#COMPACT MACHINES QUANTUM ENTANGLER FULL#

#COMPACT MACHINES QUANTUM ENTANGLER FULL#

The evolution through the unitary matrices at every layer of the model, together with the full dephasing of the density matrix at input and output, then becomes successive Bayesian updates of classical probability distributions, thus removing the quantumness of the model. By removing the off-diagonal elements, i.e., the coherence, from the density matrix of a quantum state, we reduce its representation down to a classical probability distribution over a given basis. We investigate and numerically quantify the competing effect between decoherence and increasing bond dimension of two common tensor network QML models, namely the unitary TTN and the MERA. In this work, we focus on discriminative QML. 2019), although their compilations into hardware-dependent native gates are more costly because of the need to compile generic unitaries.

They provide circuit variational ansatze more general than those with common parametrized gate sets (Mitarai et al. Such models employ fully parametrized unitary tensor nodes that form a rich subset of larger unitaries with respect to all input and output qubits upon tensor contractions. Tensor network QML models are linear classifiers on a feature space whose dimension grows exponentially in the number of data qubits and where the feature map is non-linear. 2019) have been explored for this purpose mindful of feasible implementations, such as normalized input states, on a quantum computer. 2006) and the multiscale entanglement renormalization ansatz (MERA) (Vidal 2007) for quantum-inspired tensor network ML algorithms (Stoudenmire 2018 Reyes and Stoudenmire 2021 Wall and D’Aguanno 2021), there have been efforts to variationally train the generic unitary nodes in TNs to perform quantum machine learning (QML) on data-encoded qubits. In addition to applying TNs such as the tree tensor network (TTN) (Shi et al. This motivates the usage of such networks to perform discriminative tasks, in a manner similar to classical machine learning (ML) using neural networks with layers like convolution and pooling that perform sequential feature abstraction to reduce the dimension and to obtain a hierarchical representation of the data (Levine et al. Some tensor networks allow for interpretations of coarse-grained states at increasing levels of the network as a renormalization group or scale transformation that retains information necessary to understand the physics on longer length scales (Evenbly and Vidal 2009 Bridgeman and Chubb 2017). Many tensor network topologies are designed to represent the low-energy states of physically realistic systems by capturing certain entanglement entropy and correlation scalings of the state generated by the network (Evenbly and Vidal 2011 Eisert 2013 Convy et al. Tensor networks (TNs) are compact data structures engineered to efficiently approximate certain classes of quantum states used in the study of quantum many-body systems.

Compact machines quantum entangler