Query Grover algorithm¶

see paper "Variational learning algorithms for quantum query complexity" arxiv-link for details

In [1]:

import numpy as np
import torch

try:
    import numqi
except ImportError:
    %pip install numqi
    import numqi

import numpy as np import torch try: import numqi except ImportError: %pip install numqi import numqi

In [2]:

def hf_grover_oracle_wrapper(x:int):
    def hf0(q0):
        q0 = q0.copy()
        q0[x] *= -1
        return q0
    return hf0

def hf_grover_oracle_wrapper(x:int): def hf0(q0): q0 = q0.copy() q0[x] *= -1 return q0 return hf0

In [3]:

num_qubit = 4
num_query = 3
model = numqi.query.QueryGroverModel(num_qubit, num_query, use_fractional=False)
theta_optim = numqi.optimize.minimize(model, theta0='uniform', tol=1e-10, num_repeat=3, early_stop_threshold=1e-4)
print('error rate:', model.error_rate.item())
print('loss function:', theta_optim.fun)

if theta_optim.fun < 1e-5:
    np_rng = np.random.default_rng()
    xstar = np_rng.integers(2**num_qubit)
    hf_oracle = hf_grover_oracle_wrapper(xstar)

    with torch.no_grad():
        unitary_list = model.manifold_SU().detach().numpy().transpose(0,2,1)
    q0 = np.zeros(2**num_qubit, dtype=np.complex128)
    q0[0] = 1
    for ind0 in range(num_query):
        q0 = unitary_list[ind0] @ q0
        q0 = hf_oracle(q0)
    q0 = unitary_list[-1] @ q0
    prob = (q0.conj() * q0).real
    x_found = np.argmax(prob)
    assert x_found==xstar
    assert abs(prob.max() - 1) < 1e-4

num_qubit = 4 num_query = 3 model = numqi.query.QueryGroverModel(num_qubit, num_query, use_fractional=False) theta_optim = numqi.optimize.minimize(model, theta0='uniform', tol=1e-10, num_repeat=3, early_stop_threshold=1e-4) print('error rate:', model.error_rate.item()) print('loss function:', theta_optim.fun) if theta_optim.fun < 1e-5: np_rng = np.random.default_rng() xstar = np_rng.integers(2**num_qubit) hf_oracle = hf_grover_oracle_wrapper(xstar) with torch.no_grad(): unitary_list = model.manifold_SU().detach().numpy().transpose(0,2,1) q0 = np.zeros(2**num_qubit, dtype=np.complex128) q0[0] = 1 for ind0 in range(num_query): q0 = unitary_list[ind0] @ q0 q0 = hf_oracle(q0) q0 = unitary_list[-1] @ q0 prob = (q0.conj() * q0).real x_found = np.argmax(prob) assert x_found==xstar assert abs(prob.max() - 1) < 1e-4

[round=0] min(f)=2.2386411613339874e-09, current(f)=2.2386411613339874e-09
error rate: 3.2048981246646235e-09
loss function: 2.2386411613339874e-09