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 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.
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.
Variational methods have long been used to study strongly-correlated quantum systems. Despite the successes of classical protocols, these are limited in the study of quantum systems, either due to numerical errors like the sign problem or the massive memory requirement to represent large quantum systems. Variational quantum eigensolvers (VQEs) overcome these problems and as a result have been an exciting area of research for the past decade. VQEs use a hybrid classical-quantum set-up, where a cost function (usually the expectation value of an operator) is produced by the quantum processor and then optimized on a classical computer. VQEs have been applied to fields such as quantum chemistry, condensed matter physics, high-energy physics, and classical optimization problems. In this thesis, we investigate VQEs to study gauge theories, which describe fundamental physical interactions and are hard to simulate classically. We use two different approaches in implementing a VQE to study two classes of problems. In the first half of the thesis, we design a VQE to study the U(1) Higgs gauge theory in one spatial dimension. This model is particularly interesting due to the presence of a topological term, which is a candidate to explain the observed CP violation in the universe. In order to perform a quantum simulation of the U(1) Higgs model, the theory is cast on a lattice. In the limit where the lattice size is large and the lattice spacing is small, the continuum limit can be reached and the results correctly resemble the original theory. However, when the lattice is too small or the spacing too big, results are spoiled by finite size effects. In this thesis, we investigate the effects of a finite lattice and determine the parameters to correctly reproduce a first-order phase transition of the continuous theory. Importantly, to resemble a realistic experiment, we include the statistical and intrinsic quantum noise in our VQE. We design the protocol to be applied on a microwave-photonic platform, which is well-suited due to the bosonic nature of the theory's electrical modes. \nIn the second half of the thesis, we design a new class of VQEs, based on a measurement-based quantum computer (MBQC) instead of the typical circuit-based set-up. Rather than performing gates on an initial state, a MBQC transforms an initial state by entangling it with a number of auxiliary qubits which are subsequently measured, resulting in a modification of the initial state. In this part of the thesis, we compare the standard, circuit-based VQE with our newly-designed measurement-based VQE (MB-VQE) through two meaningful examples. First, we introduce a novel way to construct variational state families, using measurement-based techniques, that is more costly to access with circuit-based VQEs. We apply this technique to find the ground state of a two-dimensional, periodic Z2 matter-free lattice gauge theory. In the second approach, we directly translate \nthe circuit-based VQE to a MB-VQE and apply this to the U(1) Schwinger lattice gauge theory, which is used as a benchmarking problem for VQEs. These examples demonstrate that there are specific problems which are better suited for a MB-VQE.
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.
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers.Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the system dimension, where the interactions between divided subsystems are taken as an effective Hamiltonian expanded by the reduced basis.Then the effective Hamiltonian is further solved by the VQE, which we call deep VQE.Deep VQE allows us to apply quantum-classical hybrid algorithms on small-scale quantum computers to large systems with strong intrasubsystem interactions and weak intersubsystem interactions, or strongly correlated spin models on large regular lattices.As proof-of-principle numerical demonstrations, we use the proposed method for quasi-one-dimensional models, including one-dimensionally coupled 12-qubit Heisenberg antiferromagnetic models on kagome lattices as well as two-dimensional Heisenberg antiferromagnetic models on square lattices.The largest problem size of 64 qubits is solved by simulating 20-qubit quantum computers with a reasonably good accuracy approximately a few %.The proposed scheme enables us to handle the problems of > 1000 qubits by concatenating VQEs with a few tens of qubits.While it is unclear how accurate ground-state energy can be obtained for such a large system, our numerical results on a 64-qubit system suggest that deep VQE provides a good approximation (discrepancy within a few percent) and has room for further improvement.Therefore, deep VQE provides us a promising pathway to solve practically important problems on noisy intermediate-scale quantum computers.
Anharmonic potential quantum system play crucial role in physics as they provide a more realistic description of oscillatory phenomena, which often deviate from the idealized harmonic model. However, simulating such system on classical computers is highly challenging due to nonlinear interactions, large state spaces, and the exponential scaling of memory and computational resources. In this work, quantum simulation is employed to model a quantum anharmonic oscillator (QAHO) using a 3-qubit system implemented on IBM's Quantum Experiences platform. A quantum circuit with a filter-based design and Toffoli gates is constructed to track quantum state evolution, capturing key phenomena like quantum revival. The framework is further extended to n-qubit system to enhance resolution and scalability. For energy estimation, the Variational Quantum Eigensolver (VQE) with a TwoLocal ansatz and variational Quantum Deflation (VQD), are used to compute ground and excited state energies. The proposed approach achieves high accuracy with an error of only 1.11% compared to exact methods. Notably, VQE outperforms classical approximations such as perturbation theory (error 6.71%) and the Wentzel-Kramers-Brillouin (WKB) approximation(error 5.36%), yielding more precise energy values. These results highlight the potential of quantum simulation and VQD as effective tools for investigating complex quantum system, paving the way for future application in quantum chemistry and materials science as quantum hardware continues to advance.
This paper presents the results of the "Geometrogenesis v13" simulation, a computational model exploring the emergence of fundamental cosmological constants from principles of quantum information theory. Using a hybrid quantum-classical (HQC) simulation engine, a classical scalar field was coupled with a network of Variational Quantum Eigensolver (VQE) agents governed by an Ising Hamiltonian. Experimental results demonstrate that the system converges to a specific "Island of Stability". The simulation reproduced the scalar spectral index of the Cosmic Microwave Background with a value of ns = 0.9679, which is statistically consistent with Planck 2018 satellite measurements (0.9649 ± 0.0042) within 1σ. This suggests that the structure of the observable universe can be explained as the ground state of an energy and information optimization process. Note: This entry includes the full paper in English and the original summary in Spanish.