Searcharxiv⌕ Search

arXiv subjects

Francesco Petruccione

Publications and source records attributed to Francesco Petruccione.

At least 55 records · Page 3Linked to original sources
arXiv2023

Hierarchical quantum circuit representations for neural architecture search

Machine learning with hierarchical quantum circuits, usually referred to as Quantum Convolutional Neural Networks (QCNNs), is a promising prospect for near-term quantum computing. The QCNN is a circuit model inspired by the architecture of Convolutional Neural Networks (CNNs). CNNs are successful because they do not need manual feature design and can learn high-level features from raw data. Neural Architecture Search (NAS) builds on this success by learning network architecture and achieves state-of-the-art performance. However, applying NAS to QCNNs presents unique challenges due to the lack of a well-defined search space. In this work, we propose a novel framework for representing QCNN architectures using techniques from NAS, which enables search space design and architecture search. Using this framework, we generate a family of popular QCNNs, those resembling reverse binary trees. We then evaluate this family of models on a music genre classification dataset, GTZAN, to justify the importance of circuit architecture. Furthermore, we employ a genetic algorithm to perform Quantum Phase Recognition (QPR) as an example of architecture search with our representation. This work provides a way to improve model performance without increasing complexity and to jump around the cost landscape to avoid barren plateaus. Finally, we implement the framework as an open-source Python package to enable dynamic QCNN creation and facilitate QCNN search space design for NAS.

quant-ph↗
arXiv2023

Hybrid Genetic Optimisation for Quantum Feature Map Design

Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and doesn't require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20\% larger) that improve further with circuit parameter training.

quant-ph↗
arXiv2023

Classical Ensembles of Single-Qubit Quantum Variational Circuits for Classification

The quantum asymptotically universal multi-feature (QAUM) encoding architecture was recently introduced and showed improved expressivity and performance in classifying pulsar stars. The circuit uses generalized trainable layers of parameterized single-qubit rotation gates and single-qubit feature encoding gates. Although the improvement in classification accuracy is promising, the single-qubit nature of this architecture, combined with the circuit depth required for accuracy, limits its applications on NISQ devices due to their low coherence times. This work reports on the design, implementation, and evaluation of ensembles of single-qubit QAUM classifiers using classical bagging and boosting techniques. We demonstrate an improvement in validation accuracy for pulsar star classification. We find that this improvement is not problem-specific as we observe consistent improvements for the MNIST Digits and Wisconsin Cancer datasets. We also observe that the boosting ensemble achieves an acceptable level of accuracy with only a small amount of training, while the bagging ensemble achieves higher overall accuracy with ample training time. This shows that classical ensembles of single-qubit circuits present a new approach for certain classification problems.

quant-ph↗
arXiv2022

Statistical and machine learning approaches for prediction of long-time excitation energy transfer dynamics

One of the approaches used to solve for the dynamics of open quantum systems is the hierarchical equations of motion (HEOM). Although it is numerically exact, this method requires immense computational resources to solve. The objective here is to demonstrate whether models such as SARIMA, CatBoost, Prophet, convolutional and recurrent neural networks are able to bypass this requirement. We are able to show this successfully by first solving the HEOM to generate a data set of time series that depict the dissipative dynamics of excitation energy transfer in photosynthetic systems then, we use this data to test the models ability to predict the long-time dynamics when only the initial short-time dynamics is given. Our results suggest that the SARIMA model can serve as a computationally inexpensive yet accurate way to predict long-time dynamics.

quant-ph↗
arXiv2022

Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps

We study the convex combinations of the $(d+1)$ generalized Pauli dynamical maps in a Hilbert space of dimension $d$. For certain choices of the decoherence function, the maps are noninvertible and they remain under convex combinations as well. For the case of dynamical maps characterized by the decoherence function $(1-e^{-ct})/n$ with the decoherence parameter $n$ and decay factor $c$, we evaluate the fraction of invertible maps obtained upon mixing, which is found to increase superexponentially with dimension $d$.

quant-ph↗
arXiv2022

Compact quantum kernel-based binary classifier

Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in parallel. For practical applications of these quantum machine learning methods, an important issue is to minimize the size of quantum circuits. We present the simplest quantum circuit for constructing a kernel-based binary classifier. This is achieved by generalizing the interference circuit to encode data labels in the relative phases of the quantum state and by introducing compact amplitude encoding, which encodes two training data vectors into one quantum register. When compared to the simplest known quantum binary classifier, the number of qubits is reduced by two and the number of steps is reduced linearly with respect to the number of training data. The two-qubit measurement with post-selection required in the previous method is simplified to single-qubit measurement. Furthermore, the final quantum state has a smaller amount of entanglement than that of the previous method, which advocates the cost-effectiveness of our method. Our design also provides a straightforward way to handle an imbalanced data set, which is often encountered in many machine learning problems.

quant-ph↗
arXiv2022

Configurable sublinear circuits for quantum state preparation

The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A persistent obstacle to using such algorithms for solving a wide range of real-world problems is the cost of loading classical data to a quantum state. Several quantum circuit-based methods have been proposed for encoding classical data as probability amplitudes of a quantum state. However, they require either quantum circuit depth or width to grow linearly with the data size, even though the other dimension of the quantum circuit grows logarithmically. In this paper, we present a configurable bidirectional procedure that addresses this problem by tailoring the resource trade-off between quantum circuit width and depth. In particular, we show a configuration that encodes an $N$-dimensional state by a quantum circuit with $O(\sqrt{N})$ width and depth and entangled information in ancillary qubits. We show a proof-of-principle on five quantum computers and compare the results.

quant-ph↗
arXiv2021

Machine learning for excitation energy transfer dynamics

A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through photosynthetic light harvesting complexes (LHCs). The hierarchical equations of motion (HEOM) was adapted by Ishizaki and Fleming (J. Chem. Phys., 2009) to simulate open quantum dynamics in the biological regime. We generate a set of time dependent observables that depict the coherent propagation of electronic excitations through the LHCs by solving the HEOM. We solve the inverse problem using classical machine learning (ML) models as this is a computationally intractable problem. The objective here is to determine whether a trained ML model can perform Hamiltonian tomography by using the time dependence of the observables as inputs. We demonstrate the capability of convolutional neural networks to tackle this research problem. The models developed here can predict Hamiltonian parameters such as excited state energies and inter-site couplings of a system up to 99.28\% accuracy and mean-squared error as low as 0.65.

quant-ph↗
arXiv2021

Bad vibrations: Quantum tunnelling in the context of SARS-CoV-2 infection

The SARS-CoV-2 pandemic has added new urgency to the study of viral mechanisms of infection. But while vaccines offer a measure of protection against this specific outbreak, a new era of pandemics has been predicted. In addition to this, COVID-19 has drawn attention to post-viral syndromes and the healthcare burden they entail. It seems integral that knowledge of viral mechanisms is increased through as wide a research field as possible. To this end we propose that quantum biology might offer essential new insights into the problem, especially with regards to the important first step of virus-host invasion. Research in quantum biology often centres around energy or charge transfer. While this is predominantly in the context of photosynthesis there has also been some suggestion that cellular receptors such as olfactory or neural receptors might employ vibration assisted electron tunnelling to augment the lock-and-key mechanism. Quantum tunnelling has also been observed in enzyme function. Enzymes are implicated in the invasion of host cells by the SARS-CoV-2 virus. Receptors such as olfactory receptors also appear to be disrupted by COVID-19. Building on these observations we investigate the evidence that quantum tunnelling might be important in the context of infection with SARS-CoV-2. We illustrate this with a simple model relating the vibronic mode of, for example, a viral spike protein to the likelihood of charge transfer in an idealised receptor. Our results show a distinct parameter regime in which the vibronic mode of the spike protein enhances electron transfer. With this in mind, novel therapeutics to prevent SARS-CoV-2 transmission could potentially be identified by their vibrational spectra.

physics.bio-ph↗
arXiv2021

A divide-and-conquer algorithm for quantum state preparation

Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

quant-ph↗
arXiv2021

Near Term Algorithms for Linear Systems of Equations

Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an exponential speed-up over classical algorithms in some cases, it requires a fault-tolerant quantum computer, which is unlikely to be available in the near term. Thus, attention has turned to the investigation of quantum algorithms for noisy intermediate-scale quantum (NISQ) devices where several near-term approaches to solving systems of linear equations have been proposed. This paper focuses on the Variational Quantum Linear Solvers (VQLS), and other closely related methods. This paper makes several contributions that include: the first application of the Evolutionary Ansatz to the VQLS (EAVQLS), the first implementation of the Logical Ansatz VQLS (LAVQLS), based on the Classical Combination of Quantum States (CQS) method, the first proof of principle demonstration of the CQS method on real quantum hardware and a method for the implementation of the Adiabatic Ansatz (AAVQLS). These approaches are implemented and contrasted.

quant-ph↗
arXiv2021

Pseudomode description of general open quantum system dynamics: non-perturbative master equation for the spin-boson model

We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set of damped harmonic oscillators - the pseudomodes - thereby forming an enlarged open system whose dynamics is governed by a Markovian master equation. Each pseudomode is connected to one of the poles of the spectral density when analytically continued to the lower-half complex frequency plane. Here, we extend previous results to a completely generic class of open system models, and discuss how our framework can be used as a powerful and versatile tool for analyzing non-Markovian open system dynamics. The effectiveness of the method is demonstrated on the spin-boson model by accurately benchmarking its predictions against numerically exact results.

quant-ph↗
arXiv2021

A Comparison of Various Classical Optimizers for a Variational Quantum Linear Solver

Variational Hybrid Quantum Classical Algorithms (VHQCAs) are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices. These algorithms employ a parameterized quantum circuit (ansatz) and a quantum-classical feedback loop. A classical device is used to optimize the parameters in order to minimize a cost function that can be computed far more efficiently on a quantum device. The cost function is constructed such that finding the ansatz parameters that minimize its value, solves some problem of interest. We focus specifically on the Variational Quantum Linear Solver (VQLS), and examine the effect of several gradient-free and gradient-based classical optimizers on performance. We focus on both the average rate of convergence of the classical optimizers studied, as well as the distribution of their average termination cost values, and how these are affected by noise. Our work demonstrates that realistic noise levels on NISQ devices present a challenge to the optimization process. All classical optimizers appear to be very negatively affected by the presence of realistic noise. If noise levels are significantly improved, there may be a good reason for preferring gradient-based methods in the future, which performed better than the gradient-free methods with the only shot-noise present. The gradient-free optimizers, Simultaneous Perturbation Stochastic Approximation (SPSA) and Powell's method, and the gradient-based optimizers, AMSGrad and BFGS performed the best in the noisy simulation, and appear to be less affected by noise than the rest of the methods. SPSA appears to be the best performing method. COBYLA, Nelder-Mead and Conjugate-Gradient methods appear to be the most heavily affected by noise, with even slight noise levels significantly impacting their performance.

quant-ph↗
arXiv2021

Robust quantum classifier with minimal overhead

To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the potential to significantly enhance existing classical machine learning methods, and several quantum algorithms for binary classification based on the kernel method have been proposed. These algorithms rely on estimating an expectation value, which in turn requires an expensive quantum data encoding procedure to be repeated many times. In this work, we calculate explicitly the number of repetition necessary for acquiring a fixed success probability and show that the Hadamard-test and the swap-test circuits achieve the optimal variance in terms of the quantum circuit parameters. The variance, and hence the number of repetition, can be further reduced only via optimization over data-related parameters. We also show that the kernel-based binary classification can be performed with a single-qubit measurement regardless of the number and the dimension of the data. Finally, we show that for a number of relevant noise models the classification can be performed reliably without quantum error correction. Our findings are useful for designing quantum classification experiments under limited resources, which is the common challenge in the noisy intermediate-scale quantum era.

quant-ph↗
arXiv2021

Initial entanglement, entangling unitaries, and completely positive maps

The problem of conditions on the initial correlations between the system and the environment that lead to completely positive (CP) or not-completely positive (NCP) maps has been studied by various authors. Two lines of study may be discerned: one concerned with families of initial correlations that induce CP dynamics under the application of an arbitrary joint unitary on the system and environment; the other concerned with specific initial states that may be highly entangled. Here we study the latter problem, and highlight the interplay between the initial correlations and the unitary applied. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.

quant-ph↗
arXiv2020

Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes

We develop an exact framework to describe the non-Markovian dynamics of an open quantum system interacting with an environment modeled by a generalized spectral density function. The approach relies on mapping the initial system onto an auxiliary configuration, comprising the original open system coupled to a small number of discrete modes, which in turn are each coupled to an independent Markovian reservoir. Based on the connection between the discrete modes and the poles of the spectral density function, we show how expanding the system using the discrete modes allows for the full inclusion non-Markovian effects within an enlarged open system whose dynamics is governed by an exact Lindblad master equation. Initially we apply this result to obtain a generalization of the pseudomode method [B. M. Garraway, Phys. Rev. A 55, 2290 (1997)] in cases where the spectral density function has a Lorentzian structure. For many other types of spectral density function, we extend our proof to show that an open system dynamics may be modeled physically using discrete modes which admit a non-Hermitian coupling to the system, and for such cases determine the equivalent master equation to no longer be of Lindblad form. For applications involving two discrete modes, we demonstrate how to convert between pathological and Lindblad forms of the master equation using the techniques of the pseudomode method.

quant-ph↗
arXiv2020

Negative contributions to entropy production induced by quantum coherences

The entropy production in dissipative processes is the essence of the arrow of time and the second law of thermodynamics. For dissipation of quantum systems, it was recently shown that the entropy production contains indeed two contributions: a classical one and a quantum one. Here we show that for degenerate (or near-degenerate) quantum systems there are additional quantum contributions which, remarkably, can become negative. Furthermore, such negative contributions are related to significant changes in the ongoing thermodynamics. This includes phenomena such as generation of coherences between degenerate energy levels (called horizontal coherences), alteration of energy exchanges and, last but not least, reversal of the natural convergence of the populations toward the thermal equilibrium state. Going further, we establish a complementarity relation between horizontal coherences and population convergence, particularly enlightening for understanding heat flow reversals. Conservation laws of the different types of coherences are derived. Some consequences for thermal machines and resource theory of coherence are suggested.

quant-ph↗