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The training of Neural Networks is a compute intensive task that, in current classical implementations, relies on gradient descent algorithms and a certain learning rate that controls the granularity of the search for a solution. This paper explores a new hybrid quantum-classical approach, which is not only novel for exploding quantum computing to partially solve the problem, but also for being the first approach that adjusts the learning rate with exact information pertaining to the solution of this training problem. The Quantum Adaptive Learning Rate approach is tested in a proof of concept classification problem. Key aspects of the practical implementation of the Harrow, Hasidim and Lloy (HHL) quantum algorithm are discussed. 

Due to the limitations of current NISQ systems, error mitigation strategies are under development to alleviate the negative effects of error-inducing noise on quantum applications. This work proposes the use of machine learning (ML) as an error mitigation strategy, using ML to identify the accurate solutions to a quantum application in the presence of noise. Methods of encoding the probabilistic solution space of a basis-encoded quantum algorithm are researched to identify the characteristics which represent good ML training inputs. A multilayer perceptron artificial neural network (MLP ANN) was trained on the results of 8-state and 16-state basis-encoded quantum applications both in the presence of noise and in noise-free simulation. It is demonstrated using simulated quantum hardware and probabilistic noise models that a sufficiently trained model may identify accurate solutions to a quantum applications with over 90% precision and 80% recall on select data. The model makes confident predictions even with enough noise that the solutions cannot be determined by direct observation, and when it cannot, it can identify the inconclusive experiments as candidates for other error mitigation techniques. 

Multiplication is a frequent computation in many algorithms, classical and quantum. This paper targets the implementation of quantum integer multiplication. Quantum array multipliers take inspiration from classical array multipliers, with the result of reduced circuit depth. They take advantage of the quantum phase domain, through rotations controlled by the multiplier’s qubits. This work further explores this implementation by applying approximate rotations. Although this approach can have an impact on the accuracy of the result, the reduction in depth can result in better outcomes when noise is involved. 

This paper proposes a new and improved implementation of a quantum integer multiplier. Performing arithmetic computations is sometimes a necessary step in the implementation of quantum algorithms. In this work, Quantum Fourier Transform is used in order to perform scalable arithmetic in a generic bit-width quantum system. In the phase domain, addition can be implemented through accumulated controlled rotations on the qubits’ state. Leveraging this, and inspired by the classical implementation of an array multiplier, a new integer multiplier is fully designed and tested in a quantum environment. The depth of a quantum circuit is the number of computational steps necessary to completion, and it is a key parameter that reflects on the performance of the design. The new design reduces the quantum depth of the design from the exponential order of the previously proposed designs to polynomial order. 

This article offers perspective on quantum computing programming languages, as well as their emerging runtimes and algorithmic modalities. With the scientific high-performance computing (HPC) community as a target audience, we describe the current state of the art in the field, and outline programming paradigms for scientific workflows. One take-home message is that there is significant work required to first refine the notion of the quantum processing unit in order to integrate in the HPC environments. Programming for today’s quantum computers is making significant strides toward modern HPC-compatible workflows, but key challenges still face the field. 

Binary Neural Networks (BNNs) are the result of a simplification of network parameters in Artificial Neural Networks (ANNs). The computational complexity of training ANNs increases significantly as the size of the network increases. This complexity can be greatly reduced if the parameters of the network are binarized. Binarization, which is a one bit quantization, can also come with complications including error and information loss. The implementation of BNNs on quantum hardware could potentially provide a computational advantage over its classical counterpart. This is due to the fact that binarized parameters fit nicely to the nature of quantum hardware. Quantum superposition allows the network to be trained more efficiently, without using back propagation techniques, with the application of Grover’s Algorithm for the training process. This paper looks into two BNN designs that utilize only quantum hardware, as opposed to hybrid quantum-classical implementations. It also provides practical implementations for both of them. Looking into their scalability, improvements on the design are proposed to reduce complexity even further.