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Hands-On Quantum Machine Learning with Python

Bayesian Rejection Sampling

Explore Bayesian rejection sampling methods in quantum Bayesian networks to calculate conditional probabilities based on measured quantum states. Learn how to evaluate factors like survival and norm favorability by analyzing quantum measurement outcomes and estimating probabilities for different passenger groups.

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Our QBN is well trained. However, when we look back to all the CPT it consists of (see the lesson titled Estimating a Variable), we haven’t completed it. We still miss the CPT of being favored by a Norm given the passenger’s Sex and Age, and we miss the CPT of Survival given the Norm and the Pclass. Let’s catch up on this.

Javascript (babel-node)
def get_trained_qbn_norm(passengers, params):
    prepared_passengers = prepare_data(passengers, params)
    norm_params = calculate_norm_params(prepared_passengers)
    surv_params = calculate_surv_params(prepared_passengers)
    def qbn_titanic(): 
        def circuit(qc, qr=None, cr=None):
            apply_ischild_sex(qc)
            apply_norm(qc, norm_params)
            apply_class(qc)
            apply_survival(qc, surv_params)
            qc.measure(QPOS_ISCHILD, cr[0])
            qc.measure(QPOS_SEX, cr[1])
            qc.measure(QPOS_NORM, cr[2])
        return as_pqc(QUBITS, circuit, hist=False, cnt_classical=3, measure=True, shots=10000)
    return qbn_titanic()

Again, estimating the numbers in the CPT of a Bayesian network builds upon counting how many times that event occurred in our training data.

First, we need to change the variables we measure.

Instead of the qubit at position QPOS_SURV that represents whether a passenger survived, we measure the qubits ...