874 research outputs found
Expressibility-Enhancing Strategies for Quantum Neural Networks
Quantum neural networks (QNNs), represented by parameterized quantum
circuits, can be trained in the paradigm of supervised learning to map input
data to predictions. Much work has focused on theoretically analyzing the
expressive power of QNNs. However, in almost all literature, QNNs' expressive
power is numerically validated using only simple univariate functions. We
surprisingly discover that state-of-the-art QNNs with strong expressive power
can have poor performance in approximating even just a simple sinusoidal
function. To fill the gap, we propose four expressibility-enhancing strategies
for QNNs: Sinusoidal-friendly embedding, redundant measurement,
post-measurement function, and random training data. We analyze the
effectiveness of these strategies via mathematical analysis and/or numerical
studies including learning complex sinusoidal-based functions. Our results from
comparative experiments validate that the four strategies can significantly
increase the QNNs' performance in approximating complex multivariable functions
and reduce the quantum circuit depth and qubits required.Comment: 16 pages, 11 figure
Efficient Online Quantum Generative Adversarial Learning Algorithms with Applications
The exploration of quantum algorithms that possess quantum advantages is a
central topic in quantum computation and quantum information processing. One
potential candidate in this area is quantum generative adversarial learning
(QuGAL), which conceptually has exponential advantages over classical
adversarial networks. However, the corresponding learning algorithm remains
obscured. In this paper, we propose the first quantum generative adversarial
learning algorithm-- the quantum multiplicative matrix weight algorithm
(QMMW)-- which enables the efficient processing of fundamental tasks. The
computational complexity of QMMW is polynomially proportional to the number of
training rounds and logarithmically proportional to the input size. The core
concept of the proposed algorithm combines QuGAL with online learning. We
exploit the implementation of QuGAL with parameterized quantum circuits, and
numerical experiments for the task of entanglement test for pure state are
provided to support our claims
The effect of the processing and measurement operators on the expressive power of quantum models
There is an increasing interest in Quantum Machine Learning (QML) models, how
they work and for which applications they could be useful. There have been many
different proposals on how classical data can be encoded and what circuit
ans\"atze and measurement operators should be used to process the encoded data
and measure the output state of an ansatz. The choice of the aforementioned
operators plays a determinant role in the expressive power of the QML model. In
this work we investigate how certain changes in the circuit structure change
this expressivity. We introduce both numerical and analytical tools to explore
the effect that these operators have in the overall performance of the QML
model. These tools are based on previous work on the teacher-student scheme,
the partial Fourier series and the averaged operator size. We focus our
analysis on simple QML models with two and three qubits and observe that
increasing the number of parameterized and entangling gates leads to a more
expressive model for certain circuit structures. Also, on which qubit the
measurement is performed affects the type of functions that QML models could
learn. This work sketches the determinant role that the processing and
measurement operators have on the expressive power of simple quantum circuits
Hierarchical quantum classifiers
Quantum circuits with hierarchical structure have been used to perform binary
classification of classical data encoded in a quantum state. We demonstrate
that more expressive circuits in the same family achieve better accuracy and
can be used to classify highly entangled quantum states, for which there is no
known efficient classical method. We compare performance for several different
parameterizations on two classical machine learning datasets, Iris and MNIST,
and on a synthetic dataset of quantum states. Finally, we demonstrate that
performance is robust to noise and deploy an Iris dataset classifier on the
ibmqx4 quantum computer
Are Quantum Circuits Better than Neural Networks at Learning Multi-dimensional Discrete Data? An Investigation into Practical Quantum Circuit Generative Models
Are multi-layer parameterized quantum circuits (MPQCs) more expressive than
classical neural networks (NNs)? How, why, and in what aspects? In this work,
we survey and develop intuitive insights into the expressive power of MPQCs in
relation to classical NNs. We organize available sources into a systematic
proof on why MPQCs are able to generate probability distributions that cannot
be efficiently simulated classically. We first show that instantaneous quantum
polynomial circuits (IQPCs), are unlikely to be simulated classically to within
a multiplicative error, and then show that MPQCs efficiently generalize IQPCs.
We support the surveyed claims with numerical simulations: with the MPQC as the
core architecture, we build different versions of quantum generative models to
learn a given multi-dimensional, multi-modal discrete data distribution, and
show their superior performances over a classical Generative Adversarial
Network (GAN) equipped with the Gumbel Softmax for generating discrete data. In
addition, we address practical issues such as how to efficiently train a
quantum circuit with only limited samples, how to efficiently calculate the
(quantum) gradient, and how to alleviate modal collapse. We propose and
experimentally verify an efficient training-and-fine-tuning scheme for lowering
the output noise and decreasing modal collapse. As an original contribution, we
develop a novel loss function (MCR loss) inspired by an information-theoretical
measure -- the coding rate reduction metric, which has a more expressive and
geometrically meaningful latent space representations -- beneficial for both
model selection and alleviating modal collapse. We derive the gradient of our
MCR loss with respect to the circuit parameters under two settings: with the
radial basis function (RBF) kernel and with a NN discriminator and conduct
experiments to showcase its effectiveness
- …