arXiv:2410.22485v1 Announce Type: new
Abstract: 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
With the increasing accessibility of physical quantum computers, research on their applications in various fields has been advancing rapidly. In this paper, we present the first study of quantum cosmology conducted on physical quantum computers using a newly proposed Hybrid Quantum-Classical (HQC) algorithm, instead of the commonly used Variational Quantum Eigensolver (VQE).
The specific problem tackled in this study is solving a constrained Hamiltonian equation derived from quantizing the Friedmann equation in cosmology. This constraint equation is of the form H|ψ> = 0, where H is a Hamiltonian operator and |ψ> = |ψ(θ)> represents the wave function of the cosmic quantum state described by the phase angle θ.
To solve this constraint equation, we iteratively use the quantum computer to compute the eigenvalues of H, while a classical computer manages the underlying probability density function within the Probabilistic Bisection Algorithm (PBA) to update θ. This iteration continues until a desired accuracy is achieved, resulting in a solution where H|ψ> = 0.
Implementing our algorithm on IBM’s quantum computers, we are able to obtain a high-precision solution for θ with an error of approximately 1 percent.
Future Roadmap
Challenges
- Scale and Complexity: One of the main challenges in the future development of quantum cosmology is scaling the algorithm to handle more complex cosmological models and larger systems. As our understanding of the universe and cosmological phenomena advances, the need for more powerful quantum algorithms and hardware increases.
- Error Correction: Quantum computers are inherently prone to errors due to various factors such as noise, decoherence, and gate imperfections. Developing error correction techniques and implementing them effectively will be crucial in realizing the full potential of quantum cosmology on physical quantum computers.
- Data Handling and Analysis: Quantum algorithms generate vast amounts of data, and analyzing this data efficiently and accurately poses a challenge. Developing techniques to handle and extract meaningful insights from quantum cosmology data will be important for further advancements in the field.
- Integration with Classical Approaches: Quantum algorithms and classical approaches need to be effectively integrated to leverage the strengths of both. Finding efficient ways to combine quantum and classical computations will be essential for solving more complex cosmological problems.
Opportunities
- Unprecedented Computing Power: Quantum computers have the potential to provide computational power beyond the capabilities of classical computers. This opens up opportunities for tackling computationally intensive problems in cosmology, enabling more accurate simulations and predictions.
- Exploring New Cosmological Models: Quantum cosmology offers the possibility of exploring and understanding new models and phenomena that are beyond the reach of classical computations. This could lead to breakthroughs in our understanding of the early universe, dark matter, and other fundamental aspects of cosmology.
- Optimization and Simulation: Quantum algorithms can be applied to optimization problems and simulations in cosmology. This could enhance our ability to optimize complex cosmological models and simulate the behavior of physical systems more accurately.
- Interdisciplinary Collaborations: The intersection of quantum computing and cosmology presents opportunities for collaborations between physicists, computer scientists, mathematicians, and other researchers. This interdisciplinary approach can lead to innovative solutions and advancements at the intersection of these fields.
In conclusion, the use of physical quantum computers and the development of the Hybrid Quantum-Classical algorithm present new possibilities for conducting quantum cosmology research. While there are challenges to overcome, such as scale and complexity, error correction, data handling, and integration with classical approaches, the opportunities for unprecedented computing power, exploring new cosmological models, optimization and simulation, and interdisciplinary collaborations are immense. With further advancements, quantum cosmology has the potential to revolutionize our understanding of the universe.