9.4 Classical Benchmark
There is a deep connection between the QCBM and its classical counterpart – the Restricted Boltzmann Machine [60]. The RBM, introduced and discussed in Chapter 5 in the context of quantum annealing, is a generative model inspired by statistical physics, where the probability of a particular data sample, v, is given by the Boltzmann distribution:
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Here, E(v) is the (positive) energy of the data sample (data samples with lower energy have higher probabilities) and Z is the partition function, namely the normalisation factor of the probability density:
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Alternatively, we can use the inherent probabilistic nature of quantum mechanics that allows us to model the probability distribution using a quantum state 
:
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where Pv is the measurement operator introduced in Section 1.2.3 and, since the quantum state 
is a unit vector, we have
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We realise this approach in the QCBM, where generative...
