<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:

def expect(qubits, meas):
    "For the VQE simulation without sampling."
    result = {}
    i = np.arange(len(qubits))
    meas = tuple(meas)

    def to_mask(n):
        return reduce(lambda acc, im: acc | (n & (1 << im[0])) << (im[1] - im[0]), enumerate(meas), 0)

    def to_key(k):
        return tuple(1 if k & (1 << i) else 0 for i in meas)

    mask = reduce(lambda acc, v: acc | (1 << v), meas, 0)

    cnt = defaultdict(float)
    for i, v in enumerate(qubits):
        p = v.real ** 2 + v.imag ** 2
        if p != 0.0:
            cnt[i & mask] += p
    return {to_key(k): v for k, v in cnt.items()}