Particle collisions on a quantum computer

James Scoville

An algorithm is presented to simulate fluid dynamics on a three qubit type II quantum computer: a lattice of small quantum computers that communicate classical information. The algorithm presented is called a three qubit factorized quantum lattice gas algorithm. It is modeled after classical lattice gas algorithms which move virtual particles along an imaginary lattice and change the particles' momentums using collision rules when they meet at a lattice node. Instead of moving particles, the quantum algorithm presented here moves probabilities, which interact via a unitary collision operator. Probabilities are determined using ensemble measurement and are moved with classical communications channels. The lattice node spacing is defined to be a microscopic scale length. A mesoscopic governing equation for the lattice is derived for the most general three qubit collision operator which preserves particle number. In the continuum limit of the lattice, a governing macroscopic partial differential equation-the diffusion equation-is derived for a particular collision operator using a Chapman-Enskog expansion. A numerical simulation of the algorithm is carried out on a conventional desktop computer and compared to the analytic solution of the diffusion equation. The simulation agrees very well with the known solution.

Qipeng Liu, Mark Zhandry

Annie Y. Wei, Preksha Naik, Aram W. Harrow +1 more

Identifying jets formed in high-energy particle collisions requires solving optimization problems over potentially large numbers of final-state particles. In this work, we consider the possibility of using quantum computers to speed up jet clustering algorithms. Focusing on the case of electron-positron collisions, we consider a well-known event shape called thrust whose optimum corresponds to the most jetlike separating plane among a set of particles, thereby defining two hemisphere jets. We show how to formulate thrust both as a quantum annealing problem and as a Grover search problem. A key component of our analysis is the consideration of realistic models for interfacing classical data with a quantum algorithm. With a sequential computing model, we show how to speed up the well-known $O({N}^{3})$ classical algorithm to an $O({N}^{2})$ quantum algorithm, including the $O(N)$ overhead of loading classical data from $N$ final-state particles. Along the way, we also identify a way to speed up the classical algorithm to $O({N}^{2}\mathrm{log}N)$ using a sorting strategy inspired by the siscone jet algorithm, which has no natural quantum counterpart. With a parallel computing model, we achieve $O(N\mathrm{log}N)$ scaling in both the classical and quantum cases. Finally, we consider the generalization of these quantum methods to other jet algorithms more closely related to those used for proton-proton collisions at the Large Hadron Collider.

Heine Olsson Aabø

Julian Schuhmacher, Guo-Xian Su, Jesse J. Osborne +3 more

Scattering experiments are at the heart of high-energy physics (HEP), breaking matter down to its fundamental constituents, probing its formation, and providing deep insight into the inner workings of nature. In the current huge drive to forge quantum computers into complementary venues that are ideally suited to capture snapshots of far-from-equilibrium HEP dynamics, a major goal is to utilize these devices for scattering experiments. A major obstacle in this endeavor has been the hardware overhead required to access the late-time post-collision dynamics while implementing the underlying gauge symmetry. Here, we report on the first quantum simulation of scattering in a lattice gauge theory (LGT), performed on \texttt{IBM}'s \texttt{ibm\_marrakesh} quantum computer. Specifically, we quantum-simulate the collision dynamics of electrons and positrons as well as mesons in a $\mathrm{U}(1)$ LGT representing $1+1$D quantum electrodynamics (QED), uncovering rich post-collision dynamics that we can precisely tune with a topological $Θ$-term and the fermionic mass. By monitoring the time evolution of the scattering processes, we are able to distinguish between two main regimes in the wake of the collision. The first is characterized by the delocalization of particles when the topological $Θ$-term is weak, while the second regime shows localized particles with a clear signature when the $Θ$-term is nontrivial. Furthermore, we show that by quenching to a small mass at the collision point, inelastic scattering occurs with a large production of matter reminiscent of quantum many-body scarring. Our work provides a major step forward in the utility of quantum computers for investigating the real-time quantum dynamics of HEP collisions.