Optimal Tuning of Quantum Generative Adversarial Networks for Multivariate Distribution Loading

Agliardi, Gabriele; Prati, Enrico

doi:10.3390/quantum4010006

Cited by 25 publications

(11 citation statements)

References 67 publications

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“…One possible approach utilizes quantum generative adversarial networks (qGAN) to tune the parameters in variational circuits to load a given distribution [43]. Some work on using qGANs to produce multivariate quantum states has also been conducted [44,45]. Alternatively, Rattew et al demonstrate how normal distributions may be efficiently produced in a manner resistant to most hardware errors [46].…”

Section: Discussionmentioning

confidence: 99%

Preparing Arbitrary Continuous Functions in Quantum Registers With Logarithmic Complexity

Rattew¹,

Koczor²

2022

Preprint

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Quantum computers will be able solve important problems with significant polynomial and exponential speedups over their classical counterparts, for instance in option pricing in finance, and in real-space molecular chemistry simulations. However, key applications can only achieve their potential speedup if their inputs are prepared efficiently. We effectively solve the important problem of efficiently preparing quantum states following arbitrary continuous (as well as more general) functions with complexity logarithmic in the desired resolution, and with rigorous error bounds. This is enabled by the development of a fundamental subroutine based off of the simulation of rank-1 projectors. Combined with diverse techniques from quantum information processing, this subroutine enables us to present a broad set of tools for solving practical tasks, such as state preparation, numerical integration of Lipschitz continuous functions, and superior sampling from probability density functions. As a result, our work has significant implications in a wide range of applications, for instance in financial forecasting, and in quantum simulation.

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Section: Discussionmentioning

confidence: 99%

Preparing Arbitrary Continuous Functions in Quantum Registers With Logarithmic Complexity

Rattew¹,

Koczor²

2022

Preprint

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“…If T can be calculated by some arithmetic, V can be implemented by so-called Grover-Rudolph method [41], using a logarithmic number of arithmetic circuits with respect to the number of grid points for discrete approximation. Recently, some methods that avoid usage of arithmetic circuits have been proposed [42][43][44][45][46], including variational ones such as quantum generative adversarial network [47][48][49][50][51][52][53][54].…”

Section: A Modified Quantum Walk Operatormentioning

confidence: 99%

Quantum algorithms for Monte Carlo integration using pseudo-random numbers

Miyamoto

2021

2021 IEEE International Conference on Quantum Computing and Engineering (QCE)

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“…Alternatively, another encoding option consists in storing the information as coefficients of a superposition of quantum states [27][28][29][30][31][32]. The encoding efficiency becomes exponential as an n-qubit state is an element of a 2 n -dimensional vector space.…”

Section: Introductionmentioning

confidence: 99%

Quantum activation functions for quantum neural networks

Maronese

Destri

Prati

2022

Quantum Inf Process

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The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here, we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement–based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik’s theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.

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Optimal Tuning of Quantum Generative Adversarial Networks for Multivariate Distribution Loading

Cited by 25 publications

References 67 publications

Preparing Arbitrary Continuous Functions in Quantum Registers With Logarithmic Complexity

Preparing Arbitrary Continuous Functions in Quantum Registers With Logarithmic Complexity

Quantum algorithms for Monte Carlo integration using pseudo-random numbers

Quantum activation functions for quantum neural networks

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