New Quantum Computing Framework Simplifies Scattering Amplitude Calculations in Particle Physics

A new framework for computing scattering amplitudes in quantum field theory using quantum computers has been proposed. The framework, which uses the Lehmann-Symanzik-Zimmermann (LSZ) reduction formula, is nonperturbative and only requires constructing one-particle states of zero momentum. This makes it ideal for scatterings involving a small number of particles and bound states. The framework could be particularly advantageous for exclusive hadron scatterings. The authors demonstrated the framework’s effectiveness using the one-flavor Gross-Neveu model. This new approach could lead to more accurate and efficient calculations of scattering amplitudes, enhancing our understanding of particle physics.

What is the New Framework for Computing Scattering Amplitudes in Quantum Field Theory?

The article discusses a new general framework for computing scattering amplitudes in quantum field theory with quantum computers. This framework, which utilizes the Lehmann-Symanzik-Zimmermann (LSZ) reduction formula, is nonperturbative, meaning it does not rely on small parameters for its calculations. The framework only requires the construction of one-particle states of zero momentum, eliminating the need for wave packets of incoming particles. This makes it ideal for scatterings involving a small number of particles and bound states.

The framework is expected to have particular advantages when applied to exclusive hadron scatterings. As a proof of concept, the authors conducted simulations on classical hardware. They demonstrated that in the one-flavor Gross-Neveu model, the fermion propagator, the connected fermion four-point function, and the propagator of a fermion-antifermion bound state obtained from their proposed quantum algorithm have the desired pole structure crucial to the implementation of the LSZ reduction formula.

Why is the Calculation of Scattering Amplitudes in Quantum Field Theory Important?

The calculation of scattering amplitudes in quantum field theory has long been a core topic in theoretical particle physics. All tests of theories against experiments in particle accelerators entail theoretical predictions of scattering amplitudes. Despite the huge success of the perturbative approach to the calculation of scattering amplitudes, there are still circumstances in which the perturbative framework does not work. This is particularly the case where the coupling constants are large, as is the case for quantum chromodynamics at low energies.

To date, first-principle nonperturbative calculations of scattering amplitudes in quantum field theory are not available. The main obstacle is that real-time dynamics cannot be simulated in traditional path-integral lattice quantum field theory. Simulating real-time Hamiltonian evolutions in quantum field theory requires unbearable computational cost on a classical computer.

How Can Quantum Computers Help in the Calculation of Scattering Amplitudes?

In a series of papers, Jordan, Lee, and Preskill (JLP) proposed that with the help of quantum computers, simulations of Hamiltonian evolutions of scattering processes in quantum field theory can be achieved with affordable computational cost on the lattice. This makes nonperturbative evaluations of scattering amplitudes possible. These works have spurred a series of research on the applications of quantum computing in particle physics, ranging from time evolutions in quantum field theory to calculations of nonperturbative quantities and thermodynamics at finite chemical potential.

However, the quantum-computational framework developed by JLP, while fully general, may encounter difficulties in practice. One major difficulty is that one has to prepare spatially well-separated wave packets of incoming particles in the initial state. This sets a constraint on the lattice spacing and the lattice size, and generally implies a larger lattice size than required.

What is the Lehmann-Symanzik-Zimmermann (LSZ) Reduction Formula?

The Lehmann-Symanzik-Zimmermann (LSZ) reduction formula is a method used in quantum field theory to calculate scattering amplitudes from correlation functions. It is named after the physicists Harry Lehmann, Kurt Symanzik, and Wolfhart Zimmermann who developed it in the 1950s.

In the conventional perturbative approach, scattering amplitudes are computed using the LSZ reduction formula. This formula relates scattering amplitudes to n-point correlation functions, which can be expanded as power series in the coupling constant using the Feynman diagram technique.

What are the Implications of this New Framework?

The new framework proposed by the authors offers a promising approach to computing scattering amplitudes in quantum field theory with quantum computers. By eliminating the need for wave packets of incoming particles and incorporating scatterings of bound states, the framework simplifies the process and makes it more efficient.

The successful demonstration of the framework in the one-flavor Gross-Neveu model suggests its potential applicability to other quantum field theories. This could pave the way for more accurate and efficient calculations of scattering amplitudes, contributing to our understanding of fundamental processes in particle physics.