"""
\********************************************************************************
* Copyright (c) 2023 the Qrisp authors
*
* This program and the accompanying materials are made available under the
* terms of the Eclipse Public License 2.0 which is available at
* http://www.eclipse.org/legal/epl-2.0.
*
* This Source Code may also be made available under the following Secondary
* Licenses when the conditions for such availability set forth in the Eclipse
* Public License, v. 2.0 are satisfied: GNU General Public License, version 2
* with the GNU Classpath Exception which is
* available at https://www.gnu.org/software/classpath/license.html.
*
* SPDX-License-Identifier: EPL-2.0 OR GPL-2.0 WITH Classpath-exception-2.0
********************************************************************************/
"""
import numpy as np
from qrisp import QuantumArray, QuantumVariable, gate_wrap, gphase, h, mcp, mcz, x, merge, recursive_qs_search, IterationEnvironment, conjugate, invert
# Applies the grover diffuser onto the (list of) quantum variable input_object
def diffuser(input_object, phase=np.pi, state_function=None):
"""
Applies the Grover diffuser onto (multiple) QuantumVariables.
Parameters
----------
input_object : QuantumVariable or list[QuantumVariable]
The (list of) QuantumVariables to apply the Grover diffuser on.
state_function : function
A Python function preparing the initial state. The default is None.
Examples
--------
We apply the Grover diffuser onto several QuantumChars:
>>> from qrisp import QuantumChar
>>> from qrisp.grover import diffuser
>>> q_ch_list = [QuantumChar(), QuantumChar(), QuantumChar()]
>>> diffuser(q_ch_list)
>>> print(q_ch_list[0].qs)
::
┌────────────┐
q_ch_0.0: ┤0 ├
│ │
q_ch_0.1: ┤1 ├
│ │
q_ch_0.2: ┤2 ├
│ │
q_ch_0.3: ┤3 ├
│ │
q_ch_0.4: ┤4 ├
│ │
q_ch_1.0: ┤5 ├
│ │
q_ch_1.1: ┤6 ├
│ │
q_ch_1.2: ┤7 diffuser ├
│ │
q_ch_1.3: ┤8 ├
│ │
q_ch_1.4: ┤9 ├
│ │
q_ch_2.0: ┤10 ├
│ │
q_ch_2.1: ┤11 ├
│ │
q_ch_2.2: ┤12 ├
│ │
q_ch_2.3: ┤13 ├
│ │
q_ch_2.4: ┤14 ├
└────────────┘
"""
init_state = True if state_function is not None else False
if init_state:
def inv_state_function(args):
with invert():
state_function(*args)
if isinstance(input_object, QuantumArray):
input_object = [qv for qv in input_object.flatten()]
if isinstance(input_object, list):
if init_state:
with conjugate(inv_state_function)(input_object):
tag_state(
{qv: "0" * qv.size for qv in input_object}, binary_values=True, phase=phase
)
else:
[h(qv) for qv in input_object]
tag_state(
{qv: "0" * qv.size for qv in input_object}, binary_values=True, phase=phase
)
[h(qv) for qv in input_object]
gphase(np.pi, input_object[0][0])
else:
if init_state:
with conjugate(inv_state_function)(input_object):
tag_state(
{input_object: input_object.size * "0"}, binary_values=True, phase=phase
)
else:
h(input_object)
tag_state(
{input_object: input_object.size * "0"}, binary_values=True, phase=phase
)
h(input_object)
gphase(np.pi, input_object[0])
return input_object
def tag_state(tag_specificator, binary_values=False, phase=np.pi):
"""
Applies a phase tag to (multiple) QuantumVariables. The tagged state is specified in
the dictionary ``tag_specificator``. This dictionary should contain the
QuantumVariables as keys and the labels of the states which should be tagged as
values.
Parameters
----------
tag_specificator : dict
A dictionary specifying which state should be tagged.
binary_values : bool, optional
If set to True, the values in the tag_specificator dict have to be bitstrings
instead of labels. The default is False.
phase : float or sympy.Symbol, optional
Specify the phase shift the tag should perform. The default is pi, i.e. a
multi-controlled Z gate.
Examples
--------
We construct an oracle that tags the states -3 and 2 on two QuantumFloats ::
from qrisp.grover import tag_state
def test_oracle(qf_list):
tag_dic = {qf_list[0] : -3, qf_list[1] : 2}
tag_state(tag_dic)
"""
qv_list = list(tag_specificator.keys())
states = [tag_specificator[qv] for qv in qv_list]
if not len(states):
states = ["1" * qv.size for qv in qv_list]
bit_string = ""
from qrisp.misc import bin_rep
for i in range(len(qv_list)):
if binary_values:
bit_string += states[i][::-1]
else:
bit_string += bin_rep(qv_list[i].encoder(states[i]), qv_list[i].size)[::-1]
qubit_list = sum([list(qv.reg) for qv in qv_list], [])
state = bit_string
if state[-1] == "0":
x(qubit_list[-1])
# The control state is the state we are looking for without the base qubit
ctrl_state = state[:-1]
if phase == np.pi:
mcz(qubit_list, ctrl_state=ctrl_state + "1")
else:
mcp(phase, qubit_list, ctrl_state=ctrl_state + "1")
# Apply the final x gate
if state[-1] == "0":
x(qubit_list[-1])
[docs]def grovers_alg(
qv_list,
oracle_function,
kwargs={},
iterations=0,
winner_state_amount=None,
exact=False,
):
r"""
Applies Grover's algorithm to a given oracle (in the form of a Python function).
Parameters
----------
qv_list : QuantumVariable or list[QuantumVariable]
A (list of) QuantumVariables on which to execute Grover's algorithm.
oracle_function : function
A Python function tagging the winner states.
kwargs : dict, optional
A dictionary containing keyword arguments for the oracle. The default is {}.
iterations : int, optional
The amount of Grover iterations to perfrom.
winner_state_amount : int, optional
If not given the amount of iterations, the established formula will be used
based on the amount of winner states. The default is 1.
exact : bool, optional
If set to True, the `exact version <https://arxiv.org/pdf/quant-ph/0106071.pdf>`
of Grover's algorithm will be evaluated. For this, the correct
``winner_state_amount`` has to be supplied and the oracle has to support the
keyword argument ``phase`` which specifies how much the winner states are
phaseshifted (in standard Grover this would be $\pi$).
Raises
------
Exception
Applied oracle introducing new QuantumVariables without uncomputing/deleting
Examples
--------
We construct an oracle that tags the states -3 and 2 on two QuantumFloats and apply
Grover's algorithm to it. ::
from qrisp import QuantumFloat
#Create list of QuantumFloats
qf_list = [QuantumFloat(2, signed = True), QuantumFloat(2, signed = True)]
from qrisp.grover import tag_state, grovers_alg
def test_oracle(qf_list):
tag_dic = {qf_list[0] : -3, qf_list[1] : 2}
tag_state(tag_dic)
grovers_alg(qf_list, test_oracle)
>>> from qrisp.misc import multi_measurement
>>> print(multi_measurement(qf_list))
{(-3, 2): 0.9966, (0, 0): 0.0001, (0, 1): 0.0001, (0, 2): 0.0001, (0, 3): 0.0001,
(0, -4): 0.0001, (0, -3): 0.0001, (0, -2): 0.0001, (0, -1): 0.0001, (1, 0): 0.0001,
(1, 1): 0.0001, (1, 2): 0.0001, (1, 3): 0.0001, (1, -4): 0.0001, (1, -3): 0.0001,
(1, -2): 0.0001, (1, -1): 0.0001, (2, 0): 0.0001, (2, 1): 0.0001, (2, 2): 0.0001,
(2, 3): 0.0001, (2, -4): 0.0001, (2, -3): 0.0001, (2, -2): 0.0001, (2, -1): 0.0001,
(3, 0): 0.0001, (3, 1): 0.0001, (3, 2): 0.0001, (3, 3): 0.0001, (3, -4): 0.0001,
(3, -3): 0.0001, (3, -2): 0.0001, (3, -1): 0.0001, (-4, 0): 0.0001, (-4, 1): 0.0001,
(-4, 2): 0.0001, (-4, 3): 0.0001, (-4, -4): 0.0001, (-4, -3): 0.0001,
(-4, -2): 0.0001, (-4, -1): 0.0001, (-3, 0): 0.0001, (-3, 1): 0.0001,
(-3, 3): 0.0001, (-3, -4): 0.0001, (-3, -3): 0.0001, (-3, -2): 0.0001,
(-3, -1): 0.0001, (-2, 0): 0.0001, (-2, 1): 0.0001, (-2, 2): 0.0001,
(-2, 3): 0.0001, (-2, -4): 0.0001, (-2, -3): 0.0001, (-2, -2): 0.0001,
(-2, -1): 0.0001, (-1, 0): 0.0001, (-1, 1): 0.0001, (-1, 2): 0.0001,
(-1, 3): 0.0001, (-1, -4): 0.0001, (-1, -3): 0.0001, (-1, -2): 0.0001,
(-1, -1): 0.0001}
**Exact Grovers Algorithm**
In the next example, we will showcase the ``exact`` functionality. For this we
create an oracle, which tags all the states of a QuantumVariable, that contain 3
ones and 2 zeros.
To count the amount of ones we use quantum phase estimation on the operator
.. math::
U = \text{exp}\left(\frac{i 2 \pi}{2^k}
\sum_{i = 0}^{n-1} ( 1 - \sigma_{z}^i )\right)
::
from qrisp import QPE, p, QuantumVariable, lifted
from qrisp.grover import grovers_alg, tag_state
import numpy as np
def U(qv, prec = None, iter = 1):
for i in range(qv.size):
p(iter*2*np.pi/2**prec, qv[i])
@lifted
def count_ones(qv):
prec = int(np.ceil(np.log2(qv.size+1)))
res = QPE(qv, U, precision = prec, iter_spec = True, kwargs = {"prec" : prec})
return res<<prec
Quick test:
>>> qv = QuantumVariable(5)
>>> qv[:] = {"11000" : 1, "11010" : 1, "11110" : 1}
>>> count_qf = count_ones(qv)
>>> count_qf.qs.statevector()
sqrt(3)*(|11000>*|2> + |11010>*|3> + |11110>*|4>)/3
We now define the oracle ::
def counting_oracle(qv, phase = np.pi, k = 1):
count_qf = count_ones(qv)
tag_state({count_qf : k}, phase = phase)
count_qf.uncompute()
And evaluate Grover's algorithm ::
n = 5
k = 3
qv = QuantumVariable(n)
import math
grovers_alg(qv, counting_oracle, exact = True, winner_state_amount = math.comb(n,k), kwargs = {"k" : k}) # noqa
>>> print(qv)
{'11100': 0.1,
'11010': 0.1,
'10110': 0.1,
'01110': 0.1,
'11001': 0.1,
'10101': 0.1,
'01101': 0.1,
'10011': 0.1,
'01011': 0.1,
'00111': 0.1}
We see that contrary to regular Grover's algorithm, the states which have not been
tagged by the oracle have 0 percent measurement probability.
"""
if exact and winner_state_amount is None:
raise Exception(
"Tried to call exact Grover's algorithm without specifying "
"winner_state_amount"
)
elif winner_state_amount is None:
winner_state_amount = 1
if isinstance(qv_list, list):
N = 2 ** sum([qv.size for qv in qv_list])
elif isinstance(qv_list, QuantumArray):
N = 2 ** sum([qv.size for qv in qv_list.flatten()])
elif isinstance(qv_list, QuantumVariable):
N = 2**qv_list.size
if exact:
# Implementation for phase calculation for exact grovers alg as in
# https://arxiv.org/pdf/quant-ph/0106071.pdf
iterations = 1
tmp = (
np.sin(np.pi / (4 * (iterations - 1) + 6))
* (N / winner_state_amount) ** 0.5
)
while tmp > 1:
iterations += 1
tmp = (
np.sin(np.pi / (4 * (iterations - 1) + 6))
* (N / winner_state_amount) ** 0.5
)
phi = 2 * np.arcsin(
np.sin(np.pi / (4 * (iterations - 1) + 6))
* (N / winner_state_amount) ** 0.5
)
else:
if iterations == 0:
iterations = np.pi / 4 * np.sqrt(N / winner_state_amount)
iterations = int(np.round(iterations))
for qv in qv_list:
h(qv)
merge(qv_list)
qs = recursive_qs_search(qv_list)[0]
qv_amount = len(qs.qv_list)
with IterationEnvironment(qs, iterations, precompile = False):
# for i in range(iterations):
if exact:
oracle_function(qv_list, phase=phi, **kwargs)
diffuser(qv_list, phase=phi)
else:
oracle_function(qv_list, **kwargs)
diffuser(qv_list)
if qv_amount != len(qs.qv_list):
raise Exception("Applied oracle introducing new QuantumVariables without uncomputing/deleting")
# Workaround to keep the docstring but still gatewrap
temp = diffuser.__doc__
diffuser = gate_wrap(permeability=[], is_qfree=False)(diffuser)
diffuser.__doc__ = temp
temp = tag_state.__doc__
tag_state = gate_wrap(permeability="args", is_qfree=True)(tag_state)
tag_state.__doc__ = temp