Cosmology is in an era of rapid discovery especially in areas related to dark energy, dark matter and inflation. Quantum cosmology treats the cosmology quantum mechanically and is important when quantum effects need to be accounted for, especially in the very early Universe. Quantum computing is an emerging new method of computing which excels in simulating quantum systems. Quantum computing may have some advantages when simulating quantum cosmology, especially because the Euclidean action of gravity is unbounded from below, making the implementation of Monte Carlo simulation problematic. In this paper we present several examples of the application of quantum computing to cosmology. These include a dark energy model that is related to Kaluza-Klein theory, dark matter models where the dark sector is described by a self interacting gauge field or a conformal scalar field and an inflationary model with a slow roll potential. We implement quantum computations in the IBM QISKit software framework and show how to apply the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) algorithms to solve the Wheeler-DeWitt equation that can be used to describe the cosmology in the mini-superspace approximation. We find excellent agreement with classical computing results and describe the accuracy of the different quantum algorithms. Finally we discuss how these methods can be scaled to larger problems going beyond the mini-superspace approximation where the quantum computer may exceed the performance of classical computation.
Cosmology is in an era of rapid discovery especially in areas related to dark energy, dark matter and inflation. Quantum cosmology treats the cosmology quantum mechanically and is important when quantum effects need to be accounted for, especially in the very early Universe. Quantum computing is an emerging new method of computing which excels in simulating quantum systems. Quantum computing may have some advantages when simulating quantum cosmology, especially because the Euclidean action of gravity is unbounded from below, making the implementation of Monte Carlo simulation problematic. In this paper we present several examples of the application of quantum computing to cosmology. These include a dark energy model that is related to Kaluza-Klein theory, dark matter models where the dark sector is described by a self interacting gauge field or a conformal scalar field and an inflationary model with a slow roll potential. We implement quantum computations in the IBM QISKit software framework and show how to apply the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) algorithms to solve the Wheeler-DeWitt equation that can be used to describe the cosmology in the mini-superspace approximation. We find excellent agreement with classical computing results and describe the accuracy of the different quantum algorithms. Finally we discuss how these methods can be scaled to larger problems going beyond the mini-superspace approximation where the quantum computer may exceed the performance of classical computation.
Quantum computers are promising candidates to radically expand the domain of computational science by their increased computing power and more effective algorithms. In particular, quantum computing could have a tremendous impact on the field of quantum cosmology. The goal of quantum cosmology is to describe the evolution of the universe through the Wheeler-DeWitt equation or path integral methods without having to first formulate a full theory of quantum gravity. The quantum computer provides an advantage in this endeavor because it can perform path integrals directly in Lorentzian space and does not require constructing contour integrations in Euclidean gravity. Also, quantum computers can provide advantages in systems with fermions which are difficult to simulate on classical computers. In this study, we first employed classical computational methods to analyze a Friedmann-Robertson-Walker mini-superspace with a scalar field and visualize the calculated wavefunction of the universe for a variety of different values of the curvature of the universe and the cosmological constant. We then used IBM's Quantum Information Science Kit Python library and the variational quantum eigensolver algorithm to study the same systems on a quantum computer. The framework was extended to the world line approach to quantum field theory.
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.
With the emergence of quantum computing we can, in theory, run complex simulations with many variables. For the field of cosmology, this could lend itself to applications in modeling the early universe as a quantum system to better understand large scale properties of the universe today. Here we utilize the hybrid variational quantum eigensolver (VQE) algorithm applied to an anharmonic oscillator system using QISKit to examine it's effectiveness for these cosmological questions. We then analyze a 1+1 dimensional ring of scalar bosons acting on a lattice as a naive model of the early universe. We chose to focus on rings of 3 and 5 massive scalars in 1+1 dimensions for our study to test the effectiveness of our approach.
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 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.
One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to the Wheeler-DeWitt equation. However, solutions to the equation are known only for specific symmetry-reduced systems, including models of quantum cosmology. Novel methods, which enable solving the equation for complex gravitational configurations, are therefore worth seeking. Here, we propose and investigate a new method of solving the Wheeler-DeWitt equation for minisuperspace models (with a finite number of classical degrees of freedom). The approach employs variational quantum algorithms and is possible to implement on quantum computers. For this purpose, the gravitational system is regularized, by performing spherical compactification of the phase space. This makes the system's Hilbert space finite dimensional and allows to use SU(2) variables, which are easy to handle in quantum computing. The validity of the method is examined in the case of the flat de Sitter universe. Both an emulator of a quantum computer and the IBM superconducting quantum computer have been used. The advantages and limitations of the approach are discussed.