Simulation is an indispensable tool in both engineering and the sciences. In simulation-based modeling, a parametric simulator is adopted as a mechanistic model of a physical system. The problem of designing algorithms that optimize the simulator parameters is the focus of the emerging field of simulation-based inference (SBI), which is often formulated in a Bayesian setting with the goal of quantifying epistemic uncertainty. This work studies Bayesian SBI that leverages a parameterized quantum circuit (PQC) as the underlying simulator. The proposed solution follows the well-established principle that quantum computers are best suited for the simulation of certain physical phenomena. It contributes to the field of quantum machine learning by moving beyond the likelihood-based methods investigated in prior work and accounting for the likelihood-free nature of PQC training. Experimental results indicate that well-motivated quantum circuits that account for the structure of the underlying physical system are capable of simulating data from two distinct tasks.
Simulation is an indispensable tool in both engineering and the sciences. In simulation-based modeling, a parametric simulator is adopted as a mechanistic model of a physical system. The problem of designing algorithms that optimize the simulator parameters is the focus of the emerging field of simulation-based inference (SBI), which is often formulated in a Bayesian setting with the goal of quantifying epistemic uncertainty. This work studies Bayesian SBI that leverages a parameterized quantum circuit (PQC) as the underlying simulator. The proposed solution follows the well-established principle that quantum computers are best suited for the simulation of certain physical phenomena. It contributes to the field of quantum machine learning by moving beyond the likelihood-based methods investigated in prior work and accounting for the likelihood-free nature of PQC training. Experimental results indicate that well-motivated quantum circuits that account for the structure of the underlying physical system are capable of simulating data from two distinct tasks.
Parameterized quantum circuits (PQCs), as one of the most promising schemes to realize quantum machine learning algorithms on near-term quantum computers, have been designed to solve machine earning tasks with quantum advantages. In this paper, we explain why PQCs with different structures can achieve generative tasks in the discrete case from the perspective of probability estimation. Although different kinds of PQCs are proposed for generative tasks, the current methods often encounter the following three hurdles: (1) the mode contraction problem; (2) unexpected data are often generated with a high proportion; (3) target data cannot be sampled directly. For the purpose of tackling the above hurdles, we devise Bayesian quantum circuit (BQC) through introducing ancillary qubits to represent prior distributions. BQC advances both generative and semi-supervised quantum circuit learning tasks, where its effectiveness is validated by numerical simulations using the Rigetti Forest platform.
In the current noisy intermediate-scale quantum (NISQ)era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parameterized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parameterized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a back groundin probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then,it covers parameterized quantum circuits, the variation alquantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.
This paper explores the application of quantum computing to accelerate Bayesian inference. Traditional Bayesian inference suffers from significant computational bottlenecks, particularly in complex models with large datasets. We propose a novel approach leveraging the inherent parallelism of quantum computers to drastically reduce the time required for inference. Specifically, we design a quantum algorithm based on a parameterized quantum circuit (PQC) to perform Bayesian updating. This approach utilizes quantum superposition and interference to perform computations on multiple possibilities simultaneously. The core claim is that this method can significantly speed up Bayesian inference. We detail the mathematical formulation of the algorithm, including the quantum circuit representation and the key operations involved. The potential of this approach to overcome the limitations of classical Bayesian inference is discussed, highlighting the transformative impact of quantum computing on probabilistic reasoning and data analysis. The efficiency gains are expected to be particularly pronounced for problems where the prior distributions and the likelihood functions are highly correlated, allowing for efficient quantum interference.
Variational quantum algorithms (VQAs) have emerged as a promising quantum alternative for solving optimization and machine learning problems using parameterized quantum circuits (PQCs). The design of these circuits influences the ability of the algorithm to efficiently explore the solution space and converge to more optimal solutions. Quantum architecture search (QAS) is therefore a highly relevant topic, in which the selection of an appropriate circuit topology, gate set, and parameterization scheme is determinant to achieve good performance. In addition, it is not only problem-dependent, but the quantum hardware used also has a significant impact on the results. Therefore, we present BPQCO, a Bayesian optimization-based strategy to search for optimal PQCs adapted to the problem to be solved and to the characteristics and limitations of the chosen quantum hardware. To this end, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems (a synthetic dataset and the well-known Iris dataset), focusing on the design of the circuit ansatz. In addition, we study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers. To mitigate the effect of noise, two alternative optimization strategies based on the characteristics of the quantum system are proposed. The results obtained confirm the relevance of the presented approach and allow its adoption in further work based on the use of PQCs.
In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parametrized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then, it covers parametrized quantum circuits, the variational quantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.
The astounding acceleration in Artificial Intelligence and Quantum Computing advances naturally gives rise to a line of research, which unrolls the potential advantages of quantum computing on classical Machine Learning tasks, known as Quantum Machine Learning or Quantum Machine Intelligence. The typical objectives are either (1) exploring the potential quantum advantages on classical learning tasks or (2) levering well-established classical ML algorithms to tackle quantum-related problems on Noisy Intermediate-Scale Quantum (NISQ) devices. Along the second research direction, we study Quantum Neural Networks (QNNs) to accomplish the purpose of Bayesian learning. By observing a wide range of studies on QNNs, in which the sole training method is based on frequentist training, we find that Bayesian learning benefits QNNs from two aspects. First, Bayesian-trained models enjoy a high level of generalization due to the prior and posterior distribution usage compared to frequentist training, which will be justified by this paper’s theoretical study of model capacity. Second, Bayesian Inference offers epistemic uncertainty estimation, which merits the decision-making process. It is worth mentioning that frequentist-trained QNNs generally lack this desirable property. Under the Bayesian training procedure, our derived models can be considered a new class of QNNs (called BayesianQNNs) which possesses both desirable properties of Bayesian Inference while maintaining comparable predictive performance as frequentist counterparts. The proposed Bayesian Quantum Neural Networks is justified by empirical evidence from numerical experiments.