Evaluation of Phase Shifts for Non-Relativistic Elastic Scattering Using Quantum Computers: A Variational Approach

Alapfogalmak

This paper introduces a novel quantum algorithm, V-TEPS, for calculating phase shifts in non-relativistic elastic scattering processes, demonstrating its potential for efficient simulation of scattering phenomena on quantum computers.

Kivonat

Bibliographic Information:

Turro, F., Wendt, K. A., Quaglioni, S., Pederiva, F., & Roggero, A. (2024). Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers. arXiv preprint arXiv:2407.04155v2.

Research Objective:

This research paper aims to develop an efficient quantum algorithm for calculating phase shifts in non-relativistic elastic scattering processes, a crucial problem in various fields of physics.

Methodology:

The authors propose a two-step quantum algorithm called Variational Time Evolution Phase Shift (V-TEPS). First, they initialize a quantum system in a truncated plane wave state and evolve it in time using the system's Hamiltonian. Then, they introduce a variational approach by adding a fictitious phase to a detector state and maximizing the overlap probability between the evolved state and the detector state to extract the phase shift. The algorithm is tested using classical simulations with Gaussian and Lennard-Jones potentials in both spatial lattice and momentum basis representations. Finally, the authors implement the algorithm on IBM quantum processors to assess its performance under realistic noise conditions.

Key Findings:

• The V-TEPS algorithm accurately calculates phase shifts for various potentials and momenta, showing good agreement with exact solutions obtained from classical methods.
• The variational approach enhances the algorithm's robustness against noise, making it suitable for near-term quantum devices.
• Implementing the algorithm on IBM quantum processors demonstrates its feasibility and highlights the impact of error mitigation techniques.

Main Conclusions:

The V-TEPS algorithm presents a promising approach for simulating scattering processes on quantum computers. Its efficiency and noise resilience make it a valuable tool for studying quantum systems in nuclear physics, condensed matter physics, and other fields.

Significance:

This research contributes significantly to the development of quantum algorithms for simulating complex physical phenomena. The V-TEPS algorithm offers a practical pathway for leveraging quantum computers to address computationally challenging problems in scattering theory, potentially leading to new insights and discoveries.

Limitations and Future Research:

• The current implementation focuses on single-channel scattering with central potentials. Future work could extend the algorithm to multi-channel scattering and more complex interactions.
• Exploring different quantum state preparation techniques and error mitigation strategies could further improve the algorithm's performance on near-term quantum devices.
• Investigating the algorithm's scalability for larger systems and higher energies will be crucial for addressing more realistic scattering problems.

Statisztikák

The paper uses a spatial lattice with 6000 points and a lattice spacing of 0.02 fm for Gaussian potential simulations.
For Lennard-Jones potential simulations, a lattice spacing of 0.02 Å is used.
The momentum basis set simulations utilize up to 512 momenta with a momentum spacing of 0.0084 fm⁻¹ or 0.013 Å⁻¹.
The IBM quantum processor simulations are performed on the "ibm_perth" and "ibm_brisbane" devices.
The quantum circuits for the simulations involve up to 196 CNOT gates in the computational basis and 63 CNOT gates in the eigenbasis of the Hamiltonian.

Idézetek

"This work presents a quantum algorithm for a direct evaluation of phase shifts for a generic elastic scattering process, allowing the calculations of angular and total cross section."
"Our method provides an alternative scheme useful in computing phase shifts for elastic scattering in both single and multi-channel cases."
"We found that such variational method makes the TEPS algorithm resistant to some noise sources of quantum processors."

Főbb Kivonatok

Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers

by Francesco Tu... : arxiv.org 11-22-2024

https://arxiv.org/pdf/2407.04155.pdf

Mélyebb kérdések

How might this algorithm be adapted for use in other areas of quantum physics beyond scattering theory?

The V-TEPS algorithm, while specifically designed for calculating phase shifts in scattering processes, leverages fundamental principles of quantum mechanics that can be extended to other areas of quantum physics. Here are some potential adaptations:

Condensed Matter Physics:

Impurity Scattering: V-TEPS could be adapted to study the scattering of electrons or phonons off impurities in materials. This could provide insights into transport properties and material characteristics.
Optical Lattices: By simulating the dynamics of ultracold atoms in optical lattices, modified V-TEPS algorithms could be used to investigate quantum phases of matter, such as Bose-Einstein condensates and Mott insulators.

Quantum Chemistry:

Molecular Collisions: The algorithm could be modified to simulate collisions between molecules, potentially aiding in understanding chemical reaction rates and pathways.
Molecular Spectroscopy: By analyzing the time evolution of molecular wave packets under the influence of external fields, V-TEPS could contribute to the interpretation of spectroscopic data.

Quantum Information Science:

Quantum Simulation Benchmarks: V-TEPS could serve as a benchmark for the performance of quantum computers, as accurately simulating scattering processes is a computationally demanding task for classical computers.
Quantum Algorithm Development: The core principles of V-TEPS, such as real-time evolution and variational optimization, could inspire the development of novel quantum algorithms for other complex problems.
The key adaptation would involve tailoring the Hamiltonian, initial state preparation, and detector state to the specific physical system and observable of interest.

Could classical computing advancements eventually outperform the efficiency of V-TEPS for calculating phase shifts, or are there inherent limitations?

This is a complex question at the heart of the quantum advantage debate. While classical computing advancements continue to improve, there are inherent limitations when simulating quantum systems, particularly those involving many-body interactions.
Classical Limitations:

Exponential Scaling: Classical methods for simulating quantum systems often face exponential scaling of computational resources with the number of particles or degrees of freedom. This makes accurate simulations of large systems intractable.
Fermion Sign Problem: For fermionic systems, classical Monte Carlo simulations suffer from the sign problem, where the computational cost increases exponentially with system size and inverse temperature.
Potential of V-TEPS:

Quantum Speedup: V-TEPS, being a quantum algorithm, has the potential to circumvent the exponential scaling limitations of classical methods, offering a polynomial scaling advantage.
Direct Quantum Simulation: By directly simulating the quantum system on a quantum computer, V-TEPS avoids the sign problem altogether.
However:

Quantum Hardware Maturity: The full potential of V-TEPS relies on the development of fault-tolerant, large-scale quantum computers, which are still under development.
Algorithm Optimization: Further research is needed to optimize quantum algorithms like V-TEPS for specific problems and hardware constraints.
Conclusion:
It is unlikely that classical computing advancements alone will completely outperform the efficiency of V-TEPS for calculating phase shifts in complex quantum systems. Quantum algorithms have the potential to tackle problems that are fundamentally intractable for classical computers. However, realizing this potential hinges on significant progress in quantum hardware and algorithm development.

What breakthroughs in quantum hardware would be most impactful in unlocking the full potential of quantum algorithms like V-TEPS for real-world scientific applications?

Several key breakthroughs in quantum hardware would significantly impact the applicability of V-TEPS and similar quantum algorithms for real-world scientific problems:

Increased Qubit Count and Connectivity: A larger number of qubits with higher connectivity would allow for the simulation of more complex systems with greater accuracy. This is crucial for tackling real-world problems that often involve many particles or degrees of freedom.
Improved Qubit Coherence Times: Longer coherence times are essential for performing more complex and longer quantum computations. This would enable the implementation of more sophisticated quantum algorithms and reduce the impact of noise on the results.
Higher Gate Fidelity: Reducing the error rates of quantum gates is crucial for obtaining reliable and accurate results. Higher gate fidelity would minimize the accumulation of errors during computation, leading to more trustworthy simulations.
Efficient Qubit Initialization and Measurement: Faster and more accurate initialization of qubits in desired states and efficient measurement of the final qubit states are essential for reducing the overall runtime and improving the signal-to-noise ratio of quantum computations.
Development of Quantum Error Correction: Implementing robust error correction schemes is vital for mitigating the effects of noise and decoherence, which are inherent in current quantum hardware. This would pave the way for fault-tolerant quantum computers capable of performing long and complex calculations.
Specialized Quantum Hardware Architectures: Designing and building quantum computers specifically optimized for certain types of problems, such as simulating scattering processes, could lead to significant performance gains.
These advancements, combined with ongoing research in quantum algorithm design and error mitigation techniques, would unlock the full potential of quantum computing for addressing challenging scientific problems in fields ranging from materials science and drug discovery to high-energy physics and cosmology.