Quantum Boltzmann Machine

By Mohammad H. Amin, Evgeny Andriyash, Jason Tyler Rolfe, B. Kulchytskyy, Roger G. Melko. 2016

599 citations recorded by the source corpus.

Inspired by the success of Boltzmann Machines based on classical Boltzmann distribution, we propose a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian. Due to the non-commutative nature of quantum mechanics, the training process of the Quantum Boltzmann Machine (QBM) can become nontrivial. We circumvent the problem by introducing bounds on the quantum probabilities. This allows us to train the QBM efficiently by sampling. We show examples of QBM training with and without the bound, using exact diagonalization, and compare the results with classical Boltzmann training. We also discuss the possibility of using quantum annealing processors like D-Wave for QBM training and application.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/ab1258b286c729e2c0cd2546ec0f79ad21bd3883

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Citations in the corpus

Quantum computing for finance: Overview and prospects (2018, unknown): “…( √ N ) Online perceptron [26] O ( √ N ) Least-squares ﬁtting [27] O (log N ) Classical Boltzmann machine [28] O ( √ N ) Quantum Boltzmann machine [29, 30] O (log N ) Quantum PCA [22] O (log N ) Quantum support vector machine [23] O (log N ) Quantum reinforcement learning [31] O ( √ N ) Table III.”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, unknown): “, quantum classifier [19], quantum convolution [27], and quantum Boltzmann machine [2], etc.”
Quantum Entanglement in Neural Network States (2017, methodology): “We focus on the quantum states represented by the restricted Boltzmann machine (RBM), which is a stochastic artiﬁcial neural network with widespread applications [40, 48–50].”
Strawberry Fields: A Software Platform for Photonic Quantum Computing (2018, unknown): “[30] M.”
Entanglement Induced Barren Plateaus (2020, methodology): “We focus on two types of QNNs depicted in Figure 1, feed-forward unitary quantum neural networks inspired by QAOA, and Quantum Boltzmann machines [8, 19, 22].”
Barren plateaus in variational quantum computing (2024, unknown): “Thus, noise leads to an extended PQC V θ that can act in a larger space, which could be exponentially large (although not necessarily) and thus substantially aggravates the curse of dimensionality.”
Adiabatic Quantum Computing (2016, background): “StoqAQC approaches for this problem were developed in (Adachi and Henderson, 2015; Amin et al., 2016; Benedetti et al., 2016) Neither the classical nor the quantum computational complexity is known in this case, but scaling of the solution time with problem size is not the only relevant criterion:…”
A generative modeling approach for benchmarking and training shallow quantum circuits (2018, background): “For example, learning probabilistic generative models is in many cases an intractable task, and quantum-assisted algorithms have been proposed for both gate-based [17, 18] and quantum annealing devices [19–23].”
Neuro-inspired computing chips (2020, methodology): “Quantum computing approaches, such as the quantum Boltzmann machine 83 , could potentially exponentially speed up machine learning tech - niques compared with the best classical computers.”