mipt_pideal.py

"""
demo example of mipt in tc style, with ideal p for each history trajectory
p is also jittable now, change parameter p doesn't trigger recompiling
"""

from functools import partial
import time
import numpy as np
from scipy import stats
import tensorcircuit as tc

K = tc.set_backend("jax")
tc.set_dtype("complex128")
# tf backend is slow (at least on cpu)


def delete2(pick, plist):
    # pick = 0, 1 : return plist[pick]/(plist[0]+plist[1])
    # pick = 2: return 1
    indicator = (K.sign(1.5 - pick) + 1) / 2  # 0,1 : 1, 2: 0
    p = 0
    p += 1 - indicator
    p += indicator / (plist[0] + plist[1]) * (plist[0] * (1 - pick) + plist[1] * pick)
    return p


@partial(K.jit, static_argnums=(2, 3))
def circuit_output(random_matrix, status, n, d, p):
    """
    mipt circuit

    :param random_matrix: a float or complex tensor containing 4*4 random haar matrix wth size [d*n, 4, 4]
    :type random_matrix: _type_
    :param status: a int tensor with element in 0 or 1 or 2 (no meausrement) with size d*n
    :type status: _type_
    :param n: number of qubits
    :type n: _type_
    :param d: number of depth
    :type d: _type_
    :param p: measurement ratio
    :type p: float
    :return: output state
    """
    random_matrix = K.reshape(random_matrix, [d, n, 4, 4])
    status = K.reshape(status, [d, n])
    inputs = None
    bs_history = []
    prob_history = []
    for j in range(d):
        if inputs is None:
            c = tc.Circuit(n)
        else:
            c = tc.Circuit(n, inputs=inputs)
        for i in range(0, n, 2):
            c.unitary(i, (i + 1) % n, unitary=random_matrix[j, i])
        for i in range(1, n, 2):
            c.unitary(i, (i + 1) % n, unitary=random_matrix[j, i])
        inputs = c.state()
        c = tc.Circuit(n, inputs=inputs)
        for i in range(n):
            pick, plist = c.general_kraus(
                [
                    K.sqrt(p) * K.convert_to_tensor(np.array([[1.0, 0], [0, 0]])),
                    K.sqrt(p) * K.convert_to_tensor(np.array([[0, 0], [0, 1.0]])),
                    K.sqrt(1 - p) * K.eye(2),
                ],
                i,
                status=status[j, i],
                with_prob=True,
            )
            bs_history.append(pick)
            prob_history.append(delete2(pick, plist))
            inputs = c.state()
            c = tc.Circuit(n, inputs=inputs)
        inputs = c.state()
        inputs /= K.norm(inputs)
    bs_history = K.stack(bs_history)
    prob_history = K.stack(prob_history)
    return inputs, bs_history, prob_history, K.sum(K.log(prob_history + 1e-11))


@partial(K.jit, static_argnums=(2, 3))
def cals(random_matrix, status, n, d, p):
    state, bs_history, prob_history, prob = circuit_output(
        random_matrix, status, n, d, p
    )
    rho = tc.quantum.reduced_density_matrix(state, cut=[i for i in range(n // 2)])
    return (
        tc.quantum.entropy(rho),
        tc.quantum.renyi_entropy(rho, k=2),
        bs_history,
        prob_history,
        prob,
    )


if __name__ == "__main__":
    n = 12
    d = 12
    st = np.random.uniform(size=[d * n])
    ## assume all X gate instead
    rm = [stats.unitary_group.rvs(4) for _ in range(d * n)]
    rm = [r / np.linalg.det(r) for r in rm]
    rm = np.stack(rm)
    time0 = time.time()
    print(cals(rm, st, n, d, 0.6))
    time1 = time.time()
    st = np.random.uniform(size=[d * n])
    print(cals(rm, st, n, d, 0.1))
    time2 = time.time()
    print(f"compiling time {time1-time0}, running time {time2-time1}")