Quantum Computing Shows Promise in Simulating Complex Fermionic Systems, Study Reveals

Quantum computing holds significant potential for simulating fermionic systems, such as nuclear physics and electronic systems. The Lipkin-Meshkov-Glick (LMG) model, a nuclear shell model-type system, can be simulated using quantum computing. Quantum algorithms are increasingly being used in nuclear physics, with variational quantum algorithms proving particularly effective due to their hybrid nature, combining quantum and classical processes. The LMG model Hamiltonian is encoded for quantum computing using Pauli spin matrices. Simulations of the LMG model on quantum computers have yielded promising results, demonstrating the potential of quantum computing in simulating complex fermionic systems.

What is the Potential of Quantum Computing in Simulating Fermionic Systems?

Quantum computing has the potential to provide significant advantages for specific computational tasks, particularly in the simulation of fermionic systems. These systems, which include applications in nuclear physics and electronic systems, are well-suited to quantum computation. The Lipkin-Meshkov-Glick (LMG) model, an exactly solvable nuclear shell model-type system, is one such system that can be simulated using quantum computing.

The LMG model is a simple shell model consisting of two levels separated by an energy, with a permutation-symmetric potential. The two levels are each N-fold degenerate, and a standard treatment considers N-fermions in the system. The Hamiltonian for the model is given as a function of the energy and the strength of pair de-excitations between the two levels.

The LMG model is applicable as a test platform for quantum computing algorithms applied to nuclear physics due to its exactly solvable nature and the ability to scale the model indefinitely by increasing the number of particles in the system. The model has already been studied using real and simulated quantum computers, particularly for calculation of its ground state, but also for excited states using a quantum-assisted algorithm.

How are Quantum Algorithms Used in Nuclear Physics?

The use of quantum algorithms to perform calculations in nuclear physics is a rapidly developing field. The exponential scaling of Hilbert space with the number of quantum bits (qubits) and the ability of multiple qubits to exhibit highly entangled wave functions give quantum computers the potential to have a great impact in simulating many-body quantum systems.

Richard Feynman first proposed using quantum computers to study quantum systems in the 1980s. Since then, various algorithms have been developed that are able to perform calculations on many-body quantum systems, such as Quantum Phase Estimation (QPE) and Quantum Imaginary Time Evolution. However, these algorithms are often too complex to be fully implemented on current quantum computers.

Current quantum computers are said to be in the Noisy Intermediate-Scale Quantum (NISQ) era. This is due to the low numbers of qubits and large amounts of noise and error present within the devices. Current devices also have low coherence times, restricting the amount of time a qubit can maintain its state. This limits the length of the quantum circuit or circuit depth that quantum computers can use and still produce meaningful results.

What are Variational Quantum Algorithms?

Variational quantum algorithms have established themselves due to the relative ease of running them on NISQ-era quantum computers. These are hybrid algorithms, meaning they use both quantum and classical processes in tandem, reducing the amount of computational work needed to be performed on the quantum computer. Working in conjunction with a classical computer allows for reduced circuit depths and improved error rates by reducing the number of gates in the quantum circuit.

The Variational Quantum Eigensolver (VQE) algorithm uses the variational principle of quantum mechanics to approximate the ground state of some Hamiltonian. In the work presented here, a version of the VQE is applied which targets any eigenvalue of a quantum system by minimizing the variance of the Hamiltonian rather than the expectation value.

Application of the method is made to the simplified nuclear model due to Lipkin, Meshkov, and Glick. The presentation proceeds with a description of the implementation of the algorithm followed by results on simulated and real quantum computers.

How is the LMG Model Encoded for Quantum Computing?

The LMG model Hamiltonian must be encoded in such a way as to allow it to be processed by a quantum computer. For circuit-based quantum computers, this form is conveniently expressed as linear combinations of Pauli spin matrices. Often a representation of a Hamiltonian in second-quantized form leads to a mapping from creation and annihilation operators to Pauli strings, keeping the second quantized representation where solutions of any particle number can be.

The encoding methodology is a crucial step in the process of simulating the LMG model on a quantum computer. It involves translating the Hamiltonian of the model into a form that can be processed by a quantum computer. This is typically done by expressing the Hamiltonian as linear combinations of Pauli spin matrices.

The encoding process is complex and requires a deep understanding of both the LMG model and the workings of quantum computers. However, once completed, it allows for the simulation of the LMG model on both real and simulated quantum computers, providing valuable insights into the behavior of fermionic systems.

What are the Results of Simulating the LMG Model on Quantum Computers?

The results of simulating the LMG model on quantum computers are promising. Using both quantum simulators and real quantum hardware accessed via IBM cloud-based quantum computers, researchers were able to obtain all eigenvalues for the cases of three and seven fermions (nucleons) in the LMG model.

These results demonstrate the potential of quantum computing in simulating complex fermionic systems. They also highlight the advantages of using quantum algorithms, such as the Variational Quantum Eigensolver, in reducing the computational workload and improving error rates.

While the field of quantum computing is still in its early stages, these results provide a glimpse into the future of computational physics. As quantum computers become more powerful and more accessible, we can expect to see even more complex and accurate simulations of quantum systems.