14.2 Bayesian Quantum Circuit
Parameterised quantum circuits can be used to construct a quantum state with desired properties and to modify it in a controlled way. Measuring the final state is then equivalent to drawing a sample from a probability distribution in the form of a bitstring. This is the key concept behind the Quantum Circuit Born Machine (QCBM) we considered in Chapter 9. The Bayesian Quantum Circuit (BQC) is another quantum generative machine learning model that extends the capabilities of QCBM [88]. Unlike QCBM, which operates only on data qubits, encoding the desired probability distribution, BQC has additional ancillary qubits encoding the prior distribution. The BQC circuit is shown in Figure 14.1.
Figure 14.1: Schematic representation of BQC.
The first m quantum registers in the circuit are ancillary qubits. After applying K operator blocks U(γi)i=1,…,K, to the initial state 
⊗m, we construct the state 
,
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