23 research outputs found
ANALOG QUANTUM SIMULATORS FOR QUANTUM ADVANTAGE AND QUANTUM MACHINE LEARNING
No full textPh.DDOCTOR OF PHILOSOPHY (CQT
Variational Quantum Simulation: A Case Study for Understanding Warm Starts
No full textThe barren plateau phenomenon, characterized by loss gradients that vanish exponentially with system size, poses a challenge to scaling variational quantum algorithms. Here we explore the potential of warm starts, whereby one initializes closer to a solution in the hope of enjoying larger loss variances. Focusing on an iterative variational method for learning shorter-depth circuits for quantum real-Time evolution we conduct a case study to elucidate the potential and limitations of warm starts. We start by proving that the iterative variational algorithm will exhibit substantial (at worst vanishing polynomially in system size) gradients in a small region around the initializations at each time step. Convexity guarantees for these regions are then established, suggesting trainability for polynomial-size time steps. However, our study highlights scenarios where a good minimum shifts outside the region with trainability guarantees. Our analysis leaves open the question whether such minima jumps necessitate optimization across barren plateau landscapes or whether there exist gradient flows, i.e., fertile valleys away from the plateau with substantial gradients, that allow for training. While our main focus is on this case study of variational quantum simulation, we end by discussing how our results work in other iterative settings.QI
Exponential concentration in quantum kernel methods
No full textAbstract Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods
A Unified Framework for Trace-induced Quantum Kernels
No full textQuantum kernel methods are promising candidates for achieving a practical
quantum advantage for certain machine learning tasks. Similar to classical
machine learning, an exact form of a quantum kernel is expected to have a great
impact on the model performance. In this work we combine all trace-induced
quantum kernels, including the commonly-used global fidelity and local
projected quantum kernels, into a common framework. We show how generalized
trace-induced quantum kernels can be constructed as combinations of the
fundamental building blocks we coin "Lego" kernels, which impose an inductive
bias on the resulting quantum models. We relate the expressive power and
generalization ability to the number of non-zero weight Lego kernels and
propose a systematic approach to increase the complexity of a quantum kernel
model, leading to a new form of the local projected kernels that require fewer
quantum resources in terms of the number of quantum gates and measurement
shots. We show numerically that models based on local projected kernels can
achieve comparable performance to the global fidelity quantum kernel. Our work
unifies existing quantum kernels and provides a systematic framework to compare
their properties.Comment: 12 + 15 pages, 5 figure
Exponential concentration in quantum kernel methods
No full textKernel methods in Quantum Machine Learning (QML) have recently gained
significant attention as a potential candidate for achieving a quantum
advantage in data analysis. Among other attractive properties, when training a
kernel-based model one is guaranteed to find the optimal model's parameters due
to the convexity of the training landscape. However, this is based on the
assumption that the quantum kernel can be efficiently obtained from quantum
hardware. In this work we study the performance of quantum kernel models from
the perspective of the resources needed to accurately estimate kernel values.
We show that, under certain conditions, values of quantum kernels over
different input data can be exponentially concentrated (in the number of
qubits) towards some fixed value. Thus on training with a polynomial number of
measurements, one ends up with a trivial model where the predictions on unseen
inputs are independent of the input data. We identify four sources that can
lead to concentration including: expressivity of data embedding, global
measurements, entanglement and noise. For each source, an associated
concentration bound of quantum kernels is analytically derived. Lastly, we show
that when dealing with classical data, training a parametrized data embedding
with a kernel alignment method is also susceptible to exponential
concentration. Our results are verified through numerical simulations for
several QML tasks. Altogether, we provide guidelines indicating that certain
features should be avoided to ensure the efficient evaluation of quantum
kernels and so the performance of quantum kernel methods.Comment: 15+50 pages, 15 figure
Variational quantum simulation: a case study for understanding warm starts
No full textThe barren plateau phenomenon, characterized by loss gradients that vanish
exponentially with system size, poses a challenge to scaling variational
quantum algorithms. Here we explore the potential of warm starts, whereby one
initializes closer to a solution in the hope of enjoying larger loss variances.
Focusing on an iterative variational method for learning shorter-depth circuits
for quantum real and imaginary time evolution we conduct a case study to
elucidate the potential and limitations of warm starts. We start by proving
that the iterative variational algorithm will exhibit substantial (at worst
vanishing polynomially in system size) gradients in a small region around the
initializations at each time-step. Convexity guarantees for these regions are
then established, suggesting trainability for polynomial size time-steps.
However, our study highlights scenarios where a good minimum shifts outside the
region with trainability guarantees. Our analysis leaves open the question
whether such minima jumps necessitate optimization across barren plateau
landscapes or whether there exist gradient flows, i.e., fertile valleys away
from the plateau with substantial gradients, that allow for training.Comment: 9 + 26 pages, 5 + 2 figure
Subtleties in the trainability of quantum machine learning models
No full textA new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This field, called quantum machine learning (QML), aims to achieve a speedup over traditional machine learning for data analysis. However, its success usually hinges on efficiently training the parameters in quantum neural networks, and the field of QML is still lacking theoretical scaling results for their trainability. Some trainability results have been proven for a closely related field called variational quantum algorithms (VQAs). While both fields involve training a parametrized quantum circuit, there are crucial differences that make the results for one setting not readily applicable to the other. In this work, we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models. Our results indicate that features deemed detrimental for VQA trainability can also lead to issues such as barren plateaus in QML. Consequently, our work has implications for several QML proposals in the literature. In addition, we provide theoretical and numerical evidence that QML models exhibit further trainability issues not present in VQAs, arising from the use of a training dataset. We refer to these as dataset-induced barren plateaus. These results are most relevant when dealing with classical data, as here the choice of embedding scheme (i.e., the map between classical data and quantum states) can greatly affect the gradient scaling.QI
Signatures of a sampling quantum advantage in driven quantum many-body systems
No full textA crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can perform a computation task that is classically intractable. A key question is to identify setups that can achieve such goal within current technologies. In this work, we provide formal evidence that sampling bit-strings from a periodic evolution of a unitary drawn from the circular orthogonal ensemble (COE) cannot be efficiently simulated with classical computers. As the statistical properties of COE coincide with a large class of driven analog quantum systems thanks to the Floquet eigenstate thermalization hypothesis, our results indicate the possibility that those driven systems could constitute practical candidates for a sampling quantum advantage. To further support this, we give numerical examples of driven disordered Ising chains and 1D driven Bose-Hubbard model.QI
Subtleties in the trainability of quantum machine learning models
No full textA new paradigm for data science has emerged, with quantum data, quantum
models, and quantum computational devices. This field, called Quantum Machine
Learning (QML), aims to achieve a speedup over traditional machine learning for
data analysis. However, its success usually hinges on efficiently training the
parameters in quantum neural networks, and the field of QML is still lacking
theoretical scaling results for their trainability. Some trainability results
have been proven for a closely related field called Variational Quantum
Algorithms (VQAs). While both fields involve training a parametrized quantum
circuit, there are crucial differences that make the results for one setting
not readily applicable to the other. In this work we bridge the two frameworks
and show that gradient scaling results for VQAs can also be applied to study
the gradient scaling of QML models. Our results indicate that features deemed
detrimental for VQA trainability can also lead to issues such as barren
plateaus in QML. Consequently, our work has implications for several QML
proposals in the literature. In addition, we provide theoretical and numerical
evidence that QML models exhibit further trainability issues not present in
VQAs, arising from the use of a training dataset. We refer to these as
dataset-induced barren plateaus. These results are most relevant when dealing
with classical data, as here the choice of embedding scheme (i.e., the map
between classical data and quantum states) can greatly affect the gradient
scaling.Comment: 12+12 pages, 8+2 figure
Latent Style-based Quantum GAN for high-quality Image Generation
No full textQuantum generative modeling is among the promising candidates for achieving a practical advantage in data analysis. Nevertheless, one key challenge is to generate large-size images comparable to those generated by their classical counterparts. In this work, we take an initial step in this direction and introduce the Latent Style-based Quantum GAN (LaSt-QGAN), which employs a hybrid classical-quantum approach in training Generative Adversarial Networks (GANs) for arbitrary complex data generation. This novel approach relies on powerful classical auto-encoders to map a high-dimensional original image dataset into a latent representation. The hybrid classical-quantum GAN operates in this latent space to generate an arbitrary number of fake features, which are then passed back to the auto-encoder to reconstruct the original data. Our LaSt-QGAN can be successfully trained on realistic computer vision datasets beyond the standard MNIST, namely Fashion MNIST (fashion products) and SAT4 (Earth Observation images) with 10 qubits, resulting in a comparable performance (and even better in some metrics) with the classical GANs. Moreover, we analyze the barren plateau phenomena within this context of the continuous quantum generative model using a polynomial depth circuit and propose a method to mitigate the detrimental effect during the training of deep-depth networks. Through empirical experiments and theoretical analysis, we demonstrate the potential of LaSt-QGAN for the practical usage in the context of image generation and open the possibility of applying it to a larger dataset in the future
