quantum Computing leverages the laws of quantum mechanics to build computers endowed with tremendous computing power. The field is attracting ever-increasing attention from both academic and private sectors, as testif...
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ISBN:
(纸本)9783030504335;9783030504328
quantum Computing leverages the laws of quantum mechanics to build computers endowed with tremendous computing power. The field is attracting ever-increasing attention from both academic and private sectors, as testified by the recent demonstration of quantum supremacy in practice. However, the intrinsic restriction to linear operations significantly limits the range of relevant use cases for the application of quantum Computing. In this work, we introduce a novel variational algorithm for quantum Single Layer Perceptron. Thanks to the universal approximation theorem, and given that the number of hidden neurons scales exponentially with the number of qubits, our framework opens to the possibility of approximating any function on quantum computers. Thus, the proposed approach produces a model with substantial descriptive power, and widens the horizon of potential applications already in the NISQ era, especially the ones related to quantum Artificial Intelligence. In particular, we design a quantum circuit to perform linear combinations in superposition and discuss adaptations to classification and regression tasks. After this theoretical investigation, we also provide practical implementations using various simulation environments. Finally, we test the proposed algorithm on synthetic data exploiting both simulators and real quantum devices.
variationalquantumalgorithms (VQA) aim to enhance the capabilities of Noisy Intermediate-Scale quantum (NISQ) devices. These algorithms utilize parameterized circuits and classical optimizers to iteratively execute ...
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ISBN:
(纸本)9798400701627
variationalquantumalgorithms (VQA) aim to enhance the capabilities of Noisy Intermediate-Scale quantum (NISQ) devices. These algorithms utilize parameterized circuits and classical optimizers to iteratively execute circuits with varying parameters. However, VQA faces computational overheads due to repeated iterations and random restarts. Prior work suggests using basic sub-graphs to transfer parameters for the input graph, reducing optimizer overheads but limiting applicability to structured regular graphs. In real-world applications, random irregular graphs are common, and existing methods are not scalable or practical for such graphs. This paper presents a framework that aims to improve random irregular graphs in VQA. The framework uses graph similarity and important features like total edge counts, average edge counts, and variance. It follows an iterative process to choose basis sub-graphs from a small database and adjust parameters accordingly. Classical optimizers then utilize these parameters to determine when to restart and perform gradient descent. This approach increases the chances of reaching global maximum points.
Sampling from distributions is an important capability for a range of tasks in science and engineering, including in machine learning applications. quantum computers hold promise for the capability of sampling from di...
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In this work we develop tools to address combinatorial optimization problems with a cardinality constraint, in which only a subset of variables end up having nonzero values. Firstly, we introduce a new heuristic pruni...
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In this work we develop tools to address combinatorial optimization problems with a cardinality constraint, in which only a subset of variables end up having nonzero values. Firstly, we introduce a new heuristic pruning method that iteratively discards variables through a hybrid quantum-classical optimization step. Secondly, we analyse the use of soft constraints in the form of 'chemical potentials' to control the number of non-zero variables. We illustrate the power of both techniques using the problem of index tracking, which aims to mimicking the performance of a financial index with a balanced subset of assets. We also compare the performance of different state-of-the-art quantumvariational optimization algorithms in our pruning method.
Solving optimisation problems is a promising near-term application of quantum computers. quantum variational algorithms (QVAs) leverage quantum superposition and entanglement to optimise over exponentially large solut...
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Solving optimisation problems is a promising near-term application of quantum computers. quantum variational algorithms (QVAs) leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an alternating sequence of classically tunable unitaries. However, prior work has primarily addressed discrete optimisation problems. In addition, these algorithms have been designed generally under the assumption of an unstructured solution space, which constrains their speedup to the theoretical limits for the unstructured Grover's quantum search algorithm. In this paper, we show that QVAs can efficiently optimise continuous multivariable functions by exploiting general structural properties of a discretised continuous solution space with a convergence that exceeds the limits of an unstructured quantum search. We present the quantum multivariable optimisation algorithm and demonstrate its advantage over pre-existing methods, particularly when optimising high-dimensional and oscillatory functions.
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