Abstract
A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing finite-volume one- and two-particle Green's functions on the quantum hardware. Particle decay rates and two particle scattering cross sections are extracted from the imaginary parts of the Green's function. A $0+1$ dimensional implementation of this method is demonstrated on IBM's superconducting quantum hardware for the decay of a heavy scalar particle to a pair of light scalars.
Highlights
Quantum field theories describe three of the four fundamental forces of nature
Bounds on the finite volume error of 1 → N decay rates and 2 → N scattering cross sections computed with this method have been determined
More work will need to be done to understand how different truncations effect the error in the computed decay rate
Summary
Quantum field theories describe three of the four fundamental forces of nature. In particular, quantum chromodynamics (QCD) describes the strong interactions that bind quarks into hadrons [1]. A method of extracting particle decay rates and scattering cross sections from a Green’s function calculated on a quantum computer is demonstrated. This method only requires the ability to prepare initial particle states and perform real time evolution. A 0 þ 1 dimensional demonstration is performed using IBM’s superconducting hardware This calculation is demonstrated for a specific model, the approach is based on general properties of Green’s functions, and it is expected that it can be applied to particle decays or scattering in other theories. The systematic errors present in extracting a decay rate from a finite volume Green’s function are analyzed in Appendixes C 2 and C 3. The data from running on IBM’s quantum processor are in Appendix G
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