Quantum computing has become increasingly popular in recent years, since it has the potential to outperform classical computation, at least in specific tasks. In principle, this advantage could help many fields of physics research, such as cosmology. Numerical simulations of cosmological observables have become more and more complex and demanding in terms of resources. Quantum computers might help and this thesis is devoted to develop this idea within the NISQ era and its limitations. The work focuses both on introducing quantum algorithms in existing classical codes and on developing a hybrid code to simulate the evolution of DM. The first analysis substitutes the Fast Fourier Transform with the Quantum Fourier Transform to compute the matter power spectrum and shows that the current generation of quantum computers is not enough to produce physically relevant results. The second analysis considers the development of a hybrid classical-quantum code to solve Schr\"{o}dinger-Poisson equations in one dimension. Results in ideal simulators prove that the code can be used to find the correct solution, while real quantum computers allow recovering part of the expected signal only at the price of introducing approximations.
Quantum computing has become increasingly popular in recent years, since it has the potential to outperform classical computation, at least in specific tasks. In principle, this advantage could help many fields of physics research, such as cosmology. Numerical simulations of cosmological observables have become more and more complex and demanding in terms of resources. Quantum computers might help and this thesis is devoted to develop this idea within the NISQ era and its limitations. The work focuses both on introducing quantum algorithms in existing classical codes and on developing a hybrid code to simulate the evolution of DM. The first analysis substitutes the Fast Fourier Transform with the Quantum Fourier Transform to compute the matter power spectrum and shows that the current generation of quantum computers is not enough to produce physically relevant results. The second analysis considers the development of a hybrid classical-quantum code to solve Schr"{o}dinger-Poisson equations in one dimension. Results in ideal simulators prove that the code can be used to find the correct solution, while real quantum computers allow recovering part of the expected signal only at the price of introducing approximations.
Quantum computing is emerging as a promising tool for astrophysics and cosmology, with the potential to address computationally intensive problems more efficiently than classical approaches. In this review, we report recent advances from the INAF Spoke-10 initiative within the Italian National Research Center for High Performance Computing, Big Data and Quantum Computing (ICSC), focused on quantum algorithms and machine learning techniques for astronomical data analysis. We concentrate on two application areas: (1) quantum machine learning for high-energy transients, specifically the detection of Gamma-Ray Bursts (GRBs) with quantum deep-learning models; and (2) quantum algorithms for cosmology, including Quantum Markov Chain Monte Carlo and Quantum Genetic Algorithms, together with developments of Quantum Fourier Transform methods. Quantum machine learning models for GRB detection, such as autoencoders, are tested on simulated space telescope data, achieving performance comparable to classical deep learning methods and indicating potential benefits in data-limited or constrained scenarios. For cosmology, hybrid quantum–classical algorithms have been developed to determine best-fit parameters, sample posterior distributions for standard cosmological models, and perform Quantum Fast Fourier transforms for the Cosmic Microwave Background (CMB) radiation. These methods are validated on benchmark problems, providing results consistent with established classical methods. We discuss the implications for astrophysical and cosmological analysis. While the field is still in its early stages and no quantum advantage has yet been demonstrated in the presented problems, the progress summarized here highlights both the current capabilities of Noisy Intermediate-Scale Quantum (NISQ) devices and the open challenges. For quantum machine learning, we demonstrated that these algorithms are more effective when data is scarce or highly complex, which might hint at future quantum advantages. We outline future directions for integrating quantum processors into astronomical pipelines and the steps required to realize practical quantum advantages in data-intensive astrophysics and cosmology.
Abstract State-of-the-art cosmological simulations on classical computers are limited by time, energy, and memory usage. Quantum computers can perform some calculations exponentially faster than classical computers, using exponentially less energy and memory, and may enable extremely large simulations that accurately capture the whole dynamic range of structure in the universe within statistically representative cosmic volumes. However, not all computational tasks exhibit a “quantum advantage.” Quantum circuits act linearly on quantum states, so nonlinearities (e.g., self-gravity in cosmological simulations) pose a significant challenge. Here we outline one potential approach to overcome this challenge and solve the (nonlinear) Schrödinger–Poisson equations for the evolution of self-gravitating dark matter, based on a hybrid quantum–classical variational algorithm framework (Lubasch et al.). We demonstrate the method with a proof-of-concept mock quantum simulation, envisioning a future where quantum computers will one day lead simulations of dark matter.
In this thesis, we aim to answer one research question: What is the algorithmic role of classical computing in scaling up quantum computing applicability? Quantum computers have promising potential in offering more efficient solutions to some of the most demanding computational problems in the industry. There has been phenomenal progress in the theory and realization of quantum computers in the last few decades. However, quantum computing is a nascent field of technology and scaling up its computing capacity remains impeded by many open engineering/scientific challenges. One emerging solution to alleviate some of the present limitations is finding clever use of classical pre- and post-processing techniques in tandem with quantum algorithms. This helps to advantageously use scarce quantum computing resources for only a portion of a problem that benefits the most from a quantum computer. In other words, it leads to a hybrid framework in which quantum computers are considered special-purpose co-processors for accelerating specific computational tasks. We aim to develop a hybrid theoretical framework for the role of classical algorithms in scaling up quantum computing. We investigate this by focusing on three distinct limitations. We review each limitation in the context of a different application and propose an original hybrid classical-quantum solution to it. First, we focus on classical algorithms' role in a more resource-efficient compilation and embedding of quantum programs. We propose a classical algorithm that helps to embed larger optimization problems in a quantum annealer. Then we explore how a problem decomposition technique and preprocessing of the input problem can help solve significantly larger optimization problems on a quantum computer. Finally, we propose a completely hybrid quantum algorithm for preparing ground states of quantum Hamiltonians. We achieve orders of magnitude faster convergence by combining classical optimization with variational quantum state preparation.
Quantum computation is by far the most powerful computational model allowed by the laws of physics. By carefully manipulating microscopic systems governed by quantum mechanics, one can efficiently solve computational problems that may be classically intractable; on the contrary, such speed-ups are rarely possible without the help of classical computation, since most quantum algorithms heavily rely on subroutines that are purely classical. A better understanding of the relationship between classical and quantum computation is indispensable, in particular in an era where the first quantum device exceeding classical computational power is within reach. In the first part of the thesis, we study some differences between classical and quantum computation. We first show that quantum cryptographic hashing is maximally resilient against classical leakage, a property beyond reach for any classical hash function. Next, we consider the limitation of strong (amplitude-wise) simulation of quantum computation. We prove an unconditional and explicit complexity lower bound for a category of simulations called monotone strong simulation and further prove conditional complexity lower bounds for general strong simulation techniques. Both results indicate that strong simulation is fundamentally unscalable. In the second part of the thesis, we propose classical algorithms that facilitate quantum computing. We propose a new classical algorithm for the synthesis of a quantum algorithm paradigm called quantum signal processing. Empirically, our algorithm demonstrates numerical stability and acceleration of more than one magnitude compared to state-of-the-art algorithms. Finally, we propose a randomized algorithm for transversally switching between arbitrary stabilizer quantum error-correcting codes. It has the property of preserving the code distance and thus might prove useful for designing fault-tolerant code-switching schemes.
With physical quantum computers becoming increasingly accessible, research on their applications across various fields has advanced rapidly. In this paper, we present the first study of quantum cosmology conducted on physical quantum computers, employing a newly proposed Hybrid Quantum-Classical (HQC) algorithm rather than the commonly used Variational Quantum Eigensolver (VQE). Specifically, we solve a constrained Hamiltonian equation derived by quantizing the Friedmann equation in cosmology. To solve this constraint equation, H |psi> = 0, where H is a Hamiltonian operator and |psi> = |psi(theta)> is the wave function of phase angle theta describing the cosmic quantum state, we iteratively use the quantum computer to compute the eigenvalues of , while a classical computer manages the underlying probability density function within the Probabilistic Bisection Algorithm (PBA) to update theta until the solution of = 0 is achieved to a desired accuracy. Executing our algorithm on IBM's quantum computers, we attain a high-precision solution for theta, achieving approximately 1 percent error.
Quantum computing has emerged as a promising framework for addressing computationally demanding problems in collider physics. In recent years, a growing number of quantum algorithms have been proposed for applications ranging from event generation and parton shower simulation to the evaluation of scattering amplitudes, loop and phase-space integration, and optimization problems relevant to experimental analysis. We provide a concise overview of the main ideas behind these developments, with emphasis on the potential advantages of quantum approaches in comparison with classical methods, as well as on the current limitations imposed by noisy intermediate-scale quantum hardware.