Quantum Machine Learning by Claudio Conti

Author:Claudio Conti
Language: eng
Format: epub
ISBN: 9783031442261
Publisher: Springer International Publishing

This circumstance also shows that there is a link between energy and entropy. The ground state has a nonvanishing entropy.

6.3 Training with Entanglement

We need to develop a more general variational ansatz. First, we observe that we have a two-qubit state, which lies in a Hilbert space with dimension 4. Correspondingly, the state is determined by four complex parameters or, equivalently, the state is determined by eight real weights. However, the normalization constraint and the arbitrary absolute phase reduce the minimal number of parameters to six. This is the optimal number for a variational ansatz, i.e., the minimum number of weights to be trained. However, it happens that one uses a much larger number of weights in applications, as this helps to avoid suboptimal local minima by starting from randomly initialized values.

For the moment, let us consider only six parameters as in Fig. 6.2. We know from Sect. 6.2 that we need entanglement. The first approach is introducing an entangling gate, as the controlled-Z gate , discussed in Chap. 3.

Figure 6.7 shows the new feature map defined as follows.

Fig. 6.7A feature map including an entangling controlled-Z gate to the feature map in Fig. 6.2. The resulting state is a variational ansatz for the TIM, useful when we expect an entangled ground state

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