Improved Training of Quantum Boltzmann Machines

Richard Li, Daniel A. Lidar

Christa Zoufal, Aurélien Lucchi, Stefan Woerner

Cameron Perot

In this thesis we explore using the D-Wave Advantage 4.1 quantum annealer to sample from quantum Boltzmann distributions and train quantum Boltzmann machines (QBMs). We focus on the real-world problem of using QBMs as generative models to produce synthetic foreign exchange market data and analyze how the results stack up against classical models based on restricted Boltzmann machines (RBMs). Additionally, we study a small 12-qubit problem which we use to compare samples obtained from the Advantage 4.1 with theory, and in the process gain vital insights into how well the Advantage 4.1 can sample quantum Boltzmann random variables and be used to train QBMs. Through this, we are able to show that the Advantage 4.1 can sample classical Boltzmann random variables to some extent, but is limited in its ability to sample from quantum Boltzmann distributions. Our findings indicate that QBMs trained using the Advantage 4.1 are much noisier than those trained using simulations and struggle to perform at the same level as classical RBMs. However, there is the potential for QBMs to outperform classical RBMs if future generation annealers can generate samples closer to the desired theoretical distributions.

Hiroki Ikoma

Daniëlle Schuman, Mark V. Seebode, Tobias Rohe +5 more

Exploiting the fact that samples drawn from a quantum annealer inherently follow a boltzmann-like distribution, annealing-based Quantum Boltzmann Machines (QBMs) have gained increasing popularity in the quantum research community. While they harbor great promises for quantum speed-up, their usage currently stays a costly endeavor, as large amounts of QPU time are required to train them. This limits their applicability in the NISQ era. Following the idea of Noè et al. [1], who tried to alleviate this cost by incorporating parallel quantum annealing into their unsupervised training of QBMs, this paper presents an improved version of parallel quantum annealing that we employ to train QBMs in a supervised setting. Saving qubits to encode the inputs, the latter setting allows us to test our approach on medical images from the MedMNIST data set [2], thereby moving closer to real-world applicability of the technology. Our experiments show that QBMs using our approach already achieve reasonable results, comparable to those of similarly-sized Convolutional Neural Networks (CNNs), with a markedly smaller numbers of epochs than these classical models. Our using parallel annealing grants it a speed-up of almost 70% compared to regular annealing-based BM execution.

Fu-Wen Zhang, Yong-Gang Tan, Qing-yu Cai

Abstract Quantum machine learning based on quantum algorithms may achieve an exponential speedup over classical algorithms in dealing with some problems such as clustering. In this paper, we use the method of training the lower bound of the average log likelihood function on the quantum Boltzmann machine (QBM) to recognize the handwritten number datasets and compare the training results with classical models. We find that, when the QBM is semi-restricted, the training results get better with fewer computing resources. This shows that it is necessary to design a targeted algorithm to speed up computation and save resources.