integers]
return OracleGate(nqubits, lambda qubits: qubits in items)
def _apply_operator_Qubit(self, qubits, **options):
"""Apply this operator to a Qubit subclass.
Parameters
==========
qubits : Qubit
The qubit subclass to apply this operator to.
Returns
=======
state : Expr
The resulting quantum state.
"""
if qubits.nqubits != self.nqubits:
raise QuantumError(
'OracleGate operates on %r qubits, got: %r'
% (self.nqubits, qubits.nqubits)
)
# If function returns 1 on qubits
# return the negative of the qubits (flip the sign)
if self.search_function(qubits):
return -qubits
else:
return qubits
def _eval_args(cls, args):
if len(args) != 1:
raise QuantumError(
'Insufficient/excessive arguments to W gate. Please ' +
'supply the number of qubits to operate on.')
args = UnitaryOperator._eval_args(args)
if not args[0].is_Integer:
raise TypeError('Integer expected, got: %r' % args[0])
return args
def _validate_targets_controls(tandc):
tandc = list(tandc)
# Check for integers
for bit in tandc:
if not bit.is_Integer and not bit.is_Symbol:
raise TypeError("Integer expected, got: %r" % tandc[bit])
# Detect duplicates
if len(list(set(tandc))) != len(tandc):
raise QuantumError("Target/control qubits in a gate cannot be duplicated")
def _represent_ZGate(self, basis, **options):
format = options.get("format", "sympy")
nqubits = options.get("nqubits", 0)
if nqubits == 0:
raise QuantumError("The number of qubits must be given as nqubits.")
# Make sure we have enough qubits for the gate.
if nqubits < self.min_qubits:
raise QuantumError(
"The number of qubits %r is too small for the gate." % nqubits
)
target_matrix = self.get_target_matrix(format)
targets = self.targets
if isinstance(self, CGate):
controls = self.controls
else:
controls = []
m = represent_zbasis(controls, targets, target_matrix, nqubits, format)
return m
def _eval_args(cls, args):
if len(args) != 2:
raise QuantumError(
'Insufficient/excessive arguments to Oracle. Please ' +
'supply the number of qubits and an unknown function.')
sub_args = args[0],
sub_args = UnitaryOperator._eval_args(sub_args)
if not sub_args[0].is_Integer:
raise TypeError('Integer expected, got: %r' % sub_args[0])
if not callable(args[1]):
raise TypeError('Callable expected, got: %r' % args[1])
sub_args = UnitaryOperator._eval_args(tuple(range(args[0])))
return (sub_args, args[1])
def _eval_args(cls, args):
if len(args) != 2:
raise QuantumError(
'Insufficient/excessive arguments to Oracle. Please ' +
'supply the number of qubits and an unknown function.')
sub_args = (args[0], )
sub_args = UnitaryOperator._eval_args(sub_args)
if not sub_args[0].is_Integer:
raise TypeError('Integer expected, got: %r' % sub_args[0])
function = args[1]
if not isinstance(function, OracleGateFunction):
function = OracleGateFunction(function)
return (sub_args[0], function)
def _eval_args(cls, args):
# TODO: args[1] is not a subclass of Basic
if len(args) != 2:
raise QuantumError(
"Insufficient/excessive arguments to Oracle. Please "
+ "supply the number of qubits and an unknown function."
)
sub_args = (args[0],)
sub_args = UnitaryOperator._eval_args(sub_args)
if not sub_args[0].is_Integer:
raise TypeError("Integer expected, got: %r" % sub_args[0])
if not callable(args[1]):
raise TypeError("Callable expected, got: %r" % args[1])
return (sub_args[0], args[1])
def _apply_operator_Qubit(self, qubits, **options):
"""
qubits: a set of qubits (Qubit)
Returns: quantum object (quantum expression - QExpr)
"""
if qubits.nqubits != self.nqubits:
raise QuantumError('WGate operates on %r qubits, got: %r' %
(self.nqubits, qubits.nqubits))
# See 'Quantum Computer Science' by David Mermin p.92 -> W|a> result
# Return (2/(sqrt(2^n)))|phi> - |a> where |a> is the current basis
# state and phi is the superposition of basis states (see function
# create_computational_basis above)
basis_states = superposition_basis(self.nqubits)
change_to_basis = (2 / sqrt(2**self.nqubits)) * basis_states
return change_to_basis - qubits
def __new__(cls, *args):
if len(args) != 2:
raise QuantumError("Rk gates only take two arguments, got: %r" % args)
# For small k, Rk gates simplify to other gates, using these
# substitutions give us familiar results for the QFT for small numbers
# of qubits.
target = args[0]
k = args[1]
if k == 1:
return ZGate(target)
elif k == 2:
return PhaseGate(target)
elif k == 3:
return TGate(target)
args = cls._eval_args(args)
inst = Expr.__new__(cls, *args)
inst.hilbert_space = cls._eval_hilbert_space(args)
return inst
def _apply_operator_Qubit(self, qubits, **options):
"""Apply this gate to a Qubit."""
# Check number of qubits this gate acts on.
if qubits.nqubits < self.min_qubits:
raise QuantumError(
"Gate needs a minimum of %r qubits to act on, got: %r"
% (self.min_qubits, qubits.nqubits)
)
# If the controls are not met, just return
if isinstance(self, CGate):
if not self.eval_controls(qubits):
return qubits
targets = self.targets
target_matrix = self.get_target_matrix(format="sympy")
# Find which column of the target matrix this applies to.
column_index = 0
n = 1
for target in targets:
column_index += n * qubits[target]
n = n << 1
column = target_matrix[:, int(column_index)]
# Now apply each column element to the qubit.
result = 0
for index in range(column.rows):
# TODO: This can be optimized to reduce the number of Qubit
# creations. We should simply manipulate the raw list of qubit
# values and then build the new Qubit object once.
# Make a copy of the incoming qubits.
new_qubit = qubits.__class__(*qubits.args)
# Flip the bits that need to be flipped.
for bit in range(len(targets)):
if new_qubit[targets[bit]] != (index >> bit) & 1:
new_qubit = new_qubit.flip(targets[bit])
# The value in that row and column times the flipped-bit qubit
# is the result for that part.
result += column[index] * new_qubit
return result
def _eval_args(cls, args):
if len(args) != 4:
raise QuantumError('Insufficient/excessive arguments to Vx.')
return args
def tensor_product_simp_Mul(e):
"""Simplify a Mul with TensorProducts.
Current the main use of this is to simplify a ``Mul`` of ``TensorProduct``s
to a ``TensorProduct`` of ``Muls``. It currently only works for relatively
simple cases where the initial ``Mul`` only has scalars and raw
``TensorProduct``s, not ``Add``, ``Pow``, ``Commutator``s of
``TensorProduct``s.
Parameters
==========
e : Expr
A ``Mul`` of ``TensorProduct``s to be simplified.
Returns
=======
e : Expr
A ``TensorProduct`` of ``Mul``s.
Examples
========
This is an example of the type of simplification that this function
performs::
>>> from sympy.physics.quantum.tensorproduct import \
tensor_product_simp_Mul, TensorProduct
>>> from sympy import Symbol
>>> A = Symbol('A',commutative=False)
>>> B = Symbol('B',commutative=False)
>>> C = Symbol('C',commutative=False)
>>> D = Symbol('D',commutative=False)
>>> e = TensorProduct(A,B)*TensorProduct(C,D)
>>> e
AxB*CxD
>>> tensor_product_simp_Mul(e)
(A*C)x(B*D)
"""
# TODO: This won't work with Muls that have other composites of
# TensorProducts, like an Add, Pow, Commutator, etc.
# TODO: This only works for the equivalent of single Qbit gates.
if not isinstance(e, Mul):
return e
c_part, nc_part = e.args_cnc()
n_nc = len(nc_part)
if n_nc == 0 or n_nc == 1:
return e
elif e.has(TensorProduct):
nc_part = map(tensor_product_simp, nc_part)
nc_s = []
while nc_part:
curr = nc_part.pop(0)
n_terms = len(curr.args)
new_args = list(curr.args)
while (len(nc_part) and isinstance(curr, TensorProduct)
and isinstance(nc_part[0], TensorProduct)):
x = nc_part.pop(0)
# TODO: check the hilbert spaces of next and current here.
if n_terms != len(x.args):
raise QuantumError(
'TensorProducts of different lengths: %r and %r' %
(curr, x))
for i in range(len(new_args)):
new_args[i] = new_args[i] * x.args[i]
curr = TensorProduct(*new_args)
nc_s.append(curr)
return Mul(*c_part) * Mul(*nc_s)
else:
return e
